Projekt_EF
Mateusz Surowiec
2025-01-21
# Wczytanie danych
# Indeksy_M <- read_excel("C:/Users/Mateusz/Desktop/Semestr III/Ekonometria Finansowa/Projekt/Dane_indeksy.xlsx", sheet = "monthly")
Indeksy_D <- read_excel("C:/Users/Mateusz/Desktop/Semestr III/Ekonometria Finansowa/Projekt/Dane_indeksy.xlsx", sheet = "daily")
# Finalnie pracujemy na zlogarytmowanych danych dziennych
dax=Indeksy_D$LN_DAX
wig=Indeksy_D$LN_WIG
bux=Indeksy_D$LN_BUX
px=Indeksy_D$LN_PXPunkt 1 - wizualizacja
t=1:3242
par(mfrow = c(2,2))
plot.ts(dax,type="l", col="red", main="LN DAX ")
abline(lm(dax~t))
plot.ts(wig, type="l", col="blue", main="LN WIG")
abline(lm(wig~t))
plot.ts(bux, type="l", col="purple", main="LN BUX")
abline(lm(bux~t))
plot.ts(px, type="l", col="green", main="LN PX")
abline(lm(px~t))
Punkt 2 - testowanie stacjonarności
summary(lm(dax~t)) # trend istotny##
## Call:
## lm(formula = dax ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43916 -0.05841 0.00153 0.07440 0.26558
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.931e+00 3.575e-03 2497.9 <2e-16 ***
## t 2.600e-04 1.910e-06 136.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1018 on 3240 degrees of freedom
## Multiple R-squared: 0.8512, Adjusted R-squared: 0.8512
## F-statistic: 1.854e+04 on 1 and 3240 DF, p-value: < 2.2e-16summary(lm(wig~t)) # trend istotny##
## Call:
## lm(formula = wig ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48345 -0.06941 0.03154 0.08508 0.25620
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.750e+00 4.377e-03 1770.51 <2e-16 ***
## t -4.729e-05 2.338e-06 -20.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1246 on 3240 degrees of freedom
## Multiple R-squared: 0.1121, Adjusted R-squared: 0.1118
## F-statistic: 409.1 on 1 and 3240 DF, p-value: < 2.2e-16summary(lm(bux~t)) # trend istotny##
## Call:
## lm(formula = bux ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.35853 -0.10588 0.02086 0.10916 0.27775
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.687e+00 4.802e-03 2017.2 <2e-16 ***
## t 4.403e-04 2.565e-06 171.6 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1367 on 3240 degrees of freedom
## Multiple R-squared: 0.9009, Adjusted R-squared: 0.9009
## F-statistic: 2.946e+04 on 1 and 3240 DF, p-value: < 2.2e-16summary(lm(px~t)) # trend istotny##
## Call:
## lm(formula = px ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50408 -0.05735 0.00913 0.06933 0.23464
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.762e+00 3.779e-03 1789.44 <2e-16 ***
## t 1.371e-04 2.018e-06 67.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1076 on 3240 degrees of freedom
## Multiple R-squared: 0.5876, Adjusted R-squared: 0.5875
## F-statistic: 4617 on 1 and 3240 DF, p-value: < 2.2e-16# ponieważ trendy są istotne, uwzględniamy je w teście
# sprawdzane jest 12 lagów, ale finalnie przyjęte jest mniej
adf_dax = ur.df(dax, type = c("trend"), lags = 12, selectlags ="BIC" )
adf_wig= ur.df(wig, type = c("trend"), lags = 12, selectlags ="BIC" )
adf_bux = ur.df(bux, type = c("trend"), lags = 12, selectlags ="BIC" )
adf_px = ur.df(px, type = c("trend"), lags = 12, selectlags ="BIC" )
summary(adf_dax)##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.132890 -0.009003 0.000142 0.009041 0.095004
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.442e-02 1.987e-02 3.746 0.000183 ***
