------------------------------------------------------------------------------------------------------------------------------- name: log: c:\acdbookrevision\stata_final_programs_2013\racd07.txt log type: text opened on: 18 Jan 2013, 09:48:20 . . ********** OVERVIEW OF racd07.do ********** . . * STATA Program . * copyright C 2013 by A. Colin Cameron and Pravin K. Trivedi . * used for "Regression Analyis of Count Data" SECOND EDITION . * by A. Colin Cameron and Pravin K. Trivedi (2013) . * Cambridge University Press . . * This program does the analysis for chapter 7 . * 7.3 STATIC REGRESSION AND AUTOCORRELATIONS FOR STRIKES DATA . * 7.11.1 DYNAMIC REGRESSION FOR STRIKES DATA . * 7.11.2 DYNAMIC REGRESSION FOR STOCK TRADES DATA . . * To run you need files . * racd07data1strikes.dta . * racd07data2stocktrades.dta . * in your directory . . * And you need Stata user-written command . * countfit . . ********** SETUP ********** . . set more off . version 12 . clear all . set linesize 82 . set scheme s1mono // Graphics scheme . . ********** DATA DESCRIPTION . . * The original data in racd07data1strikes.dta are from . * J. Kennan, "The Duration of Contract strikes in U.S. Manufacturing", . * Journal of Econometrics, 1985, Vol. 28, pp.5-28. . * The data are also used in . * A.C. Cameron and P.K. Trivedi (1990), . * "Regression based tests for overdispersion", . * Journal of Econometrics, Vol. 46, pp. 347-364. . * For more details see these articles and racd07makedata1strikes.do . . * The original data in racd07data2stocktrades.dta are from . * R.C. Jung, R. Liesenfeld and J.-F. Richard (2011) . * "Dynamic Factor Models for Multivariate Count Data: An Application to . * Stock-Market Trading Activity," JBES, 29, 73-85. . * Data are the number of trades on the NYSE in 5 minute intervals . * for Geltfelter Company (GLT) over 39 trading days Jan 3 - Feb 18 2005 . * There are 75 5-minute intervals times 39 days . * For more details racd07makedata2stocktrades.do . . ********** 7.3 STATIC REGRESSION AND AUTOCORRELATIONS: STRIKES DATA . . use racd07data1strikes.dta, clear . . *** TABLE 7.1: VARIABLE DEFINITIONS AND SUMMARY STATISTICS . . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- STRIKES | 108 5.240741 3.751312 0 18 OUTPUT | 108 -.0036954 .0545578 -.13996 .08554 MONTH | 108 54.5 31.32092 1 108 . describe Contains data from racd07data1strikes.dta obs: 108 vars: 3 21 Jul 2011 10:36 size: 1,296 ---------------------------------------------------------------------------------- storage display value variable name type format label variable label ---------------------------------------------------------------------------------- STRIKES float %9.0g Number of strikes commenced each month OUTPUT float %9.0g Deviation of monthly industrial production from its trend level MONTH float %9.0g Month: 1968(1) to 1976(12) ---------------------------------------------------------------------------------- Sorted by: MONTH . tabulate STRIKES Number of | strikes | commenced | each month | Freq. Percent Cum. ------------+----------------------------------- 0 | 5 4.63 4.63 1 | 12 11.11 15.74 2 | 14 12.96 28.70 3 | 11 10.19 38.89 4 | 9 8.33 47.22 5 | 14 12.96 60.19 6 | 9 8.33 68.52 7 | 4 3.70 72.22 8 | 7 6.48 78.70 9 | 10 9.26 87.96 10 | 6 5.56 93.52 11 | 1 0.93 94.44 13 | 3 2.78 97.22 15 | 1 0.93 98.15 16 | 1 0.93 99.07 18 | 1 0.93 100.00 ------------+----------------------------------- Total | 108 100.00 . . *** FIGURE 7.1: STRIKES AND OUTPUT OVER TIMES . . graph twoway (line STRIKES MONTH, lwidth(medthick)) /// > (line OUTPUT MONTH, lpattern(dash) lwidth(medthick) yaxis(2)), /// > scale(1.2) yscale(range(0 20) axis(1)) yscale(range(-0.1 0.15) axis(2)) /// > legend(ring(0) rows(2) pos(12) label(1 "Strikes") /// > label(2 "Output")) ytitle("Strikes", axis(1)) ytitle("Output", axis(2)) . graph export racd07fig1.eps, replace (file racd07fig1.eps written in EPS format) . graph export racd07fig1.wmf, replace (file c:\acdbookrevision\stata_final_programs_2013\racd07fig1.wmf written in Windo > ws Metafile format) . . * Poisson QMLE with various standard errors . * Stock and Watson text suggests #lags = 0.75*T^(1/3) (= 3.57 here) . * Optimal for linear AR(1) y and error with rho=0.5 . * based on Andrews (1991, eq.5.3) . glm STRIKES OUTPUT, family(poisson) vce(robust) Iteration 0: log pseudolikelihood = -313.12939 Iteration 1: log pseudolikelihood = -311.98566 Iteration 2: log pseudolikelihood = -311.98445 Iteration 3: log pseudolikelihood = -311.98445 Generalized linear models No. of obs = 108 Optimization : ML Residual df = 106 Scale parameter = 1 Deviance = 279.7405364 (1/df) Deviance = 2.639062 Pearson = 262.5029208 (1/df) Pearson = 2.476443 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] AIC = 5.814527 Log pseudolikelihood = -311.9844508 BIC = -216.5654 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 1.18364 2.65 0.008 .8143251 5.454109 _cons | 1.653893 .0659347 25.08 0.000 1.524663 1.783123 ------------------------------------------------------------------------------ . estimates store HAC0 . glm STRIKES OUTPUT, family(poisson) vce(hac nwest 4) Iteration 0: log likelihood = -313.12939 Iteration 1: log likelihood = -311.98566 Iteration 2: log likelihood = -311.98445 Iteration 3: log likelihood = -311.98445 Generalized linear models No. of obs = 108 Optimization : ML Residual df = 106 Scale parameter = 1 Deviance = 279.7405364 (1/df) Deviance = 2.639062 Pearson = 262.5029208 (1/df) Pearson = 2.476443 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] HAC kernel (lags): Newey-West (4) AIC = 5.814527 Log likelihood = -311.9844508 BIC = -216.5654 ------------------------------------------------------------------------------ | HAC STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 1.920548 1.63 0.103 -.6299873 6.898421 _cons | 1.653893 .1033618 16.00 0.000 1.451308 1.856478 ------------------------------------------------------------------------------ . estimates store HAC4 . glm STRIKES OUTPUT, family(poisson) vce(hac nwest 8) Iteration 0: log likelihood = -313.12939 Iteration 1: log likelihood = -311.98566 Iteration 2: log likelihood = -311.98445 Iteration 3: log likelihood = -311.98445 Generalized linear models No. of obs = 108 Optimization : ML Residual df = 106 Scale parameter = 1 Deviance = 279.7405364 (1/df) Deviance = 2.639062 Pearson = 262.5029208 (1/df) Pearson = 2.476443 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] HAC kernel (lags): Newey-West (8) AIC = 5.814527 Log likelihood = -311.9844508 BIC = -216.5654 ------------------------------------------------------------------------------ | HAC STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 2.222264 1.41 0.158 -1.221341 7.489774 _cons | 1.653893 .1162186 14.23 0.000 1.426109 1.881677 ------------------------------------------------------------------------------ . estimates store HAC8 . glm STRIKES OUTPUT, family(poisson) vce(hac nwest 12) Iteration 0: log likelihood = -313.12939 Iteration 1: log likelihood = -311.98566 Iteration 2: log likelihood = -311.98445 Iteration 3: log likelihood = -311.98445 Generalized linear models No. of obs = 108 Optimization : ML Residual df = 106 Scale parameter = 1 Deviance = 279.7405364 (1/df) Deviance = 2.639062 Pearson = 262.5029208 (1/df) Pearson = 2.476443 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] HAC kernel (lags): Newey-West (12) AIC = 5.814527 Log likelihood = -311.9844508 BIC = -216.5654 ------------------------------------------------------------------------------ | HAC STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 2.401691 1.31 0.192 -1.573012 7.841445 _cons | 1.653893 .1231458 13.43 0.000 1.412532 1.895254 ------------------------------------------------------------------------------ . estimates store HAC12 . glm STRIKES OUTPUT, family(poisson) vce(hac nwest 16) Iteration 0: log likelihood = -313.12939 Iteration 1: log likelihood = -311.98566 Iteration 2: log likelihood = -311.98445 Iteration 3: log likelihood = -311.98445 Generalized linear models No. of obs = 108 Optimization : ML Residual df = 106 Scale parameter = 1 Deviance = 279.7405364 (1/df) Deviance = 2.639062 Pearson = 262.5029208 (1/df) Pearson = 2.476443 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] HAC kernel (lags): Newey-West (16) AIC = 5.814527 Log likelihood = -311.9844508 BIC = -216.5654 ------------------------------------------------------------------------------ | HAC STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 2.484867 1.26 0.207 -1.736032 8.004466 _cons | 1.653893 .1267064 13.05 0.000 1.405553 1.902233 ------------------------------------------------------------------------------ . estimates store HAC16 . . *** TABLE 7.2: POISSON ESTIMATES AND VARIOUS HAC STANDARD ERRORS . . estimates table HAC0 HAC4 HAC8 HAC12 HAC16, b(%9.3f) se -------------------------------------------------------------------------- Variable | HAC0 HAC4 HAC8 HAC12 HAC16 -------------+------------------------------------------------------------ OUTPUT | 3.134 3.134 3.134 3.134 3.134 | 1.184 1.921 2.222 2.402 2.485 _cons | 1.654 1.654 1.654 1.654 1.654 | 0.066 0.103 0.116 0.123 0.127 -------------------------------------------------------------------------- legend: b/se . . *** FIGURE 7.2: ACTUAL AND PREDICTED STRIKES OVER TIME . . quietly poisson STRIKES OUTPUT, vce(robust) . predict PREDICTED, n . correlate STRIKES PREDICTED (obs=108) | STRIKES PREDIC~D -------------+------------------ STRIKES | 1.0000 PREDICTED | 0.2265 1.0000 . graph twoway (line STRIKES MONTH, lwidth(medthick)) /// > (line PREDICTED MONTH, lpattern(dash) lwidth(medthick)), /// > scale(1.2) legend(ring(0) rows(2) pos(12) label(1 "Actual strikes") /// > label(2 "Predicted strikes")) ytitle("Strikes: actual and predicted") . graph export racd07fig2.eps, replace (file racd07fig2.eps written in EPS format) . graph export racd07fig2.wmf, replace (file c:\acdbookrevision\stata_final_programs_2013\racd07fig2.wmf written in Windo > ws Metafile format) . . *** R-SQUAREDS MENTIONED IN TEXT . . *** Deviance, Pearson and R-squared measures presented in text . * Fitted model . quietly glm STRIKES MONTH, family(poisson) vce(robust) . scalar Devfitted = e(deviance) . scalar Pearsfitted = e(deviance_p) . * Intercept-only model . quietly glm STRIKES, family(poisson) vce(robust) . scalar Devintercept = e(deviance) . scalar Pearsintercept = e(deviance_p) . * Calculate R-squared Deviance and Pearson . scalar R2_Dev = 1 - Devfitted/Devintercept . scalar R2_Pears = 1 - Pearsfitted/Pearsintercept . display "Deviance R-squared = " R2_Dev " Fitted = " Devfitted " Intercept = > " Devintercept Deviance R-squared = .04906826 Fitted = 280.87648 Intercept = 295.36976 . display "Pearson R-squared = " R2_Pears " Fitted = " Pearsfitted " Intercep > t = " Pearsintercept Pearson R-squared = .0241994 Fitted = 280.36165 Intercept = 287.31449 . * Squared correlation coefficient . quietly correlate STRIKES PREDICTED . display "Squared correlation coefficient = " r(rho)^2 Squared correlation coefficient = .05128203 . . *** TABLE 7.3: RESIDUAL AUTOCORRELATIONS . . * Residuals . quietly poisson STRIKES OUTPUT, vce(robust) . predict RESIDUAL, score . generate PEARSON = RESIDUAL/sqrt(PREDICTED) . . * Autocorrelation functions and Ljung-Box statistics . * Only use Ljung-Box or Box-Pierce for PEARSON as this is standarndized . corrgram STRIKES, lags(12) // Table 7.3 Column 1 -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4936 0.4952 27.049 0.0000 |--- |--- 2 0.4305 0.2514 47.817 0.0000 |--- |-- 3 0.3683 0.1206 63.166 0.0000 |-- | 4 0.2264 -0.0703 69.023 0.0000 |- | 5 0.1258 -0.0873 70.849 0.0000 |- | 6 0.0387 -0.0798 71.023 0.0000 | | 7 0.0073 -0.0037 71.029 0.0000 | | 8 0.0192 0.0700 71.073 0.0000 | | 9 0.0516 0.0937 71.393 0.0000 | | 10 0.0112 -0.0399 71.408 0.0000 | | 11 0.0560 0.0296 71.793 0.0000 | | 12 -0.0051 -0.1044 71.796 0.0000 | | . corrgram RESIDUAL, lags(12) // Table 7.3 Column 2 -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4656 0.4672 24.068 0.0000 |--- |--- 2 0.3983 0.2359 41.846 0.0000 |--- |- 3 0.3411 0.1214 55.012 0.0000 |-- | 4 0.1984 -0.0704 59.508 0.0000 |- | 5 0.1106 -0.0709 60.918 0.0000 | | 6 0.0292 -0.0715 61.018 0.0000 | | 7 0.0094 0.0059 61.028 0.0000 | | 8 0.0359 0.0787 61.181 0.0000 | | 9 0.0859 0.1128 62.067 0.0000 | | 10 0.0575 -0.0156 62.468 0.0000 | | 11 0.1038 0.0396 63.786 0.0000 | | 12 0.0302 -0.1121 63.899 0.0000 | | . corrgram PEARSON, lags(12) // Table 7.3 Column 3 -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4424 0.4440 21.731 0.0000 |--- |--- 2 0.3760 0.2283 37.574 0.0000 |--- |- 3 0.3231 0.1234 49.387 0.0000 |-- | 4 0.2025 -0.0369 54.07 0.0000 |- | 5 0.1084 -0.0719 55.426 0.0000 | | 6 0.0298 -0.0750 55.53 0.0000 | | 7 0.0148 0.0012 55.556 0.0000 | | 8 0.0382 0.0718 55.729 0.0000 | | 9 0.0814 0.1015 56.524 0.0000 | | 10 0.0452 -0.0193 56.772 0.0000 | | 11 0.0996 0.0541 57.987 0.0000 | | 12 0.0297 -0.0941 58.096 0.0000 | | . . * Get the z statistics by multiply autocorrelations by sqrt(T) . scalar sqrtT = sqrt(_N) . quietly corrgram PEARSON, lags(12) . matrix Zstatistics = r(AC)*I(12)*sqrtT . matrix list Zstatistics // Table 7.3 Column 4 Zstatistics[1,12] c1 c2 c3 c4 c5 c6 c7 r1 4.5976771 3.9072342 3.358009 2.1042274 1.1268802 .30993607 .15427008 c8 c9 c10 c11 c12 r1 .39707453 .84583092 .46950439 1.0352169 .30876908 . . * Compute the BP statistic (corrgram gives the LB statistics) . matrix ZstatisticsSQ = hadamard(Zstatistics,Zstatistics) . matrix BP = trace(diag(ZstatisticsSQ)) . matrix list BP symmetric BP[1,1] c1 r1 55.759374 . . * Nonstandardized case . * Applied just for PEARSON where not necessary as standardized . * But can also apply to nonstandardized such as RESIDUAL . scalar TBPstar = 0 . forvalues i = 1/12 { 2. quietly generate PL`i' = L`i'.PEARSON 3. quietly generate PL0PL`i' = PEARSON*PL`i' 4. quietly generate PL0SQPL`i'SQ = PEARSON*PEARSON*PL`i'*PL`i' 5. quietly sum PL0PL`i' 6. scalar NUMERATOR = r(sum) 7. quietly sum PL0SQPL`i'SQ 8. scalar DENOMINATOR = sqrt(r(sum)) 9. scalar T`i'star = NUMERATOR / DENOMINATOR 10. scalar T`i'starSQ = T`i'star^2 11. scalar TBPstar = TBPstar + T`i'starSQ 12. } . * List the individual statistics T* at lags 1 to 12 . scalar list T1star T2star T3star T4star T5star T6star T7star T8star /// > T9star T10star T11star T12star // Table 7.3 Column 5 T1star = 4.070692 T2star = 3.960054 T3star = 3.3988374 T4star = 2.2138469 T5star = 1.2238748 T6star = .32778475 T7star = .16866481 T8star = .43577439 T9star = 1.0631306 T10star = .54491829 T11star = 1.170747 T12star = .37589509 . * List the overall test . scalar list TBPstar TBPstar = 53.468562 . . * Yet another test . regress PEARSON L.PEARSON L2.PEARSON L3.PEARSON L4.PEARSON L5.PEARSON /// > L6.PEARSON L7.PEARSON L8.PEARSON L9.PEARSON L10.PEARSON L11.PEARSON /// > L12.PEARSON , vce(robust) Linear regression Number of obs = 96 F( 12, 83) = 3.90 Prob > F = 0.0001 R-squared = 0.3309 Root MSE = 1.3351 ------------------------------------------------------------------------------ | Robust PEARSON | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- PEARSON | L1. | .3136083 .1091597 2.87 0.005 .0964939 .5307226 L2. | .2319255 .1131578 2.05 0.044 .0068591 .4569918 L3. | .2054849 .1152998 1.78 0.078 -.0238418 .4348116 L4. | -.0007533 .1117113 -0.01 0.995 -.2229426 .2214361 L5. | -.094714 .1234872 -0.77 0.445 -.3403251 .150897 L6. | -.1578701 .1325787 -1.19 0.237 -.4215638 .1058235 L7. | -.044766 .1265306 -0.35 0.724 -.2964302 .2068983 L8. | .1505729 .1213462 1.24 0.218 -.0907798 .3919255 L9. | .1078921 .092864 1.16 0.249 -.0768106 .2925948 L10. | -.0416191 .0937056 -0.44 0.658 -.2279958 .1447577 L11. | .0639839 .1059063 0.60 0.547 -.1466596 .2746273 L12. | -.0941421 .1030877 -0.91 0.364 -.2991795 .1108953 | _cons | -.0326778 .1432344 -0.23 0.820 -.3175652 .2522096 ------------------------------------------------------------------------------ . display "chisquare(12) test = " 12*e(F) chisquare(12) test = 46.753833 . . * Yet another test number two . regress PEARSON OUTPUT L.PEARSON L2.PEARSON L3.PEARSON L4.PEARSON L5.PEARSON / > // > L6.PEARSON L7.PEARSON L8.PEARSON L9.PEARSON L10.PEARSON L11.PEARSON /// > L12.PEARSON , vce(robust) Linear regression Number of obs = 96 F( 13, 82) = 3.96 Prob > F = 0.0001 R-squared = 0.3365 Root MSE = 1.3375 ------------------------------------------------------------------------------ | Robust PEARSON | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.511773 3.019764 0.83 0.408 -3.4955 8.519046 | PEARSON | L1. | .307679 .1098356 2.80 0.006 .089181 .5261769 L2. | .2341558 .113006 2.07 0.041 .0093508 .4589608 L3. | .2091645 .117633 1.78 0.079 -.0248449 .443174 L4. | .0017562 .1134431 0.02 0.988 -.2239183 .2274307 L5. | -.0861634 .1217861 -0.71 0.481 -.3284348 .1561079 L6. | -.1531775 .1320841 -1.16 0.250 -.4159347 .1095798 L7. | -.0401237 .1279615 -0.31 0.755 -.2946798 .2144324 L8. | .158914 .1205803 1.32 0.191 -.0809588 .3987867 L9. | .113676 .0951239 1.20 0.236 -.0755557 .3029077 L10. | -.0251899 .0993199 -0.25 0.800 -.2227688 .172389 L11. | .0813878 .1074369 0.76 0.451 -.1323385 .2951141 L12. | -.0778885 .1039529 -0.75 0.456 -.284684 .1289069 | _cons | -.019741 .1417809 -0.14 0.890 -.3017883 .2623064 ------------------------------------------------------------------------------ . display "chisquare(12) test = " 12*e(F) chisquare(12) test = 47.464111 . . *** TABLE 7.4: PREDICTED PROBABILITIES . . quietly poisson STRIKES OUTPUT . forvalues i = 0/10 { 2. predict poissfit`i', pr(`i') 3. } . quietly nbreg STRIKES OUTPUT . forvalues i = 0/10 { 2. predict nb2fit`i', pr(`i') 3. } . * Table 7.4 . sum poissfit* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- poissfit0 | 108 .0076184 .0069674 .0010759 .0343531 poissfit1 | 108 .0345675 .024319 .0073535 .1158065 poissfit2 | 108 .0807541 .0412888 .025129 .1951955 poissfit3 | 108 .1294987 .0437067 .0572487 .2193387 poissfit4 | 108 .1602776 .029413 .0978176 .1953638 -------------+-------------------------------------------------------- poissfit5 | 108 .1631451 .0133924 .124629 .1754655 poissfit6 | 108 .1420717 .0219649 .070022 .1606056 poissfit7 | 108 .1086961 .0306992 .0337212 .1487071 poissfit8 | 108 .0744539 .030817 .0142095 .1270437 poissfit9 | 108 .0462992 .025213 .0053224 .0964766 -------------+-------------------------------------------------------- poissfit10 | 108 .0264159 .0177871 .0017942 .0659377 . sum nb2fit* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- nb2fit0 | 108 .0487021 .0174928 .0255538 .1024384 nb2fit1 | 108 .0935452 .0262514 .0556516 .166719 nb2fit2 | 108 .1186588 .0244708 .0796266 .1782651 nb2fit3 | 108 .1249444 .017006 .0941028 .1574386 nb2fit4 | 108 .1182736 .0085172 .0994948 .1281893 -------------+-------------------------------------------------------- nb2fit5 | 108 .1045348 .0036342 .0913453 .1077284 nb2fit6 | 108 .088103 .0065444 .0636757 .092988 nb2fit7 | 108 .0717301 .0094165 .0426949 .0818209 nb2fit8 | 108 .0568971 .0107421 .0277759 .0712288 nb2fit9 | 108 .0442295 .0108498 .0176394 .0605299 -------------+-------------------------------------------------------- nb2fit10 | 108 .0338376 .0101716 .0109832 .0504332 . . * Aside: If instead use user-written addon countfit . countfit STRIKES OUTPUT, maxcount(10) prm nograph -------------------------------------------- Variable | PRM -------------------------------+------------ Deviation of monthly industr~ | 22.971 | 3.90 Constant | 5.227 | 39.15 -------------------------------+------------ alpha | N | 108 ll | -311.984 bic | 633.333 aic | 627.969 -------------------------------------------- legend: b/t Comparison of Mean Observed and Predicted Count Maximum At Mean Model Difference Value |Diff| --------------------------------------------- PRM -0.077 4 0.047 PRM: Predicted and actual probabilities Count Actual Predicted |Diff| Pearson ------------------------------------------------ 0 0.046 0.008 0.039 21.207 1 0.111 0.035 0.077 18.305 2 0.130 0.081 0.049 3.195 3 0.102 0.129 0.028 0.637 4 0.083 0.160 0.077 3.989 5 0.130 0.163 0.034 0.744 6 0.083 0.142 0.059 2.623 7 0.037 0.109 0.072 5.102 8 0.065 0.074 0.010 0.135 9 0.093 0.046 0.046 4.999 10 0.056 0.026 0.029 3.472 ------------------------------------------------ Sum 0.935 0.974 0.518 64.408 Tests and Fit Statistics PRM BIC= 127.663 AIC= 5.815 Prefer Over Evidence . drop PRM* . countfit STRIKES OUTPUT, maxcount(10) nbreg nograph -------------------------------------------- Variable | NBRM -------------------------------+------------ STRIKES | Deviation of monthly industr~ | 25.153 | 2.48 Constant | 5.227 | 24.11 -------------------------------+------------ lnalpha | Constant | 0.314 | -4.99 -------------------------------+------------ Statistics | alpha | 0.314 N | 108 ll | -280.298 bic | 574.643 aic | 566.597 -------------------------------------------- legend: b/t Comparison of Mean Observed and Predicted Count Maximum At Mean Model Difference Value |Diff| --------------------------------------------- NBRM 0.048 9 0.021 NBRM: Predicted and actual probabilities Count Actual Predicted |Diff| Pearson ------------------------------------------------ 0 0.046 0.049 0.002 0.013 1 0.111 0.094 0.018 0.356 2 0.130 0.119 0.011 0.110 3 0.102 0.125 0.023 0.461 4 0.083 0.118 0.035 1.115 5 0.130 0.105 0.025 0.651 6 0.083 0.088 0.005 0.028 7 0.037 0.072 0.035 1.812 8 0.065 0.057 0.008 0.119 9 0.093 0.044 0.048 5.711 10 0.056 0.034 0.022 1.505 ------------------------------------------------ Sum 0.935 0.903 0.232 11.881 Tests and Fit Statistics ------------------------------------------------------------------------- NBRM BIC= 68.973 AIC= 5.246 Prefer Over Evidence . drop NBRM* . . ********** 7.11.1 DYNAMIC REGRESSION FOR STRIKES DATA . . use racd07data1strikes.dta, clear . . generate ystar = STRIKES . replace ystar = 0.5 if ystar == 0 (5 real changes made) . generate lnystar = ln(ystar) . generate ytwostar = STRIKES . replace ytwostar = 1 if STRIKES == 0 (5 real changes made) . generate dy0 = STRIKES == 0 . generate lnytwostar = ln(ytwostar) . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- STRIKES | 108 5.240741 3.751312 0 18 OUTPUT | 108 -.0036954 .0545578 -.13996 .08554 MONTH | 108 54.5 31.32092 1 108 ystar | 108 5.263889 3.720026 .5 18 lnystar | 108 1.352305 .8739339 -.6931472 2.890372 -------------+-------------------------------------------------------- ytwostar | 108 5.287037 3.691493 1 18 dy0 | 108 .0462963 .2111056 0 1 lnytwostar | 108 1.384395 .8078784 0 2.890372 . . * Zeger-Qaqish model with y* = max(y,0.5) and up to three lags . poisson STRIKES OUTPUT, vce(robust) Iteration 0: log pseudolikelihood = -311.98445 Iteration 1: log pseudolikelihood = -311.98445 Poisson regression Number of obs = 108 Wald chi2(1) = 7.01 Prob > chi2 = 0.0081 Log pseudolikelihood = -311.98445 Pseudo R2 = 0.0244 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 3.134217 1.18364 2.65 0.008 .8143251 5.454109 _cons | 1.653893 .0659347 25.08 0.000 1.524663 1.783123 ------------------------------------------------------------------------------ . estimates store ZQ0 . predict yhatZQ0, n . predict resZQ0, score . generate pearsZQ0 = resZQ0 / sqrt(yhatZQ0) . . poisson STRIKES OUTPUT L.lnystar, vce(robust) Iteration 0: log pseudolikelihood = -281.8789 Iteration 1: log pseudolikelihood = -281.87875 Iteration 2: log pseudolikelihood = -281.87875 Poisson regression Number of obs = 107 Wald chi2(2) = 26.73 Prob > chi2 = 0.0000 Log pseudolikelihood = -281.87875 Pseudo R2 = 0.1137 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.330121 1.025622 2.27 0.023 .3199396 4.340302 | lnystar | L1. | .3960842 .0854108 4.64 0.000 .228682 .5634863 | _cons | 1.060482 .1569562 6.76 0.000 .7528531 1.36811 ------------------------------------------------------------------------------ . estimates store ZQ1 . predict yhatZQ1, n (1 missing value