R04 STA1341 - Regresi dengan Peubah Lag
Package
#install.packages("dLagM")
#install.packages("dynlm")
#install.packages("MLmetrics")
library(dLagM)#bisa otomatis timeseries datanya
library(dynlm) #data harus timeseries
library(MLmetrics)
library(lmtest)
library(car)
library(readxl)Data
Download data : (Link)
#IMPORT DATA
#working directory
setwd("D:/MATERI KULIAH S2 IPB/ASPRAK 1/RESPONSI 4")
#membuka file data
data<-read_excel("data_reg_lag.xlsx")
str(data)## tibble [20 x 4] (S3: tbl_df/tbl/data.frame)
## $ t : num [1:20] 1 2 3 4 5 6 7 8 9 10 ...
## $ Yt : num [1:20] 52.9 53.8 54.9 58.2 60 63.4 68.2 78 84.7 90.6 ...
## $ Y(t-1): num [1:20] NA 52.9 53.8 54.9 58.2 60 63.4 68.2 78 84.7 ...
## $ Xt : num [1:20] 30.3 30.9 30.9 33.4 35.1 37.3 41 44.9 46.5 50.3 ...data## # A tibble: 20 x 4
## t Yt `Y(t-1)` Xt
## <dbl> <dbl> <dbl> <dbl>
## 1 1 52.9 NA 30.3
## 2 2 53.8 52.9 30.9
## 3 3 54.9 53.8 30.9
## 4 4 58.2 54.9 33.4
## 5 5 60 58.2 35.1
## 6 6 63.4 60 37.3
## 7 7 68.2 63.4 41
## 8 8 78 68.2 44.9
## 9 9 84.7 78 46.5
## 10 10 90.6 84.7 50.3
## 11 11 98.2 90.6 53.5
## 12 12 102. 98.2 52.8
## 13 13 103. 102. 55.9
## 14 14 108. 103. 63
## 15 15 125. 108. 73
## 16 16 158. 125. 84.8
## 17 17 158. 158. 86.6
## 18 18 170. 158. 98.9
## 19 19 180 170. 111.
## 20 20 198 180 125.#SPLIT DATA
train<-data[1:15,] #15 data pertama
test<-data[16:20,] # 5 data terakhir
#data time series
train.ts<-ts(train)
test.ts<-ts(test)
data.ts<-ts(data)Model KOYCK
Metode Koyck didasarkan asumsi bahwa semakin jauh jarak lag peubah independen dari periode sekarang maka semakin kecil pengaruh peubah lag terhadap peubah dependen.
Koyck mengusulkan suatu metode untuk menduga model dinamis distributed lag dengan mengasumsikan bahwa semua koefisien 𝛽 mempunyai tanda sama.
Model Koyck merupakan jenis paling umum dari model infinite distributed lag dan juga dikenal sebagai geometric lag.
#MODEL KOYCK -> estimasi parameter berebeda dengan ardl
model.koyck = koyckDlm(x = train$Xt, y = train$Yt)
summary(model.koyck)##
## Call:
## "Y ~ (Intercept) + Y.1 + X.t"
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.75605 -1.16407 0.01599 1.17295 3.28003
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.7335 2.1785 -1.714 0.1146
## Y.1 0.4214 0.1158 3.639 0.0039 **
## X.t 1.1510 0.1901 6.055 8.25e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.023 on 11 degrees of freedom
## Multiple R-Squared: 0.9934, Adjusted R-squared: 0.9922
## Wald test: 828.9 on 2 and 11 DF, p-value: 1.01e-12
##
## Diagnostic tests:
## NULL
##
## alpha beta phi
## Geometric coefficients: -6.452844 1.150951 0.4214181#Akurasi dari data training
AIC(model.koyck)## [1] 64.08525BIC(model.koyck)## [1] 66.64148fore.koyck <- forecast(model = model.koyck, x=test$Xt, h=5)
#mape data testing
mape.koyck <- MAPE(fore.koyck$forecasts, test$Yt)
mape.koyck## [1] 0.06845456#akurasi data training
GoF(model.koyck)## n MAE MPE MAPE sMAPE MASE MSE
## model.koyck 14 1.473599 -0.0004874002 0.01720083 0.01719063 0.2701945 3.216237
## MRAE GMRAE
## model.koyck 0.3967354 0.3026997Regression with Distributed Lag
Regression with Distributed Lag (lag=2)
#REGRESSION WITH DISTRIBUTED LAG-> estimasi parameter menggunakan least square
model.dlm = dlm(x = train$Xt,y = train$Yt , q = 2)
#yt=b0+bxt+b2xt-1+b3xt-2
summary(model.dlm)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4446 -0.6965 -0.2373 0.8810 1.8630
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.6779 1.8156 -5.330 0.000474 ***