## z.lag.1 -8.269e-03 2.223e-03 -3.720 0.000203 ***
## tt 2.029e-06 6.215e-07 3.265 0.001107 **
## z.diff.lag -6.845e-02 1.755e-02 -3.899 9.85e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01267 on 3225 degrees of freedom
## Multiple R-squared: 0.009514, Adjusted R-squared: 0.008592
## F-statistic: 10.33 on 3 and 3225 DF, p-value: 9.218e-07
##
##
## Value of test-statistic is: -3.7198 5.6036 7.0148
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.96 -3.41 -3.12
## phi2 6.09 4.68 4.03
## phi3 8.27 6.25 5.34summary(adf_wig)##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.154185 -0.009466 0.000279 0.009701 0.075061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.321e-02 1.487e-02 2.906 0.00369 **
## z.lag.1 -5.585e-03 1.917e-03 -2.913 0.00361 **
## tt -2.177e-07 2.721e-07 -0.800 0.42371
## z.diff.lag -3.843e-02 1.760e-02 -2.184 0.02906 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01357 on 3225 degrees of freedom
## Multiple R-squared: 0.004333, Adjusted R-squared: 0.003406
## F-statistic: 4.678 on 3 and 3225 DF, p-value: 0.002898
##
##
## Value of test-statistic is: -2.9127 2.8403 4.2604
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.96 -3.41 -3.12
## phi2 6.09 4.68 4.03
## phi3 8.27 6.25 5.34summary(adf_bux)##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.132330 -0.009860 -0.000257 0.009277 0.055891
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.744e-02 1.571e-02 2.382 0.0173 *
## z.lag.1 -3.835e-03 1.621e-03 -2.365 0.0181 *
## tt 1.822e-06 7.527e-07 2.420 0.0156 *
## z.diff.lag -2.992e-02 1.760e-02 -1.700 0.0892 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01259 on 3225 degrees of freedom
## Multiple R-squared: 0.002841, Adjusted R-squared: 0.001914
## F-statistic: 3.063 on 3 and 3225 DF, p-value: 0.02702
##
##
## Value of test-statistic is: -2.3652 3.6727 2.9524
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.96 -3.41 -3.12
## phi2 6.09 4.68 4.03
## phi3 8.27 6.25 5.34summary(adf_px)##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.092978 -0.001876 -0.000142 0.008795 0.074929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.569e-02 1.141e-02 2.251 0.024441 *
## z.lag.1 -3.807e-03 1.687e-03 -2.256 0.024125 *
## tt 6.745e-07 3.021e-07 2.232 0.025652 *
## z.diff.lag1 -5.821e-02 1.761e-02 -3.307 0.000954 ***
## z.diff.lag2 5.057e-02 1.760e-02 2.873 0.004089 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01029 on 3224 degrees of freedom
## Multiple R-squared: 0.008142, Adjusted R-squared: 0.006911
## F-statistic: 6.616 on 4 and 3224 DF, p-value: 2.67e-05
##
##
## Value of test-statistic is: -2.2562 2.3233 2.853
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.96 -3.41 -3.12
## phi2 6.09 4.68 4.03
## phi3 8.27 6.25 5.34# w każdym przypadku występuje niestacjonarność dla 1pct i 5pctPunkt 3 - rożnicowanie WIG w celu weliminowania niestacjonarności
t=1:3241
#rożnice
d_wig = diff(wig)
d_dax = diff(dax)
d_bux = diff(bux)
d_px = diff(px)
summary(lm(d_wig~t)) # trend nieistotny##
## Call:
## lm(formula = d_wig ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.150019 -0.009989 -0.000001 0.009978 0.079966
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.305e-05 4.775e-04 -0.090 0.928
## t 3.037e-08 2.551e-07 0.119 0.905
##
## Residual standard error: 0.01359 on 3239 degrees of freedom
## Multiple R-squared: 4.375e-06, Adjusted R-squared: -0.0003044
## F-statistic: 0.01417 on 1 and 3239 DF, p-value: 0.9053summary(lm(d_dax~t)) # trend nieistotny##
## Call:
## lm(formula = d_dax ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.130301 -0.010228 -0.000333 0.009573 0.099700
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.353e-04 4.490e-04 1.192 0.233
