Dr Łukasz Goczek Uniwersytet Warszawski
10000 2000 4000 6000 8000 M3 use C:\Users\as\Desktop\Money.dta, clear format t %tm (oznaczamy tsset t tsline M3 0 1960m1 1970m1 1980m1 1990m1 2000m1 2010m1 t
tsline PPI CPI 100 150 200 50 0 1960m1 1970m1 1980m1 1990m1 2000m1 2010m1 t PPI CPI
tsline FFR 10.00 FFR 15.00 20.00 0.00 5.00 1960m1 1970m1 1980m1 1990m1 2000m1 2010m1 t
dfuller M3 Dickey-Fuller test for unit root Number of obs = 565 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) 21.745-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 1.0000 Przypomnienie: H0 pierwiastek jednostkowy, proces niestacjonarny
g dm3=d.m3 dfuller dm3 Dickey-Fuller test for unit root Number of obs = 564 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -9.759-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000
dfuller FFR dfuller FFR Dickey-Fuller test for unit root Number of obs = 565 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -2.168-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.2180
g dffr=d.ffr dfuller dffr Dickey-Fuller test for unit root Number of obs = 564 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -15.872-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000
Rozwiązanie heteroskedastyczności: g lnm3=ln(m3) dfuller lnm3 Daje wynik na granicy, zatem: pperron lnm3 Phillips-Perron test for unit root Number of obs = 565 Newey-West lags = 5 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(rho) -0.329-20.700-14.100-11.300 Z(t) -2.107-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.2417 Generujemy różnice g dlnm3=d.lnm3
Generujemy różnice g dlnm3=d.lnm3 Phillips-Perron test for unit root Number of obs = 564 Newey-West lags = 5 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(rho) -183.113-20.700-14.100-11.300 Z(t) -10.465-3.430-2.860-2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000
tsline -6-4 -2 0 2 4 1960m1 1970m1 1980m1 1990m1 2000m1 2010m1 t dffr dcpi dppi dlnm3
Podobne wyniki pozostałych zmiennych. Niestacjonarne szeregi, w pierwszych różnicach stacjonarne zatem wszystko to procesy I(1) Rozważmy model autoregresyjny bez ograniczeń (VAR) z poprzedniego wykładu.
Zmienne zerojedynkowe (patrz dodatkowy tutorial ze Staty u mnie na stronie): generate m=month(dofm(t)) tab m, g(y) drop y12
varsoc dlnm3 dffr dppi dcpi, maxlag(24) exog(y*) Selection-order criteria Sample: 1961m2-2006m2 Number of obs = 541 +---------------------------------------------------------------------------+ lag LL LR df p FPE AIC HQIC SBIC ----+---------------------------------------------------------------------- 0 1209.4 1.6e-07-4.29352-4.14455-3.91258 1 1511.89 604.99 16 0.000 5.6e-08-5.35264-5.15402-4.84473* 2 1546.15 68.521 16 0.000 5.2e-08-5.42015-5.17187-4.78526 3 1588.74 85.185 16 0.000 4.7e-08-5.51846-5.22052* -4.7566 4 1611.36 45.224 16 0.000 4.6e-08-5.5429-5.19531-4.65406 5 1645.76 68.814 16 0.000 4.3e-08-5.61095-5.2137-4.59513 6 1664.92 38.313 16 0.001 4.3e-08-5.62262-5.17571-4.47982 7 1690.4 50.969 16 0.000 4.1e-08-5.65768-5.16112-4.38791 8 1713.63 46.447 16 0.000 4.0e-08-5.68439-5.13817-4.28764 