## x.t 0.3179 0.1792 1.774 0.109856
## x.1 1.5276 0.3487 4.380 0.001770 **
## x.2 0.2651 0.2440 1.087 0.305388
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.322 on 9 degrees of freedom
## Multiple R-squared: 0.9974, Adjusted R-squared: 0.9965
## F-statistic: 1133 on 3 and 9 DF, p-value: 6.471e-12
##
## AIC and BIC values for the model:
## AIC BIC
## 1 49.3705 52.19525AIC(model.dlm)## [1] 49.3705BIC(model.dlm)## [1] 52.19525fore.dlm <- forecast(model = model.dlm, x=test$Xt, h=5) #meramalkan 5 periode ke depan
#mape data testing
mape.dlm <- MAPE(fore.dlm$forecasts, test$Yt)
mape.dlm## [1] 0.08345978#akurasi data training
GoF(model.dlm)## n MAE MPE MAPE sMAPE MASE MSE
## model.dlm 13 0.9282513 -0.0002879026 0.01227837 0.01229574 0.1595847 1.210003
## MRAE GMRAE
## model.dlm 0.2350414 0.1491444Regression with Distributed Lag Optimum
#penentuan lag optimum
finiteDLMauto(formula = Yt ~ Xt,
data = data.frame(train), q.min = 1, q.max = 4 ,
model.type = "dlm", error.type = "AIC", trace = TRUE) ##q max lag maksimum## q - k MASE AIC BIC GMRAE MBRAE R.Adj.Sq Ljung-Box
## 4 4 0.09175 37.32725 40.11252 0.07960 -0.03335 0.99741 0.1363983
## 3 3 0.14898 48.42255 51.33199 0.09585 -0.20490 0.99543 0.5241058
## 2 2 0.15958 49.37050 52.19525 0.14914 -0.13532 0.99648 0.7386164
## 1 1 0.17862 51.20728 53.76351 0.20782 -0.14048 0.99688 0.8016044#model dlm dengan lag optimum
model.dlm2 = dlm(x = train$Xt,y = train$Yt , q = 4) #terdapat lag yang tidak signifikan sehingga dapat dikurangi jumlah lagnya
summary(model.dlm2)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## 1 2 3 4 5 6 7 8
## 0.75409 -0.04471 -1.43030 0.67686 -0.74270 0.49833 0.89137 -0.37952
## 9 10 11
## 0.29810 -0.66775 0.14623
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.2044 1.7540 -6.388 0.00139 **
## x.t 0.3515 0.1643 2.139 0.08540 .
## x.1 1.8517 0.3288 5.632 0.00245 **
## x.2 0.2387 0.3399 0.702 0.51374
## x.3 0.1622 0.3315 0.489 0.64543
## x.4 -0.5321 0.2764 -1.925 0.11219
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.036 on 5 degrees of freedom
## Multiple R-squared: 0.9987, Adjusted R-squared: 0.9974
## F-statistic: 772.2 on 5 and 5 DF, p-value: 3.263e-07
##
## AIC and BIC values for the model:
## AIC BIC
## 1 37.32725 40.11252AIC(model.dlm2)## [1] 37.32725BIC(model.dlm2)## [1] 40.11252fore.dlm2 <- forecast(model = model.dlm2, x=test$Xt, h=5)
mape.dlm2<- MAPE(fore.dlm2$forecasts, test$Yt)
mape.dlm2## [1] 0.1069364#akurasi data training
GoF(model.dlm2)## n MAE MPE MAPE sMAPE MASE
## model.dlm2 11 0.5936334 -4.044484e-05 0.007294734 0.007285343 0.09175168
## MSE MRAE GMRAE
## model.dlm2 0.4881084 0.1227492 0.07960168Model Autoregressive / Dynamic Regression
Apabila peubah dependen dipengaruhi oleh peubah independen pada waktu sekarang, serta dipengaruhii juga oleh peubah dependen itu sendiri pada satu waktu yang lalu maka model tersebut disebut autoregressive (Gujarati, 2004)
#MODEL AUTOREGRESSIVE
#library(dLagM) -> tidak perlu mengubah data ke bentuk tseries
model.ardl = ardlDlm(x = train$Xt, y = train$Yt, p = 1 , q = 1) #p:lag x, q:lag y
#model untuk p=1, q=1: yt=b0+b1yt-1+b2xt+b3xt-1
#model untuk p=2, q=3: yt=b0+b1yt-1+b2yt-2+b3xt+b4xt-1+b5xt-2
summary(model.ardl)##
## Time series regression with "ts" data:
## Start = 2, End = 15
##
## Call:
## dynlm(formula = as.formula(model.text), data = data, start = 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6274 -0.8401 -0.1767 0.8392 1.9447
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.3594 1.9186 -4.357 0.00143 **