## t -1.113e-07 2.399e-07 -0.464 0.643
##
## Residual standard error: 0.01278 on 3239 degrees of freedom
## Multiple R-squared: 6.647e-05, Adjusted R-squared: -0.0002423
## F-statistic: 0.2153 on 1 and 3239 DF, p-value: 0.6427summary(lm(d_bux~t)) # trend nieistotny##
## Call:
## lm(formula = d_bux ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.130535 -0.010307 -0.000440 0.009446 0.059465
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.245e-04 4.441e-04 0.506 0.613
## t 1.527e-07 2.373e-07 0.644 0.520
##
## Residual standard error: 0.01264 on 3239 degrees of freedom
## Multiple R-squared: 0.0001279, Adjusted R-squared: -0.0001808
## F-statistic: 0.4144 on 1 and 3239 DF, p-value: 0.5198summary(lm(d_px~t)) # trend nieistotny##
## Call:
## lm(formula = d_px ~ t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.090264 -0.000447 -0.000184 0.009614 0.079735
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.665e-05 3.631e-04 -0.184 0.854
## t 1.610e-07 1.940e-07 0.830 0.407
##
## Residual standard error: 0.01033 on 3239 degrees of freedom
## Multiple R-squared: 0.0002126, Adjusted R-squared: -9.603e-05
## F-statistic: 0.6889 on 1 and 3239 DF, p-value: 0.4066# tym razem bez trendu
summary(ur.df(d_wig, type = c("none"), lags = 12, selectlags ="BIC" ))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.152668 -0.009690 0.000000 0.009702 0.074927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.05737 0.02541 -41.614 <2e-16 ***
## z.diff.lag 0.01548 0.01762 0.879 0.38
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01358 on 3226 degrees of freedom
## Multiple R-squared: 0.5207, Adjusted R-squared: 0.5204
## F-statistic: 1752 on 2 and 3226 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -41.6144
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62summary(ur.df(d_dax, type = c("none"), lags = 12, selectlags ="BIC" ))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.130531 -0.009113 0.000000 0.009469 0.097918
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.05314 0.02577 -40.874 <2e-16 ***
## z.diff.lag -0.01699 0.01760 -0.965 0.334
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01269 on 3226 degrees of freedom
## Multiple R-squared: 0.5359, Adjusted R-squared: 0.5356
## F-statistic: 1862 on 2 and 3226 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -40.8736
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62summary(ur.df(d_bux, type = c("none"), lags = 12, selectlags ="BIC" ))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.131231 -0.009669 0.000061 0.009761 0.056728
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.05700 0.02524 -41.880 <2e-16 ***
## z.diff.lag 0.02698 0.01758 1.535 0.125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0126 on 3226 degrees of freedom
## Multiple R-squared: 0.5154, Adjusted R-squared: 0.5151
## F-statistic: 1715 on 2 and 3226 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -41.8799
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62summary(ur.df(d_px, type = c("none"), lags = 12, selectlags ="BIC" ))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.091791 -0.001533 0.000000 0.008915 0.076961
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.01086 0.02564 -39.428 < 2e-16 ***
## z.diff.lag -0.04884 0.01758 -2.777 0.00551 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01029 on 3226 degrees of freedom
## Multiple R-squared: 0.5326, Adjusted R-squared: 0.5323
## F-statistic: 1838 on 2 and 3226 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -39.4277
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62# ZMIENNA UZNAna ZA STACJONARNĄ!