9 1734.7 42.148 16 0.000 3.9e-08-5.70315-5.10727-4.17942 10 1762.08 54.751 16 0.000 3.8e-08-5.7452-5.09967-4.0945 11 1789.2 54.256 16 0.000 3.6e-08-5.78634-5.09115-4.00866 12 1809.08 39.748 16 0.001 3.6e-08-5.80066-5.05581-3.896 13 1828.64 39.128 16 0.001 3.5e-08-5.81384-5.01933-3.7822 14 1843.11 28.941 16 0.024 3.5e-08-5.80818-4.96402-3.64957 15 1865.32 44.41 16 0.000 3.5e-08* -5.83112* -4.9373-3.54553 16 1874.48 18.324 16 0.305 3.6e-08-5.80584-4.86237-3.39327
var dlnm3 dffr dppi dcpi, lags(1/15) lutstats exog(y*) Vector autoregression Sample: 1960m5-2006m2 No. of obs = 550 Log likelihood = 1907.55 (lutstats) AIC = -17.41533 FPE = 3.27e-08 HQIC = -16.68038 Det(Sigma_ml) = 1.14e-08 SBIC = -15.53464 Equation Parms RMSE R-sq chi2 P>chi2 ---------------------------------------------------------------- dlnm3 72.002495 0.5919 797.8297 0.0000 dffr 72.501866 0.3540 301.4258 0.0000 dppi 72.650932 0.3356 277.8 0.0000 dcpi 72.216822 0.5503 673.0012 0.0000 ----------------------------------------------------------------
vargranger Granger causality Wald tests +------------------------------------------------------------------+ Equation Excluded chi2 df Prob > chi2 --------------------------------------+--------------------------- dlnm3 dffr 24.868 15 0.052 dlnm3 dppi 29.091 15 0.016 dlnm3 dcpi 29.262 15 0.015 dlnm3 ALL 87.222 45 0.000 --------------------------------------+--------------------------- dffr dlnm3 25.544 15 0.043 dffr dppi 24.012 15 0.065 dffr dcpi 19.049 15 0.212 dffr ALL 64.809 45 0.028 --------------------------------------+--------------------------- dppi dlnm3 15.622 15 0.408 dppi dffr 19.315 15 0.200 dppi dcpi 63.206 15 0.000 dppi ALL 101.81 45 0.000 --------------------------------------+--------------------------- dcpi dlnm3 24.294 15 0.060 dcpi dffr 36.037 15 0.002 dcpi dppi 30.251 15 0.011 dcpi ALL 101.7 45 0.000 +------------------------------------------------------------------+
varnorm, jbera skewness kurtosis Jarque-Bera test +--------------------------------------------------------+ Equation chi2 df Prob > chi2 --------------------+----------------------------------- dlnm3 36.884 2 0.00000 dffr 3.0e+04 2 0.00000 dppi 1493.881 2 0.00000 dcpi 822.912 2 0.00000 ALL 3.2e+04 8 0.00000 +--------------------------------------------------------+ Skewness test +--------------------------------------------------------+ Equation Skewness chi2 df Prob > chi2 --------------------+----------------------------------- dlnm3.10562 1.023 1 0.31190 dffr -2.488 567.447 1 0.00000 dppi -.33108 10.048 1 0.00153 dcpi.16487 2.492 1 0.11445 ALL 581.009 4 0.00000 +--------------------------------------------------------+
varnorm, jbera skewness kurtosis Kurtosis test +--------------------------------------------------------+ Equation Kurtosis chi2 df Prob > chi2 --------------------+----------------------------------- dlnm3 4.2509 35.861 1 0.00000 dffr 38.815 2.9e+04 1 0.00000 dppi 11.047 1483.833 1 0.00000 dcpi 8.9833 820.420 1 0.00000 ALL 3.2e+04 4 0.00000 +--------------------------------------------------------+.