generated) . predict resZQ1, score (1 missing values generated) . predict STRIKESZQ1, xb (1 missing value generated) . generate pearsZQ1 = resZQ1 / sqrt(yhatZQ1) (1 missing value generated) . . poisson STRIKES OUTPUT L.lnystar L2.lnystar, vce(robust) Iteration 0: log pseudolikelihood = -273.95126 Iteration 1: log pseudolikelihood = -273.95121 Iteration 2: log pseudolikelihood = -273.95121 Poisson regression Number of obs = 106 Wald chi2(3) = 44.21 Prob > chi2 = 0.0000 Log pseudolikelihood = -273.95121 Pseudo R2 = 0.1338 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.192131 1.019296 2.15 0.032 .1943484 4.189914 | lnystar | L1. | .2952177 .0903188 3.27 0.001 .1181961 .4722393 L2. | .2045283 .0746091 2.74 0.006 .0582972 .3507593 | _cons | .9108763 .1511642 6.03 0.000 .6145999 1.207153 ------------------------------------------------------------------------------ . predict yhatZQ2, n (2 missing values generated) . estimates store ZQ2 . predict resZQ2, score (2 missing values generated) . generate pearsZQ2 = resZQ2 / sqrt(yhatZQ2) (2 missing values generated) . . poisson STRIKES OUTPUT L.lnystar L2.lnystar L3.lnystar, vce(robust) Iteration 0: log pseudolikelihood = -270.21687 Iteration 1: log pseudolikelihood = -270.21684 Iteration 2: log pseudolikelihood = -270.21684 Poisson regression Number of obs = 105 Wald chi2(4) = 49.59 Prob > chi2 = 0.0000 Log pseudolikelihood = -270.21684 Pseudo R2 = 0.1405 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.186976 1.018009 2.15 0.032 .1917146 4.182237 | lnystar | L1. | .2673958 .0886387 3.02 0.003 .0936672 .4411244 L2. | .1629449 .0759702 2.14 0.032 .0140461 .3118438 L3. | .1141639 .0726625 1.57 0.116 -.028252 .2565798 | _cons | .8461776 .1560318 5.42 0.000 .5403609 1.151994 ------------------------------------------------------------------------------ . predict yhatZQ3, n (3 missing values generated) . estimates store ZQ3 . predict resZQ3, score (3 missing values generated) . generate pearsZQ3 = resZQ3 / sqrt(yhatZQ3) (3 missing values generated) . . * Use following to get the Pearson statistic for NB1 overdispersion . glm STRIKES OUTPUT L.lnystar L2.lnystar L3.lnystar, family(poisson) vce(robust) Iteration 0: log pseudolikelihood = -271.3121 Iteration 1: log pseudolikelihood = -270.21813 Iteration 2: log pseudolikelihood = -270.21684 Iteration 3: log pseudolikelihood = -270.21684 Generalized linear models No. of obs = 105 Optimization : ML Residual df = 100 Scale parameter = 1 Deviance = 206.6090612 (1/df) Deviance = 2.066091 Pearson = 196.9740327 (1/df) Pearson = 1.96974 Variance function: V(u) = u [Poisson] Link function : g(u) = ln(u) [Log] AIC = 5.242226 Log pseudolikelihood = -270.2168402 BIC = -258.787 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.186976 1.018009 2.15 0.032 .1917146 4.182237 | lnystar | L1. | .2673958 .0886387 3.02 0.003 .0936672 .4411244 L2. | .1629449 .0759702 2.14 0.032 .0140461 .3118438 L3. | .1141639 .0726625 1.57 0.116 -.028252 .2565798 | _cons | .8461776 .1560318 5.42 0.000 .5403609 1.151994 ------------------------------------------------------------------------------ . . poisson STRIKES OUTPUT L.lnytwostar L.dy0, vce(robust) Iteration 0: log pseudolikelihood = -277.24805 Iteration 1: log pseudolikelihood = -277.24802 Iteration 2: log pseudolikelihood = -277.24802 Poisson regression Number of obs = 107 Wald chi2(3) = 44.42 Prob > chi2 = 0.0000 Log pseudolikelihood = -277.24802 Pseudo R2 = 0.1283 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- OUTPUT | 2.344704 1.038471 2.26 0.024 .3093384 4.380069 | lnytwostar | L1. | .4821869 .0835737 5.77 0.000 .3183854 .6459883 | dy0 | L1. | .5526772 .383839 1.44 0.150 -.1996334 1.304988 | _cons | .8959762 .1569278 5.71 0.000 .5884033 1.203549 ------------------------------------------------------------------------------ . estimates store ZQ1c . predict yhatZQ1c, n (1 missing value generated) . predict resZQ1c, score (1 missing values generated) . generate pearsZQ1c = resZQ1c / sqrt(yhatZQ1c) (1 missing value generated) . . estimates table ZQ0 ZQ1 ZQ2 ZQ3 ZQ1c, b(%9.3f) se -------------------------------------------------------------------------- Variable | ZQ0 ZQ1 ZQ2 ZQ3 ZQ1c -------------+------------------------------------------------------------ OUTPUT | 3.134 2.330 2.192 2.187 2.345 | 1.184 1.026 1.019 1.018 1.038 | lnystar | L1. | 0.396 0.295 0.267 | 0.085 0.090 0.089 L2. | 0.205 0.163 | 0.075 0.076 L3. | 0.114 | 0.073 | lnytwostar | L1. | 0.482 | 0.084 | dy0 | L1. | 0.553 | 0.384 | _cons | 1.654 1.060 0.911 0.846 0.896 | 0.066 0.157 0.151 0.156 0.157 -------------------------------------------------------------------------- legend: b/se . . * Brannas Conditional NL of INAR(1) model . generate yL1 = L.STRIKES (1 missing value generated) . generate yL2 = L2.STRIKES (2 missing values generated) . generate yL3 = L3.STRIKES (3 missing values generated) . . * Compare NLS of static model with Poisson of static model earlier . nl (STRIKES = exp({beta1}+{beta2}*OUTPUT) ), vce(robust) (obs = 108) Iteration 0: residual SS = 2001.92 Iteration 1: residual SS = 1587.385 Iteration 2: residual SS = 1429.73 Iteration 3: residual SS = 1428.403 Iteration 4: residual SS = 1428.403 Iteration 5: residual SS = 1428.403 Iteration 6: residual SS = 1428.403 Nonlinear regression Number of obs = 108 R-squared = 0.6806 Adj R-squared = 0.6746 Root MSE = 3.670899 Res. dev. = 585.3662 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /beta1 | 1.655173 .0663836 24.93 0.000 1.523561 1.786785 /beta2 | 2.992699 1.274886 2.35 0.021 .4651126 5.520286 ------------------------------------------------------------------------------ . estimates store B0 . predict yhatB0, yhat . predict resB0, residual . generate pearsB0 = resB0 / sqrt(yhatB0) . . nl (STRIKES = {rho1}*yL1 + exp({beta1}+{beta2}*OUTPUT) ) if yL1 != ., initial(rh > o1 0.5) vce(robust) (obs = 107) Iteration 0: residual SS = 1115.913 Iteration 1: residual SS = 1110.086 Iteration 2: residual SS = 1109.951 Iteration 3: residual SS = 1109.951 Iteration 4: residual SS = 1109.951 Iteration 5: residual SS = 1109.951 Nonlinear regression Number of obs = 107 R-squared = 0.7504 Adj R-squared = 0.7432 Root MSE = 3.266895 Res. dev. = 553.9518 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /rho1 | .469088 .0931431 5.04 0.000 .2843817 .6537942 /beta1 | 1.01705 .19053 5.34 0.000 .6392217 1.394878 /beta2 | 3.479712 2.129436 1.63 0.105 -.7430399 7.702464 ------------------------------------------------------------------------------ . estimates store B1 . predict yhatB1, yhat . predict resB1, residual . generate pearsB1 = resB1 / sqrt(yhatB1) (1 missing value generated) . . nl (STRIKES = {rho1}*yL1 + {rho2}*yL2 + exp({beta1}+{beta2}*OUTPUT) ) if (yL1 != > . & yL2 != .), initial(rho1 0.4 rho2 0.1) vce(robust) (obs = 106) Iteration 0: residual SS = 1368.979 Iteration 1: residual SS = 1055.534 Iteration 2: residual SS = 1040.838 Iteration 3: residual SS = 1040.745 Iteration 4: residual SS = 1040.745 Iteration 5: residual SS = 1040.745 Iteration 6: residual SS = 1040.745 Nonlinear regression Number of obs = 106 R-squared = 0.7651 Adj R-squared = 0.7559 Root MSE = 3.194273 Res. dev. = 542.9457 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /rho1 | .3504213 .1008956 3.47 0.001 .1502953 .5505472 /rho2 | .2452067 .0754637 3.25 0.002 .0955249 .3948886 /beta1 | .7388908 .2462053 3.00 0.003 .2505437 1.227238 /beta2 | 4.310547 2.851579 1.51 0.134 -1.345547 9.966641 ------------------------------------------------------------------------------ . estimates store B2 . predict yhatB2, yhat . predict resB2, residual . generate pearsB2 = resB2 / sqrt(yhatB2) (2 missing values generated) . . nl (STRIKES = {rho1}*yL1 + {rho2}*yL2 + {rho3}*yL3 + exp({beta1}+{beta2}*OUTPUT) > ) if (yL1 != . & yL2 != . & yL3 != .), initial(rho1 0.3 rho2 0.1 rho1 0.1) vce( > robust) (obs = 105) Iteration 0: residual SS = 1152.956 Iteration 1: residual SS = 1026.946 Iteration 2: residual