# Subset zmiennych do modelu
dane <- data.frame(d_dax,d_wig,d_bux,d_px)# Potwierdzenie testem ACF
par(mfrow = c(2,2))
acf(d_wig)
acf(d_dax)
acf(d_bux)
acf(d_px)
Punkt 4 - sprawdzenie odpowiedniej lizcby opóźniej w modelu VAR
#testowanie długości opóźnień w modelu VAR
subset_for_VAR = ts(dane) # ts - oznaczenie jako szereg czasowy
VARselect(subset_for_VAR, lag.max = 12, type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 12 1 1 12
##
## $criteria
## 1 2 3 4 5
## AIC(n) -3.522701e+01 -3.522920e+01 -3.523069e+01 -3.522586e+01 -3.522641e+01
## HQ(n) -3.521352e+01 -3.520491e+01 -3.519560e+01 -3.517998e+01 -3.516973e+01
## SC(n) -3.518936e+01 -3.516141e+01 -3.513278e+01 -3.509782e+01 -3.506825e+01
## FPE(n) 5.024605e-16 5.013655e-16 5.006187e-16 5.030403e-16 5.027628e-16
## 6 7 8 9 10
## AIC(n) -3.523366e+01 -3.523924e+01 -3.524077e+01 -3.528430e+01 -3.528797e+01
## HQ(n) -3.516618e+01 -3.516097e+01 -3.515170e+01 -3.518444e+01 -3.517732e+01
## SC(n) -3.504536e+01 -3.502083e+01 -3.499223e+01 -3.500563e+01 -3.497918e+01
## FPE(n) 4.991351e-16 4.963539e-16 4.955977e-16 4.744879e-16 4.727480e-16
## 11 12
## AIC(n) -3.530591e+01 -3.530853e+01
## HQ(n) -3.518446e+01 -3.517628e+01
## SC(n) -3.496699e+01 -3.493948e+01
## FPE(n) 4.643433e-16 4.631330e-16# kryteria AIC i FPE dają wartości skrajne, natomiast są mało odporne
# dobrym kryterium jest HQ i SC, dlatego przyjmujemy w tym wypadku 1 opóźnienie zgodnie z kryteriami HQ i SCPunkt 5 - szacujemy model VAR dla p=1
var <- VAR(subset_for_VAR, p = 1, type = "const")
summary(var)##
## VAR Estimation Results:
## =========================
## Endogenous variables: d_dax, d_wig, d_bux, d_px
## Deterministic variables: const
## Sample size: 3240
## Log Likelihood: 38672.299
## Roots of the characteristic polynomial:
## 0.07002 0.05951 0.05951 0.01943
## Call:
## VAR(y = subset_for_VAR, p = 1, type = "const")
##
##
## Estimation results for equation d_dax:
## ======================================
## d_dax = d_dax.l1 + d_wig.l1 + d_bux.l1 + d_px.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## d_dax.l1 -0.0676290 0.0175324 -3.857 0.000117 ***
## d_wig.l1 -0.0041183 0.0164835 -0.250 0.802726
## d_bux.l1 -0.0474981 0.0177141 -2.681 0.007369 **
## d_px.l1 -0.0269856 0.0216713 -1.245 0.213139
## const 0.0004097 0.0002241 1.828 0.067575 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.01274 on 3235 degrees of freedom
## Multiple R-Squared: 0.007241, Adjusted R-squared: 0.006013
## F-statistic: 5.899 on 4 and 3235 DF, p-value: 9.981e-05
##
##
## Estimation results for equation d_wig:
## ======================================
## d_wig = d_dax.l1 + d_wig.l1 + d_bux.l1 + d_px.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## d_dax.l1 -5.288e-03 1.869e-02 -0.283 0.7773
## d_wig.l1 -4.081e-02 1.757e-02 -2.323 0.0203 *
## d_bux.l1 -5.393e-03 1.888e-02 -0.286 0.7752
## d_px.l1 2.791e-02 2.310e-02 1.208 0.2271
## const 2.209e-06 2.389e-04 0.009 0.9926
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.01358 on 3235 degrees of freedom
## Multiple R-Squared: 0.002202, Adjusted R-squared: 0.0009684
## F-statistic: 1.785 on 4 and 3235 DF, p-value: 0.129
##
##
## Estimation results for equation d_bux:
## ======================================
## d_bux = d_dax.l1 + d_wig.l1 + d_bux.l1 + d_px.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## d_dax.l1 0.0050171 0.0173874 0.289 0.7729