## X.t 0.3563 0.1875 1.900 0.08661 .
## X.1 1.4557 0.4071 3.575 0.00505 **
## Y.1 0.1408 0.1318 1.068 0.31055
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.269 on 10 degrees of freedom
## Multiple R-squared: 0.9976, Adjusted R-squared: 0.9969
## F-statistic: 1405 on 3 and 10 DF, p-value: 2.006e-13AIC(model.ardl)## [1] 51.69462BIC(model.ardl)## [1] 54.8899fore.ardl <- forecast(model = model.ardl, x=test$Xt, h=5)
mape.ardl <- MAPE(fore.ardl$forecasts, test$Yt) #data testing
mape.ardl## [1] 0.08313896#akurasi data training
GoF(model.ardl)## n MAE MPE MAPE sMAPE MASE MSE
## model.ardl 14 0.8821232 -0.0003216464 0.01183235 0.01185341 0.1617433 1.15063
## MRAE GMRAE
## model.ardl 0.2332582 0.1391987#penentuan lag optimum
ardlBoundOrders(data = data.frame(data) , formula = Yt ~ Xt )## $p
## Xt
## 1 6
##
## $q
## [1] 1
##
## $Stat.table
## q = 1 q = 2 q = 3 q = 4 q = 5 q = 6 q = 7 q = 8
## p = 1 112.18269 109.52534 105.52217 101.63734 95.28841 88.62221 NA NA
## p = 2 107.53473 107.27801 104.24754 98.64030 82.80884 78.24396 NA NA
## p = 3 104.39360 104.39360 106.01978 99.61104 80.50702 NA NA NA
## p = 4 96.84811 96.30318 96.30318 92.11385 81.60323 NA NA NA
## p = 5 86.53889 84.38162 71.12124 71.12124 NA NA NA NA
## p = 6 -20.56587 NA NA NA NA NA NA NA
## q = 9 q = 10 q = 11 q = 12 q = 13 q = 14 q = 15
## p = 1 NA NA NA NA NA NA NA
## p = 2 NA NA NA NA NA NA NA
## p = 3 NA NA NA NA NA NA NA
## p = 4 NA NA NA NA NA NA NA
## p = 5 NA NA NA NA NA NA NA
## p = 6 NA NA NA NA NA NA NA
##
## $min.Stat
## [1] -20.56587#PEMODELAN DLM dan ARDL dengan library dynlm
#library(dynlm)
#sama dengan model dlm p=1
cons_lm1 <- dynlm(Yt ~ Xt+L(Xt),data = train.ts)
#sama dengan model ardl p=0 q=1
cons_lm2 <- dynlm(Yt ~ Xt+L(Yt),data = train.ts)
#sama dengan ardl p=1 q=1
cons_lm3 <- dynlm(Yt ~ Xt+L(Xt)+L(Yt),data = train.ts)
#sama dengan dlm p=2
cons_lm4 <- dynlm(Yt ~ Xt+L(Xt)+L(Xt,2),data = train.ts)
#Ringkasan Model
summary(cons_lm1)##
## Time series regression with "ts" data:
## Start = 2, End = 15
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4118 -0.8790 -0.3542 0.7202 2.3047
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.4870 1.6123 -5.884 0.000106 ***
## Xt 0.2557 0.1632 1.567 0.145434
## L(Xt) 1.8395 0.1927 9.547 1.17e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.277 on 11 degrees of freedom
## Multiple R-squared: 0.9974, Adjusted R-squared: 0.9969
## F-statistic: 2081 on 2 and 11 DF, p-value: 6.538e-15summary(cons_lm2)##
## Time series regression with "ts" data:
## Start = 2, End = 15
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4441 -1.1436 0.1785 1.5549 2.1584
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.54096 1.96526 -1.802 0.099 .
## Xt 0.92218 0.14482 6.368 5.31e-05 ***
## L(Yt) 0.55684 0.08922 6.241 6.34e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.827 on 11 degrees of freedom
## Multiple R-squared: 0.9946, Adjusted R-squared: 0.9936
## F-statistic: 1015 on 2 and 11 DF, p-value: 3.344e-13summary(cons_lm3)##
## Time series regression with "ts" data:
## Start = 2, End = 15
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt) + L(Yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6274 -0.8401 -0.1767 0.8392 1.9447
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.3594 1.9186 -4.357 0.00143 **