SS = 1022.548 Iteration 3: residual SS = 1022.535 Iteration 4: residual SS = 1022.535 Iteration 5: residual SS = 1022.535 Nonlinear regression Number of obs = 105 R-squared = 0.7673 Adj R-squared = 0.7557 Root MSE = 3.197711 Res. dev. = 536.9655 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /rho1 | .3193948 .099663 3.20 0.002 .1216662 .5171233 /rho2 | .1978621 .083844 2.36 0.020 .0315179 .3642062 /rho3 | .1266174 .0846741 1.50 0.138 -.0413736 .2946085 /beta1 | .5968779 .3088189 1.93 0.056 -.01581 1.209566 /beta2 | 5.106664 3.437279 1.49 0.141 -1.712801 11.92613 ------------------------------------------------------------------------------ . estimates store B3 . predict yhatB3, yhat . predict resB3, residual . generate pearsB3 = resB3 / sqrt(yhatB3) (3 missing values generated) . . *** TABLE 7.5: STRIKES ZEGER-QAQISH AUTORGEGRESSIVE MODEL ESTIMATES . . * First four columns of Table 7.5 . estimates table ZQ0 ZQ1 ZQ2 ZQ3 ZQ1c, b(%9.3f) se -------------------------------------------------------------------------- Variable | ZQ0 ZQ1 ZQ2 ZQ3 ZQ1c -------------+------------------------------------------------------------ OUTPUT | 3.134 2.330 2.192 2.187 2.345 | 1.184 1.026 1.019 1.018 1.038 | lnystar | L1. | 0.396 0.295 0.267 | 0.085 0.090 0.089 L2. | 0.205 0.163 | 0.075 0.076 L3. | 0.114 | 0.073 | lnytwostar | L1. | 0.482 | 0.084 | dy0 | L1. | 0.553 | 0.384 | _cons | 1.654 1.060 0.911 0.846 0.896 | 0.066 0.157 0.151 0.156 0.157 -------------------------------------------------------------------------- legend: b/se . . * Last three columns of Table 7.5 . estimates table B0 B1 B2 B3, b(%9.3f) se -------------------------------------------------------------- Variable | B0 B1 B2 B3 -------------+------------------------------------------------ beta1 | _cons | 1.655 1.017 0.739 0.597 | 0.066 0.191 0.246 0.309 -------------+------------------------------------------------ beta2 | _cons | 2.993 3.480 4.311 5.107 | 1.275 2.129 2.852 3.437 -------------+------------------------------------------------ rho1 | _cons | 0.469 0.350 0.319 | 0.093 0.101 0.100 -------------+------------------------------------------------ rho2 | _cons | 0.245 0.198 | 0.075 0.084 -------------+------------------------------------------------ rho3 | _cons | 0.127 | 0.085 -------------------------------------------------------------- legend: b/se . . * Correlations - The squares of these are given in second last row of Table 7.5 . correlate STRIKES yhatZQ0 yhatZQ1 yhatZQ2 yhatZQ3 yhatZQ1c yhatB0 yhatB1 yhatB2 > yhatB3 (obs=105) | STRIKES yhatZQ0 yhatZQ1 yhatZQ2 yhatZQ3 yhatZQ1c yhatB0 -------------+--------------------------------------------------------------- STRIKES | 1.0000 yhatZQ0 | 0.2271 1.0000 yhatZQ1 | 0.5273 0.4575 1.0000 yhatZQ2 | 0.5616 0.4179 0.9279 1.0000 yhatZQ3 | 0.5745 0.4045 0.9093 0.9789 1.0000 yhatZQ1c | 0.5409 0.4241 0.9676 0.9120 0.8993 1.0000 yhatB0 | 0.2274 1.0000 0.4578 0.4182 0.4050 0.4244 1.0000 yhatB1 | 0.5136 0.4393 0.9781 0.9085 0.8933 0.9676 0.4396 yhatB2 | 0.5556 0.4063 0.9136 0.9831 0.9667 0.9130 0.4067 yhatB3 | 0.5656 0.3980 0.8986 0.9663 0.9854 0.9040 0.3983 | yhatB1 yhatB2 yhatB3 -------------+--------------------------- yhatB1 | 1.0000 yhatB2 | 0.9237 1.0000 yhatB3 | 0.9077 0.9823 1.0000 . summarize STRIKES yhatZQ0 yhatZQ1 yhatZQ2 yhatZQ3 yhatZQ1c yhatB0 yhatB1 yhatB2 > yhatB3 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- STRIKES | 108 5.240741 3.751312 0 18 yhatZQ0 | 108 5.240741 .8691222 3.371063 6.834573 yhatZQ1 | 107 5.242991 1.883666 1.747631 10.51237 yhatZQ2 | 106 5.254717 2.072169 2.234505 11.6646 yhatZQ3 | 105 5.247619 2.139702 2.208586 11.58084 -------------+-------------------------------------------------------- yhatZQ1c | 107 5.242991 2.031151 1.917685 11.44826 yhatB0 | 108 5.24372 .8314178 3.442904 6.760987 yhatB1 | 107 5.24451 1.928011 1.968058 11.88861 yhatB2 | 106 5.256538 2.096139 2.17558 12.73479 yhatB3 | 105 5.249399 2.14625 2.198303 12.3648 . . * Autocorrelations . corrgram STRIKES, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4936 0.4952 27.049 0.0000 |--- |--- 2 0.4305 0.2514 47.817 0.0000 |--- |-- 3 0.3683 0.1206 63.166 0.0000 |-- | 4 0.2264 -0.0703 69.023 0.0000 |- | 5 0.1258 -0.0873 70.849 0.0000 |- | 6 0.0387 -0.0798 71.023 0.0000 | | . corrgram resZQ0, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4656 0.4672 24.068 0.0000 |--- |--- 2 0.3983 0.2359 41.846 0.0000 |--- |- 3 0.3411 0.1214 55.012 0.0000 |-- | 4 0.1984 -0.0704 59.508 0.0000 |- | 5 0.1106 -0.0709 60.918 0.0000 | | 6 0.0292 -0.0715 61.018 0.0000 | | . corrgram resZQ1, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0859 -0.0860 .81222 0.3675 | | 2 0.1400 0.1353 2.9882 0.2245 |- |- 3 0.1834 0.2163 6.7589 0.0800 |- |- 4 0.0328 0.0454 6.8806 0.1423 | | 5 0.0280 -0.0264 6.97 0.2229 | | 6 -0.0406 -0.0986 7.16 0.3063 | | . corrgram resZQ2, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0178 -0.0178 .03451 0.8526 | | 2 -0.0218 -0.0222 .08688 0.9575 | | 3 0.1464 0.1490 2.4686 0.4810 |- |- 4 0.0040 0.0042 2.4704 0.6499 | | 5 -0.0100 -0.0038 2.4817 0.7792 | | 6 -0.0753 -0.1014 3.1304 0.7923 | | . corrgram resZQ3, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.0124 0.0125 .01656 0.8976 | | 2 0.0441 0.0446 .22867 0.8920 | | 3 0.0462 0.0445 .46358 0.9268 | | 4 -0.0041 -0.0082 .46542 0.9768 | | 5 -0.0419 -0.0454 .66247 0.9850 | | 6 -0.1234 -0.1246 2.391 0.8805 | | . corrgram resZQ1c, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1299 -0.1300 1.8575 0.1729 -| -| 2 0.1268 0.1133 3.6432 0.1618 |- | 3 0.1577 0.1984 6.4339 0.0923 |- |- 4 0.0056 0.0300 6.4375 0.1688 | | 5 0.0009 -0.0466 6.4376 0.2659 | | 6 -0.0334 -0.0795 6.5665 0.3628 | | . corrgram resB0, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4657 0.4673 24.075 0.0000 |--- |--- 2 0.3985 0.2361 41.87 0.0000 |--- |- 3 0.3411 0.1212 55.037 0.0000 |-- | 4 0.1983 -0.0705 59.528 0.0000 |- | 5 0.1099 -0.0717 60.922 0.0000 | | 6 0.0283 -0.0721 61.015 0.0000 | | . corrgram resB1, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1203 -0.1204 1.5921 0.2070 | | 2 0.1377 0.1265 3.6993 0.1573 |- |- 3 0.1708 0.2123 6.9704 0.0728 |- |- 4 0.0346 0.0573 7.1057 0.1304 | | 5 0.0307 -0.0157 7.2136 0.2052 | | 6 -0.0283 -0.0816 7.3061 0.2935 | | . corrgram resB2, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0312 -0.0313 .1064 0.7443 | | 2 -0.0373 -0.0388 .2596 0.8783 | | 3 0.1334 0.1348 2.2382 0.5245 |- |- 4 0.0073 0.0099 2.2441 0.6910 | | 5 -0.0246 -0.0172 2.3125 0.8044 | | 6 -0.0760 -0.0989 2.9731 0.8122 | | . corrgram resB3, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0054 -0.0053 .0032 0.9549 | | 2 0.0323 0.0332 .11707 0.9431 | | 3 0.0409 0.0403 .30138 0.9598 | | 4 -0.0104 -0.0128 .31339 0.9889 | | 5 -0.0589 -0.0624 .70293 0.9828 | | 6 -0.1218 -0.1239 2.3871 0.8809 | | . . ** TABLE 7.5: For LB test use the (standardized) Pearson residuals . corrgram pearsZQ0, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4424 0.4440 21.731 0.0000 |--- |--- 2 0.3760 0.2283 37.574 0.0000 |--- |- 3 0.3231 0.1234 49.387 0.0000 |-- | 4 0.2025 -0.0369 54.07 0.0000 |- | 5 0.1084 -0.0719 55.426 0.0000 | | 6 0.0298 -0.0750 55.53 0.0000 | | . corrgram pearsZQ1, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1015 -0.1016 1.1339 0.2870 | | 2 0.1326 0.1249 3.0864 0.2137 |- | 3 0.1570 0.1912 5.8512 0.1191 |- |- 4 0.0777 0.0992 6.5344 0.1626 | | 5 0.0328 0.0050 6.6576 0.2474 | | 6 0.0042 -0.0490 6.6596 0.3535 | | . corrgram pearsZQ2, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0068 -0.0068 .00502 0.9435 | | 2 -0.0240 -0.0240 .06818 0.9665 | | 3 0.1215 0.1239 1.7087 0.6350 | | 4 0.0403 0.0399 1.8907 0.7559 | | 5 0.0210 0.0277 1.9406 0.8573 | | 6 -0.0155 -0.0288 1.968 0.9226 | | . corrgram pearsZQ3, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.0156 0.0158 .02638 0.8710 | | 2 0.0525 0.0531 .32697 0.8492 | | 3 0.0257 0.0234 .39994 0.9403 | | 4 0.0139 0.0104 .42135 0.9807 | | 5 -0.0097 -0.0116 .43183 0.9944 | | 6 -0.0599 -0.0604 .83889 0.9910 | | . corrgram pearsZQ1c, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1257 -0.1258 1.7394 0.1872 -| -| 2 0.1514 0.1396 4.2871 0.1172 |- |- 3 0.1329 0.1780 6.268 0.0993 |- |- 4 0.0329 0.0470 6.3903 0.1718 | | 5 0.0098 -0.0317 6.4014 0.2691 | | 6 -0.0007 -0.0413 6.4015 0.3798 | | . corrgram pearsB0, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.4437 0.4453 21.857 0.0000 |--- |--- 2 0.3774 0.2290 37.821 0.0000 |--- |- 3 0.3241 0.1232 49.707 0.0000 |-- | 4 0.2023 -0.0386 54.383 0.0000 |- | 5 0.1080 -0.0727 55.727 0.0000 | | 6 0.0290 -0.0754 55.825 0.0000 | | . corrgram pearsB1, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1063 -0.1064 1.2434 0.2648 | | 2 0.1559 0.1478 3.9422 0.1393 |- |- 3 0.1463 0.1873 6.3437 0.0960 |- |- 4 0.0734 0.0860 6.954 0.1383 | | 5 0.0330 -0.0028 7.0782 0.2149 | | 6 -0.0011 -0.0540 7.0783 0.3137 | | . corrgram pearsB2, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0213 -0.0213 .04925 0.8244 | | 2 -0.0186 -0.0192 .08724 0.9573 | | 3 0.1110 0.1127 1.4574 0.6921 | | 4 0.0419 0.0454 1.6544 0.7990 | | 5 0.0021 0.0061 1.6549 0.8945 | | 6 -0.0285 -0.0405 1.7478 0.9414 | | . corrgram pearsB3, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0065 -0.0064 .00457 0.9461 | | 2 0.0533 0.0545 .31495 0.8543 | | 3 0.0209 0.0202 .36298 0.9478 | | 4 0.0041 0.0008 .36488 0.9853 | | 5 -0.0312 -0.0337 .4742 0.9930 | | 6 -0.0646 -0.0648 .94791 0.9875 | | . . *** FIGURE 7.3: STRIKES PREDICTED FROM A DYNAMIC MODEL . . graph twoway (line STRIKES MONTH, lwidth(medthick)) /// > (line yhatB1 MONTH, lpattern(dash) lwidth(medthick)), /// > scale(1.2) legend(ring(0) rows(2) pos(12) label(1 "Actual strikes") /// > label(2 "Predicted strikes")) ytitle("Strikes: actual and predicted") . graph export racd07fig3.eps, replace (file racd07fig3.eps written in EPS format) . graph export racd07fig3.wmf, replace (file c:\acdbookrevision\stata_final_programs_2013\racd07fig3.wmf written in Windo > ws Metafile format) . . * Try Brannas model with rho1 varying with regressors . nl (STRIKES = (1/(1 + exp(-{gamma1}-{gamma2}*OUTPUT)))*yL1 + /// > exp({beta1}+{beta2}*OUTPUT) ) if yL1 != ., initial(gamma1 0.1 gamma2 0.1) vce( > robust) (obs = 107) Iteration 0: residual SS = 1104.403 Iteration 1: residual SS = 1079.552 Iteration 2: residual SS = 1079.318 Iteration 3: residual SS = 1079.318 Iteration 4: residual SS = 1079.318 Iteration 5: residual SS = 1079.318 Iteration 6: residual SS = 1079.318 Iteration 7: residual SS = 1079.318 Iteration 8: residual SS = 1079.318 Nonlinear regression Number of obs = 107 R-squared = 0.7573 Adj R-squared = 0.7479 Root MSE = 3.2371 Res. dev. = 550.9572 ------------------------------------------------------------------------------ | Robust STRIKES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /gamma1 | -.343444 .3943564 -0.87 0.386 -1.125557 .4386689 /gamma2 | 11.92097 7.203911 1.65 0.101 -2.366285 26.20823 /beta1 | 1.082671 .1690651 6.40 0.000 .7473699 1.417972 /beta2 | -.7354947 2.040532 -0.36 0.719 -4.782409 3.31142 ------------------------------------------------------------------------------ . predict yhatB1z, yhat . correlate STRIKES yhatB1z (obs=107) | STRIKES yhatB1z -------------+------------------ STRIKES | 1.0000 yhatB1z | 0.5321 1.0000 . predict resB1z, residual . generate pearsB1z = resB3 / sqrt(yhatB1z) (3 missing values generated) . corrgram resB1z, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.1095 -0.1096 1.3188 0.2508 | | 2 0.1286 0.1193 3.1557 0.2064 |- | 3 0.1865 0.2231 7.0546 0.0702 |- |- 4 0.0295 0.0538 7.1529 0.1280 | | 5 0.0550 0.0095 7.4985 0.1861 | | 6 -0.0070 -0.0549 7.5042 0.2767 | | . corrgram pearsB1z, lags(6) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0018 -0.0016 .00033 0.9855 | | 2 0.0423 0.0432 .19565 0.9068 | | 3 0.0220 0.0213 .24918 0.9693 | | 4 0.0217 0.0198 .30173 0.9897 | | 5 -0.0628 -0.0660 .74484 0.9804 | | 6 -0.0868 -0.0890 1.5993 0.9526 | | . * The range of values of rho1 . generate rho1 = 1/(1 + exp(-_b[/gamma1]-_b[/gamma2]*OUTPUT)) . summarize rho1 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- rho1 | 108 .4141168 .143774 .1179588 .6629071 . . ********** 7.11.2 DYNAMIC REGRESSION FOR STOCK TRADES DATA . . use racd07data2stocktrades.dta, clear . . describe Contains data from racd07data2stocktrades.dta obs: 2,925 vars: 10 17 Mar 2012 14:01 size: 81,900 ---------------------------------------------------------------------------------- storage display value variable name type format label variable label ---------------------------------------------------------------------------------- t float %9.0g Time in five-minute segments day float %9.0g Trading day: 1-39 segment byte %8.0g Five-miute segment of day: 1-75 glt byte %8.0g Number of Trades: Glatfelter Company ede byte %8.0g Number of Trades: ede wpp byte %8.0g Number of Trades: wpp x1 float %9.0g cos(2*pi*t/75) x2 float %9.0g sin(2*pi*t/75) x3 float %9.0g cos(4*pi*t/75) x4 float %9.0g sin(4*pi*t/75) ---------------------------------------------------------------------------------- Sorted by: t . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- t | 2925 1463 844.5191 1 2925 day | 2925 20 11.25655 1 39 segment | 2925 38 21.65241 1 75 glt | 2925 5.663248 3.899617 0 34 ede | 2925 3.313846 3.034564 0 25 -------------+-------------------------------------------------------- wpp | 2925 8.111453 5.961392 0 43 x1 | 2925 -6.36e-09 .7072277 -.9991229 1 x2 | 2925 -7.26e-17 .7072277 -.9997807 .9997807 x3 | 2925 -6.36e-09 .7072277 -.9991229 1 x4 | 2925 -1.45e-16 .7072277 -.9997807 .9997807 . tabulate glt Number of | Trades: | Glatfelter | Company | Freq. Percent Cum. ------------+----------------------------------- 0 | 81 2.77 2.77 1 | 221 7.56 10.32 2 | 303 10.36 20.68 3 | 356 12.17 32.85 4 | 340 11.62 44.48 5 | 345 11.79 56.27 6 | 286 9.78 66.05 7 | 231 7.90 73.95 8 | 195 6.67 80.62 9 | 143 4.89 85.50 10 | 113 3.86 89.37 11 | 90 3.08 92.44 12 | 55 1.88 94.32 13 | 45 1.54 95.86 14 | 37 1.26 97.13 15 | 22 0.75 97.88 16 | 15 0.51 98.39 17 | 17 0.58 98.97 18 | 5 0.17 99.15 19 | 8 0.27 99.42 20 | 3 0.10 99.52 21 | 2 0.07 99.59 22 | 2 0.07 99.66 23 | 1 0.03 99.69 25 | 2 0.07 99.76 26 | 2 0.07 99.83 27 | 2 0.07 99.90 30 | 1 0.03 99.93 32 | 1 0.03 99.97 34 | 1 0.03 100.00 ------------+----------------------------------- Total | 2,925 100.00 . . *** FIGURE 7.4: HISTOGRAM AND TIME SERIES OF NUMBER OF TRADES . . histogram glt, scale(1.9) saving(histogram, replace) (bin=34, start=0, width=1) (file histogram.gph saved) . line glt t if t < 76, scale(1.9) saving(timeseries, replace) (file timeseries.gph saved) . graph combine histogram.gph timeseries.gph, ysize(3) xsize(6) iscale(0.7) . graph export racd07fig4.wmf, replace (file c:\acdbookrevision\stata_final_programs_2013\racd07fig4.wmf written in Windo > ws Metafile format) . graph export racd07fig4.eps, replace (file racd07fig4.eps written in EPS format) . . * There is considerable autocorrelation . corrgram glt, lags(100) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.3265 0.3270 312.04 0.0000 |-- |-- 2 0.2738 0.1874 531.67 0.0000 |-- |- 3 0.2335 0.1162 691.43 0.0000 |- | 4 0.2067 0.0819 816.7 0.0000 |- | 5 0.1889 0.0642 921.27 0.0000 |- | 6 0.2068 0.0904 1046.7 0.0000 |- | 7 0.1642 0.0274 1125.9 0.0000 |- | 8 0.1353 0.0068 1179.6 0.0000 |- | 9 0.1564 0.0518 1251.4 0.0000 |- | 10 0.1353 0.0216 1305.2 0.0000 |- | 11 0.1368 0.0305 1360.2 0.0000 |- | 12 0.1370 0.0304 1415.3 0.0000 |- | 13 0.1009 -0.0106 1445.2 0.0000 | | 14 0.0999 0.0085 1474.6 0.0000 | | 15 0.1077 0.0217 1508.7 0.0000 | | 16 0.0906 0.0019 1532.9 0.0000 | | 17 0.0725 -0.0113 1548.4 0.0000 | | 18 0.0900 0.0212 1572.2 0.0000 | | 19 0.0837 0.0154 1592.9 0.0000 | | 20 0.0715 -0.0001 1607.9 0.0000 | | 21 0.0528 -0.0196 1616.2 0.0000 | | 22 0.0510 -0.0043 1623.8 0.0000 | | 23 0.0381 -0.0116 1628.1 0.0000 | | 24 0.0287 -0.0174 1630.5 0.0000 | | 25 0.0223 -0.0137 1632 0.0000 | | 26 0.0294 0.0051 1634.6 0.0000 | | 27 0.0111 -0.0169 