## d_wig.l1 0.0272471 0.0163472 1.667 0.0957 .
## d_bux.l1 -0.0299107 0.0175676 -1.703 0.0887 .
## d_px.l1 0.0082757 0.0214920 0.385 0.7002
## const 0.0004860 0.0002222 2.187 0.0288 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.01263 on 3235 degrees of freedom
## Multiple R-Squared: 0.001853, Adjusted R-squared: 0.0006193
## F-statistic: 1.502 on 4 and 3235 DF, p-value: 0.1989
##
##
## Estimation results for equation d_px:
## =====================================
## d_px = d_dax.l1 + d_wig.l1 + d_bux.l1 + d_px.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## d_dax.l1 -0.0004156 0.0142028 -0.029 0.97666
## d_wig.l1 0.0015805 0.0133532 0.118 0.90579
## d_bux.l1 0.0138319 0.0143500 0.964 0.33517
## d_px.l1 -0.0629598 0.0175557 -3.586 0.00034 ***
## const 0.0002003 0.0001815 1.103 0.26993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.01032 on 3235 degrees of freedom
## Multiple R-Squared: 0.004268, Adjusted R-squared: 0.003036
## F-statistic: 3.466 on 4 and 3235 DF, p-value: 0.007824
##
##
##
## Covariance matrix of residuals:
## d_dax d_wig d_bux d_px
## d_dax 1.623e-04 4.355e-06 1.585e-06 -4.454e-06
## d_wig 4.355e-06 1.844e-04 -2.743e-06 -1.700e-06
## d_bux 1.585e-06 -2.743e-06 1.596e-04 -6.915e-07
## d_px -4.454e-06 -1.700e-06 -6.915e-07 1.065e-04
##
## Correlation matrix of residuals:
## d_dax d_wig d_bux d_px
## d_dax 1.000000 0.02518 0.009852 -0.033885
## d_wig 0.025175 1.00000 -0.015988 -0.012133
## d_bux 0.009852 -0.01599 1.000000 -0.005304
## d_px -0.033885 -0.01213 -0.005304 1.000000Punkt 6 - wizualizacja efektów estymacji
windows(width=12, height=8) # dla systemu Windows
plot(var)Punkt 7 - badanie stabilności modelu VAR
par(mar = c(2.5, 2.5, 1.2, 1.2), cex = 0.6)
var_stab = stability(var, type = "OLS-CUSUM")
plot(var_stab)
# badanie normalności rozkładu reszt
var_norm = normality.test(var, multivariate.only = TRUE)
var_norm## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 34149, df = 8, p-value < 2.2e-16
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 1067.3, df = 4, p-value < 2.2e-16
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 33082, df = 4, p-value < 2.2e-16# Reszty nie mają rozkładu normalnego (p-value <0)badanie autokorelacji składnika losowego
var_BG <- serial.test(var, lags.pt = 4, type = "BG")
var_BG##
## Breusch-Godfrey LM test
##
## data: Residuals of VAR object var
## Chi-squared = 154.15, df = 80, p-value = 1.266e-06# Reszty wykazują na brak autokorelacji# Koło jednostkowe
roots(var)## [1] 0.07001534 0.05951115 0.05951115 0.01943226par(mfrow = c(1, 1))
root.comp = Im(roots(var, modulus=FALSE ))
root.real = Re(roots(var, modulus=FALSE ))
x = seq(-1, 1, length=1000)
y1 = sqrt(1-x^2)
y2 = -sqrt(1-x^2)
plot(c(x, x), c(y1, y2), xlab='Real part', ylab='Imaginary part', type='l', main='Unit Circle', ylim=c(-1, 1), xlim=c (-1, 1))
