------------------------------------------------------------------------------------------------------------- # Ülesande 10.2 logifail # Andmefail THHI.dta #3) Aegridade korral tuleb deklareerida, milline tunnus vastab ajale. . tsset month Time variable: month, 2008m1 to 2017m12 Delta: 1 month #4) Tutvuda aegrea diagrammiga. . twoway (tsline THHI) #5) Ühikjuure testimine Dickey-Fuller testiga. . dfuller THHI, trend regress lags(3) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 116 Number of lags = 3 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -1.821 -4.035 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.6946. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.0341536 .0187576 -1.82 0.071 -.0713268 .0030195 LD. | .3828636 .0942345 4.06 0.000 .196113 .5696142 L2D. | .1417016 .102238 1.39 0.169 -.0609101 .3443132 L3D. | -.0399269 .0967594 -0.41 0.681 -.2316813 .1518275 | _trend | .0085597 .0051785 1.65 0.101 -.0017029 .0188223 _cons | 4.304485 2.274532 1.89 0.061 -.203104 8.812075 ------------------------------------------------------------------------------ . dfuller THHI, trend regress lags(2) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 117 Number of lags = 2 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -2.004 -4.034 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.5995. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.0368091 .018372 -2.00 0.048 -.0732108 -.0004074 LD. | .391527 .0932489 4.20 0.000 .2067663 .5762877 L2D. | .1234852 .0947064 1.30 0.195 -.0641634 .3111339 | _trend | .0090298 .0050804 1.78 0.078 -.0010364 .019096 _cons | 4.63766 2.22973 2.08 0.040 .2197372 9.055584 ------------------------------------------------------------------------------ . dfuller THHI, trend regress lags(1) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 118 Number of lags = 1 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -1.892 -4.034 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.6586. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.0342687 .0181087 -1.89 0.061 -.0701419 .0016045 LD. | .4456089 .0843497 5.28 0.000 .2785128 .6127051 | _trend | .0080252 .0050129 1.60 0.112 -.0019053 .0179556 _cons | 4.372735 2.199496 1.99 0.049 .0155506 8.72992 ------------------------------------------------------------------------------ . dfuller THHI, regress lags(3) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 116 Number of lags = 3 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -0.823 -3.505 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.8123. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.0044373 .0053931 -0.82 0.412 -.0151241 .0062496 LD. | .3807623 .0949583 4.01 0.000 .1925962 .5689284 L2D. | .125882 .1025802 1.23 0.222 -.0773875 .3291514 L3D. | -.0685062 .095942 -0.71 0.477 -.2586217 .1216092 | _cons | .7494643 .745893 1.00 0.317 -.7285725 2.227501 ------------------------------------------------------------------------------ . dfuller THHI, regress lags(2) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 117 Number of lags = 2 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -1.040 -3.504 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.7385. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.0055231 .0053116 -1.04 0.301 -.0160463 .0050001 LD. | .3876208 .0941093 4.12 0.000 .2011732 .5740683 L2D. | .0940108 .0941298 1.00 0.320 -.0924773 .280499 | _cons | .8915115 .73446 1.21 0.227 -.5635862 2.346609 ------------------------------------------------------------------------------ . dfuller THHI, regress lags(1) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 118 Number of lags = 1 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -1.242 -3.504 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.6552. Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | -.006497 .0052305 -1.24 0.217 -.0168577 .0038636 LD. | .4306318 .084397 5.10 0.000 .2634576 .5978061 | _cons | 1.044155 .7223411 1.45 0.151 -.3866637 2.474974 ------------------------------------------------------------------------------ . dfuller THHI, noconstant regress lags(3) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 116 Number of lags = 3 H0: Random walk without drift, a = 0, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) 2.280 -2.598 -1.950 -1.611 -------------------------------------------------------------- Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | .000965 .0004232 2.28 0.024 .0001265 .0018034 LD. | .3842424 .0948991 4.05 0.000 .1962119 .5722728 L2D. | .1291662 .1025325 1.26 0.210 -.0739888 .3323211 L3D. | -.0687647 .0959458 -0.72 0.475 -.2588689 .1213395 ------------------------------------------------------------------------------ . dfuller THHI, noconstant regress lags(2) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 117 Number of lags = 2 H0: Random walk without drift, a = 0, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) 2.207 -2.598 -1.950 -1.611 -------------------------------------------------------------- Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | .0009051 .0004101 2.21 0.029 .0000926 .0017176 LD. | .393959 .0941592 4.18 0.000 .2074303 .5804878 L2D. | .0973454 .0942849 1.03 0.304 -.0894322 .2841231 ------------------------------------------------------------------------------ . dfuller THHI, noconstant regress lags(1) Augmented Dickey–Fuller test for unit root Variable: THHI Number of obs = 118 Number of lags = 1 H0: Random walk without drift, a = 0, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) 2.626 -2.598 -1.950 -1.611 -------------------------------------------------------------- Regression table ------------------------------------------------------------------------------ D.THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | L1. | .0010422 .0003969 2.63 0.010 .0002561 .0018283 LD. | .4404719 .0845162 5.21 0.000 .273077 .6078668 ------------------------------------------------------------------------------ #6) 1. järku diferentside leidmine . gen d_THHI=D.THHI (1 missing value generated) #7) Tutvuda diferentside aegrea diagrammiga. . twoway (tsline d_THHI) #8) Testida Dickey-Fuller testiga, kas diferentside aegrida on statsionaarne. . dfuller d_THHI, trend regress lags(3) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 115 Number of lags = 3 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -4.956 -4.035 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0002. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.6218923 .1254932 -4.96 0.000 -.8706158 -.3731688 LD. | -.0049307 .1198669 -0.04 0.967 -.242503 .2326417 L2D. | .1316013 .1120053 1.17 0.243 -.0903895 .3535921 L3D. | .1037409 .0969955 1.07 0.287 -.0885011 .2959828 | _trend | -.0005095 .0015165 -0.34 0.738 -.0035152 .0024962 _cons | .1865332 .1129735 1.65 0.102 -.0373765 .410443 ------------------------------------------------------------------------------ . dfuller d_THHI, trend regress lags(2) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 116 Number of lags = 2 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -5.032 -4.035 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0002. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5634966 .1119851 -5.03 0.000 -.7854027 -.3415906 LD. | -.0549453 .1099469 -0.50 0.618 -.2728125 .1629218 L2D. | .0711961 .0962111 0.74 0.461 -.1194527 .2618449 | _trend | -.0004774 .0014928 -0.32 0.750 -.0034354 .0024806 _cons | .1674243 .1100173 1.52 0.131 -.0505823 .385431 ------------------------------------------------------------------------------ . dfuller d_THHI, trend regress lags(1) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 117 Number of lags = 1 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -5.179 -4.034 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0001. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5186287 .1001459 -5.18 0.000 -.7170358 -.3202216 LD. | -.0921565 .0946442 -0.97 0.332 -.2796638 .0953508 | _trend | -.0007227 .0014743 -0.49 0.625 -.0036435 .0021981 _cons | .1747385 .1073647 1.63 0.106 -.0379703 .3874473 ------------------------------------------------------------------------------ . dfuller d_THHI, trend regress lags(0) Dickey–Fuller test for unit root Number of obs = 118 Variable: d_THHI Number of lags = 0 H0: Random walk with or without drift Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -6.702 -4.034 -3.448 -3.148 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5691609 .0849252 -6.70 0.000 -.7373813 -.4009405 | _trend | -.0010624 .0014542 -0.73 0.467 -.0039429 .0018182 _cons | .2140392 .1039887 2.06 0.042 .0080575 .4200209 ------------------------------------------------------------------------------ . dfuller d_THHI, regress lags(3) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 115 Number of lags = 3 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -4.964 -3.505 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.6188167 .1246532 -4.96 0.000 -.86585 -.3717834 LD. | -.0078282 .1190732 -0.07 0.948 -.2438033 .2281469 L2D. | .1299722 .1114481 1.17 0.246 -.0908918 .3508362 L3D. | .1029859 .0965777 1.07 0.289 -.0884084 .2943801 | _cons | .1545964 .0607981 2.54 0.012 .0341088 .275084 ------------------------------------------------------------------------------ . dfuller d_THHI, regress lags(2) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 116 Number of lags = 2 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -5.044 -3.505 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5603317 .111099 -5.04 0.000 -.7804602 -.3402032 LD. | -.0574488 .1092275 -0.53 0.600 -.2738691 .1589714 L2D. | .0702556 .09578 0.73 0.465 -.1195202 .2600314 | _cons | .1376619 .0584383 2.36 0.020 .0218738 .25345 ------------------------------------------------------------------------------ . dfuller d_THHI, regress lags(1) Augmented Dickey–Fuller test for unit root Variable: d_THHI Number of obs = 117 Number of lags = 1 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -5.173 -3.504 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5139571 .0993587 -5.17 0.000 -.710786 -.3171282 LD. | -.0949341 .0941592 -1.01 0.315 -.2814627 .0915944 | _cons | .1300756 .0566135 2.30 0.023 .0179247 .2422266 ------------------------------------------------------------------------------ . dfuller d_THHI, regress lags(0) Dickey–Fuller test for unit root Number of obs = 118 Variable: d_THHI Number of lags = 0 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -6.679 -3.504 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5643239 .0844963 -6.68 0.000 -.7316795 -.3969684 | _cons | .1494732 .0546815 2.73 0.007 .0411696 .2577767 ------------------------------------------------------------------------------ . dfuller d_THHI, regress lags(0) Dickey–Fuller test for unit root Number of obs = 118 Variable: d_THHI Number of lags = 0 H0: Random walk without drift, d = 0 Dickey–Fuller Test -------- critical value --------- statistic 1% 5% 10% -------------------------------------------------------------- Z(t) -6.679 -3.504 -2.889 -2.579 -------------------------------------------------------------- MacKinnon approximate p-value for Z(t) = 0.0000. Regression table ------------------------------------------------------------------------------ D.d_THHI | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | L1. | -.5643239 .0844963 -6.68 0.000 -.7316795 -.3969684 | _cons | .1494732 .0546815 2.73 0.007 .0411696 .2577767 ------------------------------------------------------------------------------ #9)a) Autokorrelatsioonifunktsiooni ACF korrelogramm . ac d_THHI #9)b) Osalise autokorrelatsiooni funktsiooni PACF korrelogramm . pac d_THHI #10) ARMA(1,0) mudeli hindamine diferentside korral . arima d_THHI, arima(1,0,0) (setting optimization to BHHH) Iteration 0: log likelihood = -93.134668 Iteration 1: log likelihood = -93.131201 Iteration 2: log likelihood = -93.130848 Iteration 3: log likelihood = -93.130752 Iteration 4: log likelihood = -93.130719 (switching optimization to BFGS) Iteration 5: log likelihood = -93.130706 Iteration 6: log likelihood = -93.130699 ARIMA regression Sample: 2008m2 thru 2017m12 Number of obs = 119 Wald chi2(1) = 19.30 Log likelihood = -93.1307 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG d_THHI | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- d_THHI | _cons | .26863 .0883672 3.04 0.002 .0954335 .4418265 -------------+---------------------------------------------------------------- ARMA | ar | L1. | .4322187 .0983864 4.39 0.000 .2393848 .6250525 -------------+---------------------------------------------------------------- /sigma | .5287735 .0322384 16.40 0.000 .4655874 .5919595 ------------------------------------------------------------------------------ Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. #11)a) Vealiimete salvestamine . predict res, residuals (1 missing value generated) #11)b) Kas salvestatud jäägid on valge müra (autokorrelatsioon puudub) . corrgram res -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial autocor] ------------------------------------------------------------------------------- 1 -0.0357 -0.0368 .15558 0.6933 | | 2 0.1049 0.1091 1.51 0.4700 | | 3 0.0129 0.0193 1.5306 0.6752 | | 4 -0.0837 -0.1026 2.407 0.6614 | | 5 0.0094 0.0039 2.4181 0.7888 | | 6 -0.0216 0.0073 2.4777 0.8710 | | 7 -0.1483 -0.1774 5.3036 0.6230 -| -| 8 -0.0795 -0.1142 6.123 0.6335 | | 9 -0.0656 -0.0283 6.6872 0.6697 | | 10 0.0509 0.0665 7.0292 0.7227 | | 11 0.1232 0.1579 9.0515 0.6171 | |- 12 0.2001 0.2522 14.438 0.2736 |- |-- 13 0.0155 0.0066 14.47 0.3416 | | 14 0.0388 0.0068 14.676 0.4006 | | 15 -0.0802 -0.1146 15.566 0.4115 | | 16 -0.0016 -0.0257 15.566 0.4836 | | 17 -0.0789 -0.0835 16.444 0.4926 | | 18 -0.0628 -0.0647 17.007 0.5227 | | 19 -0.2702 -0.3161 27.517 0.0932 --| --| 20 -0.1275 -0.1925 29.879 0.0718 -| -| 21 0.1298 0.2118 32.356 0.0539 |- |- 22 -0.0030 -0.0554 32.357 0.0715 | | 23 0.0757 -0.0347 33.216 0.0774 | | 24 0.2169 0.3143 40.347 0.0196 |- |-- 25 -0.0192 0.0571 40.404 0.0265 | | 26 0.0736 -0.0347 41.243 0.0293 | | 27 -0.0266 -0.0002 41.354 0.0381 | | 28 -0.0758 -0.0999 42.264 0.0409 | | 29 -0.0412 -0.0405 42.535 0.0502 | | 30 -0.1159 -0.0753 44.709 0.0411 | | 31 -0.0880 0.0531 45.977 0.0407 | | 32 -0.0325 0.0744 46.153 0.0504 | | 33 -0.0137 -0.0294 46.184 0.0635 | | 34 -0.0639 -0.2920 46.875 0.0698 | --| 35 0.0947 -0.0715 48.412 0.0653 | | 36 0.0267 -0.1311 48.535 0.0792 | -| 37 0.1469 0.0967 52.327 0.0487 |- | 38 -0.0009 -0.1393 52.327 0.0609 | -| 39 -0.0292 -0.1026 52.48 0.0731 | | 40 -0.1670 -0.3089 57.561 0.0355 -| --| #12) Kas salvestatud jäägid alluvad normaaljaotusele . swilk res Shapiro–Wilk W test for normal data Variable | Obs W V z Prob>z -------------+------------------------------------------------------ res | 119 0.99254 0.712 -0.759 0.77616 #13)a) THHI mmudel ARIMA(1,1,0) . arima THHI, arima(1,1,0) (setting optimization to BHHH) Iteration 0: log likelihood = -93.13467 Iteration 1: log likelihood = -93.131203 Iteration 2: log likelihood = -93.13085 Iteration 3: log likelihood = -93.130754 Iteration 4: log likelihood = -93.130721 (switching optimization to BFGS) Iteration 5: log likelihood = -93.130708 Iteration 6: log likelihood = -93.1307 ARIMA regression Sample: 2008m2 thru 2017m12 Number of obs = 119 Wald chi2(1) = 19.30 Log likelihood = -93.1307 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG D.THHI | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- THHI | _cons | .26863 .0883672 3.04 0.002 .0954335 .4418266 -------------+---------------------------------------------------------------- ARMA | ar | L1. | .4322187 .0983864 4.39 0.000 .2393848 .6250525 -------------+---------------------------------------------------------------- /sigma | .5287735 .0322384 16.40 0.000 .4655874 .5919595 ------------------------------------------------------------------------------ Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. #13)b) Vaatluste lisamine andmebaasi . tsappend, add(12) #13)c) Prognoositud väärtuste leidmine. . predict hat_THHI, y dynamic(tm(2018m1)) (1 missing value generated) #13)e) Diagramm . twoway (tsline THHI) (tsline hat_THHI) #14) MAPE leidmine #14)a) Suhteliste vigade absoluutväärtuste leidmine . gen suht_viga=abs(THHI - hat_THHI)/ THHI (13 missing values generated) #14)b) Suhteliste absoluutvigade keskväärtus ehk MAPE . mean suht_viga Mean estimation Number of obs = 119 -------------------------------------------------------------- | Mean Std. err. [95% conf. interval] -------------+------------------------------------------------ suht_viga | .0030088 .0002174 .0025784 .0034392 -------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------