1634.9 0.0000 | | 28 0.0073 -0.0116 1635.1 0.0000 | | 29 0.0001 -0.0136 1635.1 0.0000 | | 30 -0.0072 -0.0157 1635.2 0.0000 | | 31 -0.0007 0.0002 1635.2 0.0000 | | 32 -0.0336 -0.0395 1638.6 0.0000 | | 33 -0.0243 -0.0091 1640.3 0.0000 | | 34 -0.0089 0.0130 1640.6 0.0000 | | 35 -0.0246 -0.0120 1642.4 0.0000 | | 36 -0.0463 -0.0316 1648.7 0.0000 | | 37 -0.0474 -0.0225 1655.4 0.0000 | | 38 -0.0483 -0.0129 1662.3 0.0000 | | 39 -0.0402 0.0025 1667.1 0.0000 | | 40 -0.0268 0.0107 1669.2 0.0000 | | 41 -0.0076 0.0308 1669.4 0.0000 | | 42 -0.0371 -0.0159 1673.5 0.0000 | | 43 -0.0108 0.0240 1673.8 0.0000 | | 44 -0.0252 -0.0034 1675.7 0.0000 | | 45 -0.0165 0.0073 1676.5 0.0000 | | 46 -0.0238 -0.0062 1678.2 0.0000 | | 47 -0.0086 0.0181 1678.4 0.0000 | | 48 -0.0050 0.0191 1678.5 0.0000 | | 49 -0.0224 -0.0157 1680 0.0000 | | 50 -0.0163 0.0002 1680.8 0.0000 | | 51 0.0091 0.0343 1681 0.0000 | | 52 0.0210 0.0292 1682.4 0.0000 | | 53 0.0157 0.0090 1683.1 0.0000 | | 54 0.0168 0.0088 1683.9 0.0000 | | 55 0.0335 0.0306 1687.3 0.0000 | | 56 0.0408 0.0275 1692.3 0.0000 | | 57 0.0325 0.0023 1695.4 0.0000 | | 58 0.0397 0.0142 1700.1 0.0000 | | 59 0.0349 0.0018 1703.7 0.0000 | | 60 0.0453 0.0158 1709.9 0.0000 | | 61 0.0219 -0.0210 1711.3 0.0000 | | 62 0.0301 -0.0026 1714 0.0000 | | 63 0.0452 0.0176 1720.1 0.0000 | | 64 0.0573 0.0262 1730 0.0000 | | 65 0.0279 -0.0218 1732.3 0.0000 | | 66 0.0384 -0.0007 1736.7 0.0000 | | 67 0.0367 -0.0019 1740.8 0.0000 | | 68 0.0636 0.0361 1752.9 0.0000 | | 69 0.0838 0.0409 1774 0.0000 | | 70 0.0901 0.0309 1798.3 0.0000 | | 71 0.0867 0.0207 1820.8 0.0000 | | 72 0.0967 0.0313 1848.9 0.0000 | | 73 0.0868 0.0113 1871.5 0.0000 | | 74 0.0896 0.0077 1895.6 0.0000 | | 75 0.1304 0.0592 1946.7 0.0000 |- | 76 0.0840 -0.0139 1967.9 0.0000 | | 77 0.0840 0.0026 1989.1 0.0000 | | 78 0.0649 -0.0243 2001.8 0.0000 | | 79 0.0575 -0.0156 2011.7 0.0000 | | 80 0.0535 -0.0084 2020.3 0.0000 | | 81 0.0470 -0.0194 2027 0.0000 | | 82 0.0355 -0.0237 2030.8 0.0000 | | 83 0.0328 -0.0088 2034 0.0000 | | 84 0.0315 -0.0098 2037 0.0000 | | 85 0.0058 -0.0316 2037.1 0.0000 | | 86 0.0478 0.0263 2044 0.0000 | | 87 0.0339 0.0014 2047.5 0.0000 | | 88 -0.0062 -0.0448 2047.6 0.0000 | | 89 0.0029 -0.0140 2047.6 0.0000 | | 90 0.0321 0.0287 2050.7 0.0000 | | 91 0.0149 -0.0007 2051.4 0.0000 | | 92 0.0148 0.0011 2052 0.0000 | | 93 -0.0102 -0.0307 2052.4 0.0000 | | 94 -0.0365 -0.0419 2056.4 0.0000 | | 95 -0.0239 -0.0133 2058.1 0.0000 | | 96 -0.0219 -0.0053 2059.6 0.0000 | | 97 -0.0059 0.0179 2059.7 0.0000 | | 98 0.0036 0.0212 2059.7 0.0000 | | 99 -0.0233 -0.0193 2061.4 0.0000 | | 100 -0.0267 -0.0015 2063.5 0.0000 | | . . * Poisson intercept-only . poisson glt, vce(robust) Iteration 0: log pseudolikelihood = -8618.1094 Iteration 1: log pseudolikelihood = -8618.1094 Poisson regression Number of obs = 2925 Wald chi2(0) = . Prob > chi2 = . Log pseudolikelihood = -8618.1094 Pseudo R2 = 0.0000 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 1.733998 .0127319 136.19 0.000 1.709043 1.758952 ------------------------------------------------------------------------------ . estimates store INTONLY . . * Poisson with just trigonometric terms . poisson glt x1 x2 x3 x4, vce(robust) Iteration 0: log pseudolikelihood = -8374.4646 Iteration 1: log pseudolikelihood = -8374.4645 Poisson regression Number of obs = 2925 Wald chi2(4) = 188.44 Prob > chi2 = 0.0000 Log pseudolikelihood = -8374.4645 Pseudo R2 = 0.0283 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .2417415 .0176962 13.66 0.000 .2070575 .2764256 x2 | .0210718 .0176364 1.19 0.232 -.013495 .0556385 x3 | -.0201147 .0178163 -1.13 0.259 -.0550341 .0148046 x4 | .0318601 .0172686 1.84 0.065 -.0019856 .0657059 _cons | 1.71908 .0124839 137.70 0.000 1.694612 1.743548 ------------------------------------------------------------------------------ . estimates store STATIC . test x1 x2 x3 x4 ( 1) [glt]x1 = 0 ( 2) [glt]x2 = 0 ( 3) [glt]x3 = 0 ( 4) [glt]x4 = 0 chi2( 4) = 188.44 Prob > chi2 = 0.0000 . predict yhatP0, n . predict resP0, score . generate pearsP0 = resP0 / sqrt(yhatP0) . . tsline yhatP0 in 1/150 . . * Poisson with one lag of Pearson residual . poisson glt x1 x2 x3 x4 L.pearsP0, vce(robust) Iteration 0: log pseudolikelihood = -8101.0375 Iteration 1: log pseudolikelihood = -8101.0337 Iteration 2: log pseudolikelihood = -8101.0337 Poisson regression Number of obs = 2924 Wald chi2(5) = 425.45 Prob > chi2 = 0.0000 Log pseudolikelihood = -8101.0337 Pseudo R2 = 0.0597 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .2433316 .017018 14.30 0.000 .209977 .2766863 x2 | .016494 .0168764 0.98 0.328 -.0165832 .0495712 x3 | -.0186755 .0169773 -1.10 0.271 -.0519503 .0145993 x4 | .0303135 .016718 1.81 0.070 -.0024531 .0630802 | pearsP0 | L1. | .1046014 .0070295 14.88 0.000 .0908238 .118379 | _cons | 1.704473 .011964 142.47 0.000 1.681024 1.727922 ------------------------------------------------------------------------------ . estimates store P1 . predict yhatP1, n (1 missing value generated) . predict resP1, score (1 missing values generated) . generate pearsP1 = resP1 / sqrt(yhatP1) (1 missing value generated) . . * Poisson with two lags of Pearson residual . poisson glt x1 x2 x3 x4 L.pearsP0 L2.pearsP0, vce(robust) Iteration 0: log pseudolikelihood = -8018.8298 Iteration 1: log pseudolikelihood = -8018.8244 Iteration 2: log pseudolikelihood = -8018.8244 Poisson regression Number of obs = 2923 Wald chi2(6) = 503.15 Prob > chi2 = 0.0000 Log pseudolikelihood = -8018.8244 Pseudo R2 = 0.0690 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .2446722 .0168409 14.53 0.000 .2116646 .2776797 x2 | .0137407 .0166444 0.83 0.409 -.0188816 .0463631 x3 | -.0181574 .0166718 -1.09 0.276 -.0508335 .0145187 x4 | .0305194 .0166304 1.84 0.066 -.0020756 .0631143 | pearsP0 | L1. | .0869893 .0074032 11.75 0.000 .0724794 .1014992 L2. | .060331 .0070818 8.52 0.000 .0464509 .0742112 | _cons | 1.700158 .0118255 143.77 0.000 1.67698 1.723336 ------------------------------------------------------------------------------ . estimates store P2 . predict yhatP2, n (2 missing values generated) . predict resP2, score (2 missing values generated) . generate pearsP2 = resP2 / sqrt(yhatP2) (2 missing values generated) . . * Poisson with three lags of Pearson residual . poisson glt x1 x2 x3 x4 L.pearsP0 L2.pearsP0 L3.pearsP0, vce(robust) Iteration 0: log pseudolikelihood = -7987.4088 Iteration 1: log pseudolikelihood = -7987.4036 Iteration 2: log pseudolikelihood = -7987.4036 Poisson regression Number of obs = 2922 Wald chi2(7) = 524.02 Prob > chi2 = 0.0000 Log pseudolikelihood = -7987.4036 Pseudo R2 = 0.0722 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .2458214 .0168182 14.62 0.000 .2128583 .2787844 x2 | .0125986 .0165162 0.76 0.446 -.0197727 .0449698 x3 | -.0175558 .0165505 -1.06 0.289 -.0499942 .0148825 x4 | .0311392 .0166062 1.88 0.061 -.0014084 .0636868 | pearsP0 | L1. | .0812965 .0076957 10.56 0.000 .0662133 .0963798 L2. | .0514478 .0073036 7.04 0.000 .037133 .0657626 L3. | .0364929 .0077975 4.68 0.000 .0212101 .0517757 | _cons | 1.698822 .0117915 144.07 0.000 1.675711 1.721933 ------------------------------------------------------------------------------ . estimates store P3 . predict yhatP3, n (3 missing values generated) . predict resP3, score (3 missing values generated) . generate pearsP3 = resP3 / sqrt(yhatP3) (3 missing values generated) . . * Poisson with Zeger-Qaqish one lag of y as regressor . generate gltstar = glt . replace gltstar = 0.5 if gltstar == 0 (81 real changes made) . generate lngltstar = ln(gltstar) . summarize gltstar glt Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- gltstar | 2925 5.677094 3.880317 .5 34 glt | 2925 5.663248 3.899617 0 34 . poisson glt x1 x2 x3 x4 L.lngltstar, vce(robust) Iteration 0: log pseudolikelihood = -8127.2513 Iteration 1: log pseudolikelihood = -8127.251 Poisson regression Number of obs = 2924 Wald chi2(5) = 371.82 Prob > chi2 = 0.0000 Log pseudolikelihood = -8127.251 