abline(h=0)
abline(v=0)
points(root.comp, root.real, pch=19)
legend(-1, -1, legend= "Eigenvalues", pch=19)
# testy Grangera dla wszystkich 4 zmiennych - w dwie strony
causality(var, cause = c("d_wig"))## $Granger
##
## Granger causality H0: d_wig do not Granger-cause d_dax d_bux d_px
##
## data: VAR object var
## F-Test = 0.95434, df1 = 3, df2 = 12940, p-value = 0.4133
##
##
## $Instant
##
## H0: No instantaneous causality between: d_wig and d_dax d_bux d_px
##
## data: VAR object var
## Chi-squared = 3.3229, df = 3, p-value = 0.3445causality(var, cause = c("d_px"))## $Granger
##
## Granger causality H0: d_px do not Granger-cause d_dax d_wig d_bux
##
## data: VAR object var
## F-Test = 1.0873, df1 = 3, df2 = 12940, p-value = 0.353
##
##
## $Instant
##
## H0: No instantaneous causality between: d_px and d_dax d_wig d_bux
##
## data: VAR object var
## Chi-squared = 4.2133, df = 3, p-value = 0.2393causality(var, cause = c("d_dax"))## $Granger
##
## Granger causality H0: d_dax do not Granger-cause d_wig d_bux d_px
##
## data: VAR object var
## F-Test = 0.0539, df1 = 3, df2 = 12940, p-value = 0.9835
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax and d_wig d_bux d_px
##
## data: VAR object var
## Chi-squared = 6.0249, df = 3, p-value = 0.1104causality(var, cause = c("d_bux"))## $Granger
##
## Granger causality H0: d_bux do not Granger-cause d_dax d_wig d_px
##
## data: VAR object var
## F-Test = 2.6654, df1 = 3, df2 = 12940, p-value = 0.04613
##
##
## $Instant
##
## H0: No instantaneous causality between: d_bux and d_dax d_wig d_px
##
## data: VAR object var
## Chi-squared = 1.2547, df = 3, p-value = 0.7399causality(var, cause = c("d_bux","d_dax","d_px"))## $Granger
##
## Granger causality H0: d_dax d_bux d_px do not Granger-cause d_wig
##
## data: VAR object var
## F-Test = 0.55048, df1 = 3, df2 = 12940, p-value = 0.6478
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax d_bux d_px and d_wig
##
## data: VAR object var
## Chi-squared = 3.3229, df = 3, p-value = 0.3445causality(var, cause = c("d_wig","d_dax","d_px"))## $Granger
##
## Granger causality H0: d_dax d_wig d_px do not Granger-cause d_bux
##
## data: VAR object var
## F-Test = 1.0039, df1 = 3, df2 = 12940, p-value = 0.3899
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax d_wig d_px and d_bux
##
## data: VAR object var
## Chi-squared = 1.2547, df = 3, p-value = 0.7399causality(var, cause = c("d_bux","d_wig","d_px"))## $Granger
##
## Granger causality H0: d_wig d_bux d_px do not Granger-cause d_dax
##
## data: VAR object var
## F-Test = 2.9119, df1 = 3, df2 = 12940, p-value = 0.03306
##
##
## $Instant
##
## H0: No instantaneous causality between: d_wig d_bux d_px and d_dax
##
## data: VAR object var
## Chi-squared = 6.0249, df = 3, p-value = 0.1104causality(var, cause = c("d_bux","d_dax","d_wig"))## $Granger
##
## Granger causality H0: d_dax d_wig d_bux do not Granger-cause d_px
##
## data: VAR object var
## F-Test = 0.31322, df1 = 3, df2 = 12940, p-value = 0.8158
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax d_wig d_bux and d_px