## Xt 0.3563 0.1875 1.900 0.08661 .
## L(Xt) 1.4557 0.4071 3.575 0.00505 **
## L(Yt) 0.1408 0.1318 1.068 0.31055
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.269 on 10 degrees of freedom
## Multiple R-squared: 0.9976, Adjusted R-squared: 0.9969
## F-statistic: 1405 on 3 and 10 DF, p-value: 2.006e-13summary(cons_lm4)##
## Time series regression with "ts" data:
## Start = 3, End = 15
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt) + L(Xt, 2), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4446 -0.6965 -0.2373 0.8810 1.8630
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.6779 1.8156 -5.330 0.000474 ***
## Xt 0.3179 0.1792 1.774 0.109856
## L(Xt) 1.5276 0.3487 4.380 0.001770 **
## L(Xt, 2) 0.2651 0.2440 1.087 0.305388
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.322 on 9 degrees of freedom
## Multiple R-squared: 0.9974, Adjusted R-squared: 0.9965
## F-statistic: 1133 on 3 and 9 DF, p-value: 6.471e-12#SSE
deviance(cons_lm1)## [1] 17.94685deviance(cons_lm2)## [1] 36.70155deviance(cons_lm3)## [1] 16.10882deviance(cons_lm4)## [1] 15.73004Uji Diagnostik Model
Uji Non Autokorelasi
H0: tidak ada autokorelasi
H1: ada autokorelasi
#uji model
if(require("lmtest")) encomptest(cons_lm1, cons_lm2)## Encompassing test
##
## Model 1: Yt ~ Xt + L(Xt)
## Model 2: Yt ~ Xt + L(Yt)
## Model E: Yt ~ Xt + L(Xt) + L(Yt)
## Res.Df Df F Pr(>F)
## M1 vs. ME 10 -1 1.141 0.31055
## M2 vs. ME 10 -1 12.784 0.00505 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Diagnostik
#durbin watson
dwtest(cons_lm1)##
## Durbin-Watson test
##
## data: cons_lm1
## DW = 2.1065, p-value = 0.3842
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm2)##
## Durbin-Watson test
##
## data: cons_lm2
## DW = 1.441, p-value = 0.0497
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm3)##
## Durbin-Watson test
##
## data: cons_lm3
## DW = 1.9337, p-value = 0.2449
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm4)##
## Durbin-Watson test
##
## data: cons_lm4
## DW = 1.8189, p-value = 0.1911
## alternative hypothesis: true autocorrelation is greater than 0Uji Heterogenitas
H0: ragam sisaan homogen
H1: ragam sisaan tidak homogen
#heterogenitas
bptest(cons_lm1)##
## studentized Breusch-Pagan test
##
## data: cons_lm1
## BP = 1.5713, df = 2, p-value = 0.4558bptest(cons_lm2)##
## studentized Breusch-Pagan test
##
## data: cons_lm2
## BP = 3.7022, df = 2, p-value = 0.1571bptest(cons_lm3)##
## studentized Breusch-Pagan test
##
## data: cons_lm3
## BP = 4.0554, df = 3, p-value = 0.2555bptest(cons_lm4)##
## studentized Breusch-Pagan test
##
## data: cons_lm4
## BP = 2.7921, df = 3, p-value = 0.4248Uji Normalitas
H0: sisaan berdistribusi normal
H1: sisaan tidak berdistribusi normal
#shapiro wilk
shapiro.test(residuals(cons_lm1))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm1)
## W = 0.90752, p-value = 0.145shapiro.test(residuals(cons_lm2))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm2)
## W = 0.94358, p-value = 0.4661shapiro.test(residuals(cons_lm3))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm3)
## W = 0.94403, p-value = 0.4723shapiro.test(residuals(cons_lm4))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm4)
## W = 0.92477, p-value = 0.2907Perbandingan Keakuratan Ramalan
#PERBANDINGAN
akurasi <- matrix(c(mape.koyck, mape.dlm, mape.dlm2, mape.ardl))
row.names(akurasi)<- c("Koyck","DLM 1","DLM 2","Autoregressive")
colnames(akurasi) <- c("MAPE")
akurasi## MAPE
## Koyck 0.06845456
## DLM 1 0.08345978
## DLM 2 0.10693637
## Autoregressive 0.08313896#PLOT
par(mfrow=c(1,1))
plot(test$Xt, test$Yt, type="b", col="black", ylim=c(120,250))
points(test$Xt, fore.koyck$forecasts,col="red")
lines(test$Xt, fore.koyck$forecasts,col="red")
points(test$Xt, fore.dlm$forecasts,col="blue")
lines(test$Xt, fore.dlm$forecasts,col="blue")
points(test$Xt, fore.dlm2$forecasts,col="orange")
lines(test$Xt, fore.dlm2$forecasts,col="orange")
points(test$Xt, fore.ardl$forecasts,col="green")
lines(test$Xt, fore.ardl$forecasts,col="green")
legend("topleft",c("aktual", "koyck","DLM 1","DLM 2", "autoregressive"), lty=1, col=c("black","red","blue","orange","green"), cex=0.8)
Materi Pengayaan / Tambahan
#MATERI PENGAYAAN/TAMBAHAN
#Mencoba dengan Data Lain (Berganda)
#Data M1 Germany
data(M1Germany)
data1 = M1Germany[1:144,]
#Mencari orde lag optimum model DLM
# Run the search over finite DLMs according to AIC values
finiteDLMauto(formula = logprice ~ interest+logm1,
data = data.frame(data1), q.min = 1, q.max = 5,
model.type = "dlm", error.type = "AIC", trace = FALSE)## q - k MASE AIC BIC GMRAE MBRAE R.Adj.Sq Ljung-Box
## 5 5 1.77163 -463.1393 -422.0566 1.43662 -1.60494 0.98836 0#model dlm berganda
model.dlmberganda = dlm(formula = logprice ~ interest + logm1,
data = data.frame(data1) , q = 5)
summary(model.dlmberganda)##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.095761 -0.028610 -0.000012 0.029496 0.102597
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.81759 0.11384 -68.669 < 2e-16 ***