varlmar, mlag(12) Lagrange-multiplier test +--------------------------------------+ lag chi2 df Prob > chi2 ------+------------------------------- 1 15.0588 16 0.52033 2 16.4301 16 0.42337 3 9.0864 16 0.90981 4 25.9794 16 0.05432 5 23.6558 16 0.09730 6 9.2176 16 0.90418 7 18.1382 16 0.31586 8 18.5490 16 0.29274 9 23.9841 16 0.08985 10 30.2229 16 0.01688 11 27.2626 16 0.03865 12 12.3244 16 0.72136 +--------------------------------------+ H0: no autocorrelation at lag order.
varstable, graph Imaginary -1 -.5.5 1 0 All the eigenvalues lie inside the unit circle. VAR satisfies stability condition.. Roots of the companion matrix -1 -.5 0.5 1 Real
varwle Equation: dlnm3 +------------------------------------+ lag chi2 df Prob > chi2 -----+------------------------------ 1 122.6979 4 0.000 2 12.07769 4 0.017 3 14.81815 4 0.005 4 1.105539 4 0.893 5 9.81928 4 0.044 6 2.545643 4 0.636 7 7.480774 4 0.113 8 13.22252 4 0.010 9 2.737011 4 0.603 10 6.656334 4 0.155 11 14.30326 4 0.006 12 4.559196 4 0.336 13 7.040044 4 0.134 14 12.24436 4 0.016 15 10.28816 4 0.036 +------------------------------------+
varwle cd. Equation: dffr +------------------------------------+ lag chi2 df Prob > chi2 -----+------------------------------ 1 100.658 4 0.000 2 11.92328 4 0.018 3 7.11665 4 0.130 4 6.672551 4 0.154 5 2.617613 4 0.624 6 14.26101 4 0.007 7 25.09046 4 0.000 8 8.87384 4 0.064 9 4.80737 4 0.308 10 2.497883 4 0.645 11 5.015153 4 0.286 12 6.703731 4 0.152 13 15.54222 4 0.004 14 1.063314 4 0.900 15 3.162494 4 0.531 +------------------------------------+ Equation: dppi +------------------------------------+
irf set "_varbasic.irf irf create nazwa, step(30) irf cgraph (VAR dppi dcpi irf, noci) (VAR dppi dlnm3 irf, noci) (VAR dppi dffr irf, noci).05 VAR: dppi -> dcpi.001 VAR: dppi -> dlnm3 0.0005 0 -.05 0 10 20 30 step 0 10 20 30 step irf irf.2 VAR: dppi -> dffr.1 0 -.1 0 10 20 30 step irf
irf set "_varbasic.irf irf create nazwa, step(30) irf cgraph (VAR dppi dcpi fevd, noci) (VAR dppi dlnm3 fevd, noci) (VAR dppi dffr fevd, noci).4 VAR: dppi -> dcpi.06 VAR: dppi -> dlnm3.04.2.02 0 0 0 10 20 30 step 0 10 20 30 step fevd fevd.06 VAR: dppi -> dffr.04.02 0 0 10 20 30 step fevd
irf set "_varbasic.irf irf create nazwa, step(30) irf cgraph (VAR dppi dcpi irf, noci) (VAR dppi dlnm3 irf, noci) (VAR dppi dffr irf, noci)
vecrank dm3 dppi dcpi dffr, trend(constant) lags(15) sindicators(y*) max ic level99 Johansen tests for cointegration Trend: constant Number of obs = 550 Sample: 1960m5-2006m2 Lags = 15 ------------------------------------------------------------------------------- 1% maximum trace critical rank parms LL eigenvalue statistic value 0 272-2816.4821. 93.9064 54.46 1 279-2788.2315 0.09763 37.4052 35.65 2 284-2773.2145 0.05314 7.3713* 20.04 3 287-2769.5762 0.01314 0.0947 6.65 4 288-2769.5289 0.00017
vec dlnm3 dppi dcpi dffr, trend(constant) rank(2) lags(12) sindicators(y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11) alpha dforce Vector error-correction model Sample: 1960m2-2006m2 No. of obs = 553 AIC = -5.853304 Log likelihood = 1854.439 HQIC = -5.133795 Det(Sigma_ml) = 1.44e-08 SBIC = -4.011668 Equation Parms RMSE R-sq chi2 P>chi2 ---------------------------------------------------------------- D_dlnM3 58.002561 0.3348 248.6172 0.0000 D_dPPI 58.665292 0.5262 548.6824 0.0000 D_dCPI 58.220155 0.5185 531.8789 0.0000 D_dFFR 58.504407 0.4539 410.5917 0.0000 ----------------------------------------------------------------