##
## data: VAR object var
## Chi-squared = 4.2133, df = 3, p-value = 0.2393# testy Grangera dla pary wig i dax
subset_for_VAR2<-data.frame(d_wig,d_dax)
VARselect(subset_for_VAR2, lag.max = 12, type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 1 1 1 1
##
## $criteria
## 1 2 3 4 5
## AIC(n) -1.733003e+01 -1.732898e+01 -1.732745e+01 -1.732591e+01 -1.732477e+01
## HQ(n) -1.732598e+01 -1.732223e+01 -1.731800e+01 -1.731377e+01 -1.730993e+01
## SC(n) -1.731873e+01 -1.731015e+01 -1.730109e+01 -1.729202e+01 -1.728335e+01
## FPE(n) 2.976215e-08 2.979341e-08 2.983904e-08 2.988487e-08 2.991901e-08
## 6 7 8 9 10
## AIC(n) -1.732376e+01 -1.732401e+01 -1.732360e+01 -1.732306e+01 -1.732146e+01
## HQ(n) -1.730622e+01 -1.730376e+01 -1.730066e+01 -1.729742e+01 -1.729312e+01
## SC(n) -1.727481e+01 -1.726752e+01 -1.725958e+01 -1.725151e+01 -1.724238e+01
## FPE(n) 2.994918e-08 2.994192e-08 2.995418e-08 2.997017e-08 3.001830e-08
## 11 12
## AIC(n) -1.731957e+01 -1.731935e+01
## HQ(n) -1.728853e+01 -1.728561e+01
## SC(n) -1.723296e+01 -1.722520e+01
## FPE(n) 3.007507e-08 3.008182e-08var2 <- VAR(subset_for_VAR2, p = 1, type = "const")
causality(var2, cause = c("d_wig"))## $Granger
##
## Granger causality H0: d_wig do not Granger-cause d_dax
##
## data: VAR object var2
## F-Test = 0.035035, df1 = 1, df2 = 6474, p-value = 0.8515
##
##
## $Instant
##
## H0: No instantaneous causality between: d_wig and d_dax
##
## data: VAR object var2
## Chi-squared = 2.0097, df = 1, p-value = 0.1563causality(var2, cause = c("d_dax"))## $Granger
##
## Granger causality H0: d_dax do not Granger-cause d_wig
##
## data: VAR object var2
## F-Test = 0.10635, df1 = 1, df2 = 6474, p-value = 0.7443
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax and d_wig
##
## data: VAR object var2
## Chi-squared = 2.0097, df = 1, p-value = 0.1563# testy Grangera dla pary bux i dax
subset_for_VAR3<-data.frame(d_bux,d_dax)
VARselect(subset_for_VAR3, lag.max = 12, type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 1 1 1 1
##
## $criteria
## 1 2 3 4 5
## AIC(n) -1.748151e+01 -1.748129e+01 -1.748127e+01 -1.747989e+01 -1.747922e+01
## HQ(n) -1.747746e+01 -1.747454e+01 -1.747182e+01 -1.746774e+01 -1.746438e+01
## SC(n) -1.747021e+01 -1.746246e+01 -1.745491e+01 -1.744599e+01 -1.743780e+01
## FPE(n) 2.557871e-08 2.558418e-08 2.558479e-08 2.562016e-08 2.563722e-08
## 6 7 8 9 10
## AIC(n) -1.747993e+01 -1.747944e+01 -1.747825e+01 -1.747590e+01 -1.747453e+01
## HQ(n) -1.746239e+01 -1.745920e+01 -1.745531e+01 -1.745026e+01 -1.744619e+01
## SC(n) -1.743098e+01 -1.742295e+01 -1.741424e+01 -1.740435e+01 -1.739544e+01
## FPE(n) 2.561893e-08 2.563160e-08 2.566199e-08 2.572251e-08 2.575788e-08
## 11 12
## AIC(n) -1.747383e+01 -1.747555e+01
## HQ(n) -1.744279e+01 -1.744181e+01
## SC(n) -1.738722e+01 -1.738141e+01
## FPE(n) 2.577582e-08 2.573145e-08var3 <- VAR(subset_for_VAR3, p = 1, type = "const")
causality(var3, cause = c("d_bux"))## $Granger