## interest.t -1.75616 0.80358 -2.185 0.030707 *
## interest.1 1.38935 1.22707 1.132 0.259679
## interest.2 0.40776 1.23726 0.330 0.742273
## interest.3 1.23130 1.20752 1.020 0.309830
## interest.4 -0.08718 1.20869 -0.072 0.942616
## interest.5 3.06850 0.89380 3.433 0.000808 ***
## logm1.t 0.43219 0.20876 2.070 0.040474 *
## logm1.1 0.42190 0.19807 2.130 0.035109 *
## logm1.2 0.20943 0.12883 1.626 0.106532
## logm1.3 0.22053 0.13011 1.695 0.092567 .
## logm1.4 0.05513 0.21457 0.257 0.797633
## logm1.5 0.03042 0.19192 0.159 0.874296
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04343 on 126 degrees of freedom
## Multiple R-squared: 0.9894, Adjusted R-squared: 0.9884
## F-statistic: 977.9 on 12 and 126 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 -463.1393 -422.0566model.dlmberganda2 = dlm(formula = logprice ~ interest + logm1,
data = data.frame(data1) , q = 1)
summary(model.dlmberganda2)##
## Call:
## lm(formula = as.formula(model.formula), data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.134002 -0.044697 0.006407 0.036962 0.113063
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.77917 0.13299 -58.492 < 2e-16 ***
## interest.t -3.22103 0.94184 -3.420 0.000824 ***
## interest.1 6.52775 0.94501 6.908 1.66e-10 ***
## logm1.t 0.73918 0.08419 8.780 5.61e-15 ***
## logm1.1 0.63330 0.08429 7.513 6.55e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05443 on 138 degrees of freedom
## Multiple R-squared: 0.9832, Adjusted R-squared: 0.9828
## F-statistic: 2025 on 4 and 138 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 -419.7575 -401.9805#Mencari orde lag optimum model ARDL
ardlBoundOrders(data = data1 , formula = logprice ~ interest + logm1 )## $p
## interest logm1
## 65 0 4
##
## $q
## [1] 4
##
## $Stat.table
## q = 1 q = 2 q = 3 q = 4 q = 5 q = 6 q = 7
## p = 1 -760.1786 -757.9195 -846.8342 -975.2079 -965.7536 -958.9072 -956.7315
## p = 2 -760.0433 -759.3090 -843.6247 -971.2514 -961.7929 -955.2809 -953.4890
## p = 3 -753.7746 -753.7746 -841.2485 -970.4543 -961.4343 -953.7173 -950.0412
## p = 4 -829.8076 -832.6436 -832.6436 -971.0837 -962.1804 -955.0429 -953.4667
## p = 5 -749.4144 -753.2292 -962.9290 -962.9290 -961.7063 -954.3406 -951.7660
## p = 6 -742.2103 -742.9945 -891.6195 -952.3771 -952.3771 -952.2461 -950.1105
## p = 7 -728.9374 -733.0286 -851.2943 -945.7445 -944.6879 -944.6879 -949.3720
## p = 8 -747.9277 -746.2948 -812.4289 -937.9446 -938.9491 -937.3393 -937.3393
## p = 9 -722.6891 -724.5786 -863.2734 -928.9215 -927.2914 -926.8716 -936.6432
## p = 10 -714.8175 -714.5658 -816.3319 -918.5218 -918.6350 -916.9076 -921.1246
## p = 11 -703.1807 -705.3383 -794.0772 -909.6457 -908.8225 -906.9542 -912.9605
## p = 12 -716.7111 -714.7403 -774.0127 -910.0315 -910.6834 -908.7146 -909.6612
## p = 13 -697.7175 -698.1931 -793.4602 -895.5927 -894.9273 -893.5995 -897.7589
## p = 14 -686.5600 -685.7967 -766.5292 -886.0709 -885.4341 -885.2283 -890.1638
## p = 15 -676.7280 -678.3689 -753.2854 -875.6392 -874.1257 -874.3117 -879.2727
## q = 8 q = 9 q = 10 q = 11 q = 12 q = 13 q = 14
## p = 1 -954.3375 -946.6293 -936.5328 -927.7728 -920.6435 -917.5463 -918.3110
## p = 