cd. Cointegrating equations Equation Parms chi2 P>chi2 ------------------------------------------- _ce1 2 66.97018 0.0000 _ce2 2 76.4827 0.0000 -------------------------------------------
cd. Identification: beta is exactly identified Johansen normalization restrictions imposed ------------------------------------------------------------------------------ beta Coef. Std. Err. z P> z [95% Conf. Interval] -------------+---------------------------------------------------------------- _ce1 dlnm3 1..... dppi 3.47e-18..... dcpi.0026112.0119567 0.22 0.827 -.0208235.0260459 dffr -.1062535.013092-8.12 0.000 -.1319134 -.0805937 _cons -.0167214..... -------------+---------------------------------------------------------------- _ce2 dlnm3 (omitted) dppi 1..... dcpi -.777459.2198926-3.54 0.000-1.208441 -.3464774 dffr -1.771007.2407715-7.36 0.000-2.242911-1.299104 _cons.2052105..... ------------------------------------------------------------------------------
cd. Identification: beta is exactly identified Johansen normalization restrictions imposed ------------------------------------------------------------------------------ beta Coef. Std. Err. z P> z [95% Conf. Interval] -------------+---------------------------------------------------------------- _ce1 dlnm3 1..... dppi 3.47e-18..... dcpi.0026112.0119567 0.22 0.827 -.0208235.0260459 dffr -.1062535.013092-8.12 0.000 -.1319134 -.0805937 _cons -.0167214..... -------------+---------------------------------------------------------------- _ce2 dlnm3 (omitted) dppi 1..... dcpi -.777459.2198926-3.54 0.000-1.208441 -.3464774 dffr -1.771007.2407715-7.36 0.000-2.242911-1.299104 _cons.2052105..... ------------------------------------------------------------------------------
cd. ------------------------------------------------------------------------------ alpha Coef. Std. Err. z P> z [95% Conf. Interval] -------------+---------------------------------------------------------------- D_dlnM3 _ce1 L1. -.0144611.008811-1.64 0.101 -.0317303.0028081 _ce2 L1..0009488.000561 1.69 0.091 -.0001507.0020483 -------------+---------------------------------------------------------------- D_dPPI _ce1 L1. 9.327865 2.288678 4.08 0.000 4.842139 13.81359 _ce2 L1. -.6173326.1457166-4.24 0.000 -.9029318 -.3317333 -------------+---------------------------------------------------------------- D_dCPI _ce1 L1. -.6319104.7573556-0.83 0.404-2.1163.8524793 _ce2 L1. -.0699541.0482197-1.45 0.147 -.1644629.0245547 -------------+---------------------------------------------------------------- D_dFFR
Diagnostyka identyczna jak w przypadku VAR.
-1 -.5 Imaginary 0.5 1 Roots of the companion matrix Real -1-.50.51 The VECM specification imposes 2 unit moduli
1. Badanie stacjonarności 2. Sprowadzamy do tego samego poziomu integracji (pamiętajmy o sensie, czy jest sens?) różnicując 3. Wybór liczby opóźnień 4. Diagnostyka stabilność, normalność, wyłączenia opóźnień, egzogeniczność, autokorelacja. 5. Wyniki przy pomocy funkcji reakcji i dekompozycji wariancji 6. Test kointegracji. 7. Oszacowanie VEC 8. Diagnostyka jak w przypadku VAR.
Dziękuję za uwagę.