##
## Granger causality H0: d_bux do not Granger-cause d_dax
##
## data: VAR object var3
## F-Test = 7.1313, df1 = 1, df2 = 6474, p-value = 0.007594
##
##
## $Instant
##
## H0: No instantaneous causality between: d_bux and d_dax
##
## data: VAR object var3
## Chi-squared = 0.29714, df = 1, p-value = 0.5857causality(var3, cause = c("d_dax"))## $Granger
##
## Granger causality H0: d_dax do not Granger-cause d_bux
##
## data: VAR object var3
## F-Test = 0.10136, df1 = 1, df2 = 6474, p-value = 0.7502
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax and d_bux
##
## data: VAR object var3
## Chi-squared = 0.29714, df = 1, p-value = 0.5857# testy Grangera dla pary dax i px
subset_for_VAR4<-data.frame(d_dax,d_px)
VARselect(subset_for_VAR4, lag.max = 12, type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 1 1 3
##
## $criteria
## 1 2 3 4 5
## AIC(n) -1.788332e+01 -1.788411e+01 -1.788474e+01 -1.788299e+01 -1.788172e+01
## HQ(n) -1.787927e+01 -1.787736e+01 -1.787529e+01 -1.787084e+01 -1.786687e+01
## SC(n) -1.787202e+01 -1.786528e+01 -1.785837e+01 -1.784910e+01 -1.784029e+01
## FPE(n) 1.711480e-08 1.710131e-08 1.709064e-08 1.712051e-08 1.714226e-08
## 6 7 8 9 10
## AIC(n) -1.787955e+01 -1.788138e+01 -1.788206e+01 -1.788234e+01 -1.788032e+01
## HQ(n) -1.786201e+01 -1.786114e+01 -1.785912e+01 -1.785670e+01 -1.785198e+01
## SC(n) -1.783060e+01 -1.782489e+01 -1.781804e+01 -1.781079e+01 -1.780123e+01
## FPE(n) 1.717946e-08 1.714808e-08 1.713641e-08 1.713163e-08 1.716632e-08
## 11 12
## AIC(n) -1.788086e+01 -1.787994e+01
## HQ(n) -1.784982e+01 -1.784620e+01
## SC(n) -1.779425e+01 -1.778579e+01
## FPE(n) 1.715696e-08 1.717283e-08var4 <- VAR(subset_for_VAR4, p = 1, type = "const")
causality(var4, cause = c("d_px"))## $Granger
##
## Granger causality H0: d_px do not Granger-cause d_dax
##
## data: VAR object var4
## F-Test = 1.5022, df1 = 1, df2 = 6474, p-value = 0.2204
##
##
## $Instant
##
## H0: No instantaneous causality between: d_px and d_dax
##
## data: VAR object var4
## Chi-squared = 3.8847, df = 1, p-value = 0.04873causality(var4, cause = c("d_dax"))## $Granger
##
## Granger causality H0: d_dax do not Granger-cause d_px
##
## data: VAR object var4
## F-Test = 0.00025931, df1 = 1, df2 = 6474, p-value = 0.9872
##
##
## $Instant
##
## H0: No instantaneous causality between: d_dax and d_px
##
## data: VAR object var4
## Chi-squared = 3.8847, df = 1, p-value = 0.04873# funkcja odpowiedzi na impuls pochodzący od przyrostów inflacji
irf=irf(var)
plot(irf)