2 -951.1470 -943.9360 -933.7047 -924.7949 -917.5334 -913.6213 -914.4063
## p = 3 -948.4683 -941.1039 -930.8509 -922.0563 -914.5728 -910.5351 -913.4996
## p = 4 -948.2330 -941.8238 -931.5689 -923.2663 -916.2063 -911.6023 -913.9345
## p = 5 -947.5994 -939.3767 -929.0155 -920.4475 -913.5968 -909.0781 -911.6312
## p = 6 -945.5758 -937.4076 -927.2439 -919.3949 -911.9537 -907.7394 -910.2890
## p = 7 -945.5181 -937.1826 -926.9640 -917.9619 -910.2774 -905.9449 -907.8712
## p = 8 -941.9617 -933.5959 -923.3691 -914.6251 -907.0608 -902.2187 -903.9255
## p = 9 -936.6432 -935.7172 -925.2881 -917.0877 -911.6973 -903.9027 -904.6405
## p = 10 -926.6891 -926.6891 -924.6986 -917.0904 -911.4197 -903.4313 -903.0612
## p = 11 -917.9145 -918.2328 -918.2328 -919.2867 -913.3674 -904.8733 -903.6541
## p = 12 -916.1321 -914.4362 -914.4610 -914.4610 -912.5159 -904.2394 -901.6216
## p = 13 -905.4744 -903.7559 -902.4406 -902.2530 -902.2530 -902.9434 -901.2363
## p = 14 -896.2370 -896.2620 -894.2896 -897.5711 -899.1407 -899.1407 -902.2350
## p = 15 -884.5637 -886.8221 -884.9832 -890.5665 -893.2335 -891.6220 -891.6220
## q = 15
## p = 1 -908.0863
## p = 2 -904.1665
## p = 3 -903.3006
## p = 4 -903.9256
## p = 5 -901.6220
## p = 6 -900.1824
## p = 7 -897.9867
## p = 8 -894.1031
## p = 9 -894.7387
## p = 10 -893.6199
## p = 11 -893.6060
## p = 12 -892.4805
## p = 13 -892.5115
## p = 14 -893.6214
## p = 15 -891.3741
##
## $min.Stat
## [1] -977.2745
##
## $Stat.p
## interest logm1 Stat
## 65 0 4 -977.2745
## 1 0 0 -976.5191
## 2 1 0 -976.2558
## 17 0 1 -975.9606
## 66 1 4 -975.6027
## 18 1 1 -975.2079
## 49 0 3 -974.4859
## 3 2 0 -974.4275
## 33 0 2 -974.0166
## 50 1 3 -973.7500
## 67 2 4 -973.6028
## 34 1 2 -973.2324
## 19 2 1 -973.2188
## 68 3 4 -972.5992
## 4 3 0 -972.4875
## 51 2 3 -971.7743
## 20 3 1 -971.3872
## 35 2 2 -971.2514
## 69 4 4 -971.0837
## 5 4 0 -970.5114
## 52 3 3 -970.4543
## 81 0 5 -969.9284
## 53 4 3 -969.5311
## 21 4 1 -969.4756
## 36 3 2 -969.3907
## 82 1 5 -968.6783
## 37 4 2 -967.4756
## 83 2 5 -966.8835
## 84 3 5 -965.6393
## 85 4 5 -963.9662
## 86 5 5 -962.9290
## 70 5 4 -961.2547
## 54 5 3 -960.9580
## 97 0 6 -960.7402
## 6 5 0 -960.6858
## 22 5 1 -959.8419
## 98 1 6 -959.6604
## 38 5 2 -957.8547
## 99 2 6 -957.7528
## 100 3 6 -956.7875
## 101 4 6 -955.2416
## 71 6 4 -954.8953
## 87 6 5 -954.6855
## 102 5 6 -954.3662
## 103 6 6 -954.0973
## 7 6 0 -954.0615
## 113 0 7 -953.9160
## 55 6 3 -953.2860
## 23 6 1 -953.1080
## 114 1 7 -952.6540
## 39 6 2 -951.1356
## 115 2 7 -950.6562
## 116 3 7 -949.6038
## 88 7 5 -949.2090
## 72 7 4 -948.5194
## 117 4 7 -947.7999
## 104 7 6 -947.7424
## 56 7 3 -947.6915
## 8 7 0 -947.5092
## 120 7 7 -947.3660
## 24 7 1 -947.0094
## 118 5 7 -946.9631
## 119 6 7 -946.8080
## 40 7 2 -945.0123
## 129 0 8 -943.9035
## 130 1 8 -942.6627
## 131 2 8 -940.6818
## 145 0 9 -940.0114
## 132 3 8 -939.6913
## 89 8 5 -939.1878
## 73 8 4 -938.5330
## 146 1 9 -938.2680
## 133 4 8 -937.8368
## 105 8 6 -937.6834
## 57 8 3 -937.6370
## 9 8 0 -937.5705
## 121 8 7 -937.5351
## 136 7 8 -937.3948
## 25 8 1 -937.0088
## 134 5 8 -936.9393
## 135 6 8 -936.8904
## 147 2 9 -936.3875
## 148 3 