Pseudo R2 = 0.0566 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .1750245 .0177152 9.88 0.000 .1403033 .2097457 x2 | .0176664 .0169373 1.04 0.297 -.0155301 .0508628 x3 | -.0122143 .0171045 -0.71 0.475 -.0457385 .02131 x4 | .0272044 .0167066 1.63 0.103 -.0055399 .0599487 | lngltstar | L1. | .2388235 .0180476 13.23 0.000 .2034508 .2741962 | _cons | 1.350856 .030462 44.35 0.000 1.291152 1.41056 ------------------------------------------------------------------------------ . estimates store ZQ1 . predict yhatZQ1, n (1 missing value generated) . predict resZQ1, score (1 missing values generated) . generate pearsZQ1 = resZQ1 / sqrt(yhatZQ1) (1 missing value generated) . . * Brannas Conditional NL of INAR(1) model . generate one = 1 . global XLIST x1 x2 x3 x4 . generate gltL1 = L.glt (1 missing value generated) . . * Compare NLS of static model with Poisson of static model earlier . nl (glt = exp({xb: $XLIST one})), vce(robust) (obs = 2925) Iteration 0: residual SS = 58170.32 Iteration 1: residual SS = 45649.64 Iteration 2: residual SS = 41771.62 Iteration 3: residual SS = 41741.62 Iteration 4: residual SS = 41741.61 Iteration 5: residual SS = 41741.61 Iteration 6: residual SS = 41741.61 Iteration 7: residual SS = 41741.61 Nonlinear regression Number of obs = 2925 R-squared = 0.6981 Adj R-squared = 0.6976 Root MSE = 3.780883 Res. dev. = 16076.04 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /xb_x1 | .2402848 .0176734 13.60 0.000 .2056312 .2749385 /xb_x2 | .0217964 .0177241 1.23 0.219 -.0129566 .0565494 /xb_x3 | -.0166151 .0181831 -0.91 0.361 -.0522682 .0190379 /xb_x4 | .0269607 .017231 1.56 0.118 -.0068255 .0607469 /xb_one | 1.719435 .0124931 137.63 0.000 1.694939 1.743931 ------------------------------------------------------------------------------ . estimates store B0 . predict yhatB0, yhat . predict resB0, residual . generate pearsB0 = resB0 / sqrt(yhatB0) . . * Brannas Conditional NL of INAR(1) model . nl (glt = {rho1}*gltL1 + exp({xb: $XLIST one}) ) if gltL1 != ., initial(rho1 0.3 > ) vce(robust) (obs = 2924) Iteration 0: residual SS = 43745.7 Iteration 1: residual SS = 38466.26 Iteration 2: residual SS = 38372.99 Iteration 3: residual SS = 38372.84 Iteration 4: residual SS = 38372.84 Iteration 5: residual SS = 38372.84 Iteration 6: residual SS = 38372.84 Iteration 7: residual SS = 38372.84 Nonlinear regression Number of obs = 2924 R-squared = 0.7225 Adj R-squared = 0.7219 Root MSE = 3.626347 Res. dev. = 15825.49 ------------------------------------------------------------------------------ | Robust glt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /rho1 | .2831876 .0216475 13.08 0.000 .2407417 .3256335 /xb_x1 | .2422538 .0236093 10.26 0.000 .1959613 .2885463 /xb_x2 | .0138979 .0236468 0.59 0.557 -.0324681 .0602639 /xb_x3 | -.0136374 .0243204 -0.56 0.575 -.0613243 .0340496 /xb_x4 | .0282694 .0230573 1.23 0.220 -.0169409 .0734797 /xb_one | 1.386919 .0307663 45.08 0.000 1.326593 1.447245 ------------------------------------------------------------------------------ . estimates store B1 . predict yhatB1, yhat . predict resB1, residual . generate pearsB1 = resB1 / sqrt(yhatB1) (1 missing value generated) . . *** TABLE 7.6 STOCK TRADES: STATIC AND DYNAMIC MODEL ESTIMATES . . estimates table INTONLY STATIC ZQ1 P1 P3 , b(%9.3f) se -------------------------------------------------------------------------- Variable | INTONLY STATIC ZQ1 P1 P3 -------------+------------------------------------------------------------ x1 | 0.242 0.175 0.243 0.246 | 0.018 0.018 0.017 0.017 x2 | 0.021 0.018 0.016 0.013 | 0.018 0.017 0.017 0.017 x3 | -0.020 -0.012 -0.019 -0.018 | 0.018 0.017 0.017 0.017 x4 | 0.032 0.027 0.030 0.031 | 0.017 0.017 0.017 0.017 | lngltstar | L1. | 0.239 | 0.018 | pearsP0 | L1. | 0.105 0.081 | 0.007 0.008 L2. | 0.051 | 0.007 L3. | 0.036 | 0.008 | _cons | 1.734 1.719 1.351 1.704 1.699 | 0.013 0.012 0.030 0.012 0.012 -------------------------------------------------------------------------- legend: b/se . . estimates table B1, b(%9.3f) se -------------------------- Variable | B1 -------------+------------ rho1 | _cons | 0.283 | 0.022 -------------+------------ xb_x1 | _cons | 0.242 | 0.024 -------------+------------ xb_x2 | _cons | 0.014 | 0.024 -------------+------------ xb_x3 | _cons | -0.014 | 0.024 -------------+------------ xb_x4 | _cons | 0.028 | 0.023 -------------+------------ xb_one | _cons | 1.387 | 0.031 -------------------------- legend: b/se . . * Correlations . correlate glt yhatP0 yhatZQ1 yhatB1 yhatP1 yhatP3 (obs=2922) | glt yhatP0 yhatZQ1 yhatB1 yhatP1 yhatP3 -------------+------------------------------------------------------ glt | 1.0000 yhatP0 | 0.2492 1.0000 yhatZQ1 | 0.3568 0.7111 1.0000 yhatB1 | 0.3700 0.6700 0.9680 1.0000 yhatP1 | 0.3636 0.6610 0.9312 0.9884 1.0000 yhatP3 | 0.3988 0.6008 0.8455 0.8947 0.9014 1.0000 . summarize glt yhatP0 yhatZQ1 yhatB1 yhatP1 yhatP3 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- glt | 2925 5.663248 3.899617 0 34 yhatP0 | 2925 5.663248 .9684182 4.282254 7.090174 yhatZQ1 | 2924 5.664501 1.36475 2.705509 10.03784 yhatB1 | 2924 5.664942 1.440391 3.089712 14.21593 yhatP1 | 2924 5.664501 1.467732 3.39707 19.37627 -------------+-------------------------------------------------------- yhatP3 | 2922 5.667009 1.621063 2.946965 19.90041 . . * For Ljung-Box test use the Pearson residuals . corrgram glt, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.3265 0.3270 312.04 0.0000 |-- |-- 2 0.2738 0.1874 531.67 0.0000 |-- |- 3 0.2335 0.1162 691.43 0.0000 |- | 4 0.2067 0.0819 816.7 0.0000 |- | 5 0.1889 0.0642 921.27 0.0000 |- | 6 0.2068 0.0904 1046.7 0.0000 |- | 7 0.1642 0.0274 1125.9 0.0000 |- | 8 0.1353 0.0068 1179.6 0.0000 |- | 9 0.1564 0.0518 1251.4 0.0000 |- | 10 0.1353 0.0216 1305.2 0.0000 |- | . corrgram pearsP0, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.2849 0.2851 237.6 0.0000 |-- |-- 2 0.2297 0.1619 392.19 0.0000 |- |- 3 0.1824 0.0915 489.71 0.0000 |- | 4 0.1568 0.0655 561.76 0.0000 |- | 5 0.1422 0.0546 621.06 0.0000 |- | 6 0.1663 0.0861 702.2 0.0000 |- | 7 0.1298 0.0311 751.65 0.0000 |- | 8 0.1008 0.0067 781.46 0.0000 | | 9 0.1254 0.0519 827.62 0.0000 |- | 10 0.1071 0.0245 861.3 0.0000 | | . corrgram pearsZQ1, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0131 -0.0131 .50484 0.4774 | | 2 0.1333 0.1333 52.503 0.0000 |- |- 3 0.1019 0.1072 82.909 0.0000 | | 4 0.0873 0.0758 105.26 0.0000 | | 5 0.0702 0.0489 119.69 0.0000 | | 6 0.1079 0.0834 153.81 0.0000 | | 7 0.0740 0.0521 169.9 0.0000 | | 8 0.0420 0.0066 175.06 0.0000 | | 9 0.0838 0.0465 195.69 0.0000 | | 10 0.0532 0.0258 204.01 0.0000 | | . corrgram pearsB1, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0447 -0.0448 5.8469 0.0156 | | 2 0.1249 0.1233 51.523 0.0000 | | 3 0.0956 0.1080 78.274 0.0000 | | 4 0.0826 0.0790 98.266 0.0000 | | 5 0.0674 0.0530 111.59 0.0000 | | 6 0.1110 0.0920 147.69 0.0000 | | 7 0.0741 0.0598 163.8 0.0000 | | 8 0.0392 0.0080 168.3 0.0000 | | 9 0.0836 0.0466 188.82 0.0000 | | 10 0.0526 0.0279 196.95 0.0000 | | . corrgram pearsP1, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0307 -0.0308 2.7613 0.0966 | | 2 0.1293 0.1287 51.707 0.0000 |- |- 3 0.1008 0.1103 81.485 0.0000 | | 4 0.0881 0.0812 104.21 0.0000 | | 5 0.0720 0.0544 119.42 0.0000 | | 6 0.1179 0.0959 160.19 0.0000 | | 7 0.0795 0.0614 178.73 0.0000 | | 8 0.0449 0.0097 184.66 0.0000 | | 9 0.0882 0.0480 207.48 0.0000 | | 10 0.0593 0.0304 217.81 0.0000 | | . corrgram pearsP3, lags(10) -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 0.0089 0.0089 .23171 0.6303 | | 2 -0.0013 -0.0014 .23683 0.8883 | | 3 -0.0244 -0.0244 1.9735 0.5779 | | 4 0.0355 0.0360 5.6566 0.2263 | | 5 0.0384 0.0378 9.9775 0.0759 | | 6 0.0863 0.0856 31.811 0.0000 | | 7 0.0507 0.0521 39.358 0.0000 | | 8 0.0144 0.0152 39.963 0.0000 | | 9 0.0553 0.0580 48.923 0.0000 | | 10 0.0384 0.0341 53.24 0.0000 | | . . ********** CLOSE OUTPUT . . * log close . * clear . * exit . end of do-file . exit, clear