9 -936.3159
## 137 8 8 -935.5389
## 41 8 2 -935.0088
## 149 4 9 -934.3458
## 150 5 9 -934.1858
## 152 7 9 -934.0733
## 151 6 9 -932.9538
## 153 8 9 -932.3338
## 154 9 9 -930.9065
## 161 0 10 -929.8056
## 90 9 5 -929.2731
## 74 9 4 -928.5254
## 162 1 10 -928.1257
## 10 9 0 -927.9853
## 58 9 3 -927.9744
## 122 9 7 -927.9061
## 106 9 6 -927.6344
## 26 9 1 -927.4482
## 164 3 10 -926.5271
## 163 2 10 -926.2965
## 138 9 8 -926.1307
## 42 9 2 -925.4484
## 165 4 10 -924.5287
## 168 7 10 -924.2716
## 166 5 10 -924.0521
## 167 6 10 -922.7596
## 169 8 10 -922.5928
## 155 10 9 -921.2169
## 170 9 10 -921.1777
## 177 0 11 -920.2608
## 171 10 10 -920.0124
## 91 10 5 -919.0182
## 178 1 11 -918.7342
## 75 10 4 -918.4135
## 11 10 0 -917.8597
## 59 10 3 -917.7711
## 123 10 7 -917.6569
## 107 10 6 -917.3861
## 27 10 1 -917.2925
## 179 2 11 -916.9417
## 180 3 11 -916.8682
## 193 0 12 -916.1477
## 139 10 8 -915.9643
## 92 11 5 -915.3201
## 43 10 2 -915.2941
## 156 11 9 -915.0851
## 181 4 11 -914.8854
## 194 1 12 -914.4423
## 124 11 7 -914.3141
## 184 7 11 -914.1880
## 76 11 4 -914.1395
## 182 5 11 -914.0440
## 108 11 6 -913.4052
## 140 11 8 -913.3026
## 195 2 12 -913.1680
## 172 11 10 -913.0914
## 60 11 3 -912.7714
## 183 6 11 -912.7548
## 196 3 12 -912.5820
## 185 8 11 -912.5636
## 12 11 0 -912.2009
## 28 11 1 -912.0389
## 186 9 11 -911.1737
## 157 12 9 -911.1513
## 188 11 11 -911.1189
## 93 12 5 -910.7693
## 198 5 12 -910.7434
## 197 4 12 -910.6154
## 125 12 7 -910.5873
## 141 12 8 -910.0719
## 44 11 2 -910.0439
## 187 10 11 -909.9928
## 200 7 12 -909.4197
## 173 12 10 -909.2473
## 77 12 4 -909.1913
## 109 12 6 -908.7753
## 199 6 12 -908.7635
## 201 8 12 -908.1609
## 61 12 3 -908.0357
## 29 12 1 -907.8613
## 209 0 13 -907.6473
## 13 12 0 -907.6158
## 205 12 12 -907.5931
## 204 11 12 -907.5525
## 202 9 12 -907.3633
## 189 12 11 -907.3200
## 210 1 13 -906.1005
## 45 12 2 -905.9070
## 203 10 12 -905.7653
## 211 2 13 -904.7293
## 212 3 13 -903.9077
## 214 5 13 -902.0824
## 158 13 9 -901.9574
## 213 4 13 -901.9144
## 94 13 5 -901.6338
## 126 13 7 -901.3766
## 142 13 8 -900.9367
## 216 7 13 -900.5676
## 225 0 14 -900.5066
## 174 13 10 -900.1413
## 215 6 13 -900.1102
## 78 13 4 -900.0282
## 110 13 6 -899.6703
## 226 1 14 -899.0967
## 217 8 13 -899.0866
## 62 13 3 -898.8589
## 30 13 1 -898.7940
## 190 13 11 -898.4409
## 221 12 13 -898.4110
## 220 11 13 -898.3058
## 218 9 13 -898.2568
## 14 13 0 -898.2039
## 206 13 12 -897.9014
## 227 2 14 -897.3889
## 46 13 2 -896.8637
## 219 10 13 -896.6244
## 222 13 13 -896.4458
## 228 3 14 -896.2512
## 230 5 14 -895.1320
## 95 14 5 -894.6021
## 229 4 14 -894.3023
## 159 14 9 -894.2497
## 127 14 7 -893.9663
## 143 14 8 -893.6932
## 231 6 14 -893.4037
## 79 14 4 -893.1343
## 232 7 14 -893.1064
## 111 14 6 -892.6253
## 175 14 10 -892.5085
## 63 14 3 -891.9131
## 191 14 11 -891.1895
## 233 8 14 -891.1877
## 234 9 14 -891.1729
## 31 14 1 -890.7573
## 236 11 14 -890.5576
## 241 0 15 -890.5500
## 15 14 0 -890.3449
## 237 12 14 -890.1854
## 235 10 14 -889.8957
## 207 14 12 -889.7107
## 242 1 15 -889.0419
## 47 14 2 -888.9410
## 238 13 14 -888.1867
## 223 14 13 -887.7488
## 239 14 14 -887.6659
## 243 2 15 -887.3088
## 244 3 15 -886.0691
## 246 5 15 -884.7479
## 96 15 5 -884.2869
## 245 4 15 -884.1417
## 160 15 9 -883.9364
## 128 15 7 -883.6409
## 144 15 8 -883.4503
## 247 6 15 -883.0158
## 80 15 4 -882.8148
## 248 7 15 -882.7881
## 112 15 6 -882.3106
## 176 15 10 -882.2093
## 64 15 3 -881.6497
## 253 12 15 -881.4274
## 252 11 15 -881.3077
## 250 9 15 -881.1831
## 192 15 11 -880.9028
## 249 8 15 -880.8964
## 32 15 1 -880.5983
## 251 10 15 -880.2736
## 16 15 0 -880.2468
## 254 13 15 -879.4467
## 208 15 12 -879.4364
## 255 14 15 -879.2846
## 48 15 2 -878.8432
## 224 15 13 -877.4985
## 240 15 14 -877.4570model.ardlDlmberganda = ardlDlm(formula = logprice ~ interest + logm1,
data = data.frame(data1) , p = 4 , q = 4)
summary(model.ardlDlmberganda)##
## Time series regression with "ts" data:
## Start = 5, End = 144
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0290527 -0.0075965 0.0005726 0.0072745 0.0304486
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0145022 0.1822785 0.080 0.93671
## interest.t 0.0067985 0.2135315 0.032 0.97465
## interest.1 0.6093502 0.3240545 1.880 0.06238 .
## interest.2 0.0798544 0.3221168 0.248 0.80461
## interest.3 -0.3638172 0.3238873 -1.123 0.26347
## interest.4 0.2084240 0.2447331 0.852 0.39604
## logm1.t 0.0828689 0.0457486 1.811 0.07248 .
## logm1.1 -0.0092841 0.0399079 -0.233 0.81642
## logm1.2 -0.1166129 0.0390732 -2.984 0.00342 **
## logm1.3 0.0007016 0.0389297 0.018 0.98565
## logm1.4 0.0447857 0.0425474 1.053 0.29455
## logprice.1 0.3274245 0.0651574 5.025 1.7e-06 ***
## logprice.2 0.1323801 0.0684485 1.934 0.05537 .
## logprice.3 -0.1448245 0.0674268 -2.148 0.03365 *
## logprice.4 0.6730871 0.0636443 10.576 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01132 on 125 degrees of freedom
## Multiple R-squared: 0.9993, Adjusted R-squared: 0.9992
## F-statistic: 1.273e+04 on 14 and 125 DF, p-value: < 2.2e-16#model p interest 0 p logm1 4
rem.p = list(interest = c(1,2,3,4))
remove = list(p = rem.p)
model.ardlDlmberganda2 = ardlDlm(formula = logprice ~ interest + logm1,
data = data.frame(data1) , p = 4 , q = 4 ,
remove = remove)
summary(model.ardlDlmberganda2)##
## Time series regression with "ts" data:
## Start = 5, End = 144
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0290369 -0.0083445 0.0009024 0.0079199 0.0303652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.174838 0.133708 1.308 0.19333
## interest.t 0.448826 0.098736 4.546 1.24e-05 ***
## logm1.t 0.056659 0.043836 1.293 0.19849
## logm1.1 -0.017025 0.039159 -0.435 0.66446
## logm1.2 -0.118413 0.037399 -3.166 0.00193 **
## logm1.3 -0.006454 0.038112 -0.169 0.86580
## logm1.4 0.060220 0.040337 1.493 0.13789
## logprice.1 0.319059 0.062107 5.137 1.00e-06 ***
## logprice.2 0.111794 0.066101 1.691 0.09320 .
## logprice.3 -0.122129 0.065114 -1.876 0.06297 .
## logprice.4 0.699061 0.062611 11.165 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01149 on 129 degrees of freedom
## Multiple R-squared: 0.9993, Adjusted R-squared: 0.9992
## F-statistic: 1.73e+04 on 10 and 129 DF, p-value: < 2.2e-16#proses selanjutnya sama dengan praktikum dengan peubah tunggal