library(WDI)
## Warning: package 'WDI' was built under R version 4.1.2
gsyh <- WDI(country=c("US", "TR","JP"), indicator=c("NY.GDP.PCAP.CD"), start=1960, end=2020)
names(gsyh) <- c("iso2c", "Ülke", "KisiBasiGSYH", "Sene")
head(gsyh)
## iso2c Ülke KisiBasiGSYH Sene
## 1 JP Japan 40193.25 2020
## 2 JP Japan 40777.61 2019
## 3 JP Japan 39808.17 2018
## 4 JP Japan 38891.09 2017
## 5 JP Japan 39400.74 2016
## 6 JP Japan 34960.64 2015
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.1.2
ggplot(gsyh, aes(Sene, KisiBasiGSYH, color=Ülke, linetype=Ülke)) + geom_line()
TR <- cbind(gsyh$KisiBasiGSYH[gsyh$Ülke == "Turkey"], gsyh$Sene[gsyh$Ülke == "Turkey"])
TR <- TR[order(TR[,2]),]
TR
## [,1] [,2]
## [1,] 509.4240 1960
## [2,] 283.8283 1961
## [3,] 309.4466 1962
## [4,] 350.6630 1963
## [5,] 369.5835 1964
## [6,] 386.3581 1965
## [7,] 444.5495 1966
## [8,] 481.6937 1967
## [9,] 526.2135 1968
## [10,] 571.6178 1969
## [11,] 489.9304 1970
## [12,] 455.1049 1971
## [13,] 558.4209 1972
## [14,] 686.4901 1973
## [15,] 927.7992 1974
## [16,] 1136.3756 1975
## [17,] 1275.9566 1976
## [18,] 1427.3718 1977
## [19,] 1549.6444 1978
## [20,] 2079.2203 1979
## [21,] 1564.2472 1980
## [22,] 1579.0738 1981
## [23,] 1402.4064 1982
## [24,] 1310.2557 1983
## [25,] 1246.8245 1984
## [26,] 1368.4017 1985
## [27,] 1510.6763 1986
## [28,] 1705.8944 1987
## [29,] 1745.3649 1988
## [30,] 2021.8595 1989
## [31,] 2794.3505 1990
## [32,] 2735.7076 1991
## [33,] 2842.3700 1992
## [34,] 3180.1876 1993
## [35,] 2270.3373 1994
## [36,] 2897.8666 1995
## [37,] 3053.9472 1996
## [38,] 3144.3857 1997
## [39,] 4499.7375 1998
## [40,] 4116.1706 1999
## [41,] 4337.4780 2000
## [42,] 3142.9210 2001
## [43,] 3687.9561 2002
## [44,] 4760.1040 2003
## [45,] 6101.6321 2004
## [46,] 7456.2961 2005
## [47,] 8101.8569 2006
## [48,] 9791.8825 2007
## [49,] 10941.1721 2008
## [50,] 9103.4741 2009
## [51,] 10742.7750 2010
## [52,] 11420.5555 2011
## [53,] 11795.6335 2012
## [54,] 12614.7816 2013
## [55,] 12157.9904 2014
## [56,] 11006.2795 2015
## [57,] 10894.6034 2016
## [58,] 10589.6677 2017
## [59,] 9454.3484 2018
## [60,] 9121.5152 2019
## [61,] 8536.4333 2020
TR <- ts(TR[,1], start=min(gsyh$Sene), end=max(gsyh$Sene))
plot(TR, ylab="Kişi başı GSYH", xlab="Sene")
acf(TR)
pacf(TR)
plot(TR, ylab="Kişi başı GSYH", xlab="Sene")
library(dynlm)
## Warning: package 'dynlm' was built under R version 4.1.2
## Zorunlu paket yükleniyor: zoo
## Warning: package 'zoo' was built under R version 4.1.2
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
Ilkgecikme <- dynlm(TR ~ L(TR, 1))
summary(Ilkgecikme)
##
## Time series regression with "ts" data:
## Start = 1961, End = 2020
##
## Call:
## dynlm(formula = TR ~ L(TR, 1))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1903.5 -229.7 -58.7 223.2 1596.5
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 172.73437 122.19650 1.414 0.163
## L(TR, 1) 0.99022 0.02182 45.383 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 665.2 on 58 degrees of freedom
## Multiple R-squared: 0.9726, Adjusted R-squared: 0.9721
## F-statistic: 2060 on 1 and 58 DF, p-value: < 2.2e-16
Ikincigecikme <- dynlm(TR ~ L(TR, 2))
summary(Ikincigecikme)
##
## Time series regression with "ts" data:
## Start = 1962, End = 2020
##
## Call:
## dynlm(formula = TR ~ L(TR, 2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1719.8 -492.9 -260.8 275.6 2637.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 363.85199 180.93530 2.011 0.0491 *
## L(TR, 2) 0.97998 0.03277 29.905 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 984.6 on 57 degrees of freedom
## Multiple R-squared: 0.9401, Adjusted R-squared: 0.939
## F-statistic: 894.3 on 1 and 57 DF, p-value: < 2.2e-16
Ucuncugecikme <- dynlm(TR ~ L(TR, 3))
summary(Ucuncugecikme)
##
## Time series regression with "ts" data:
## Start = 1963, End = 2020
##
## Call:
## dynlm(formula = TR ~ L(TR, 3))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2281.4 -587.7 -239.6 450.4 3316.5
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 571.80137 234.78995 2.435 0.0181 *
## L(TR, 3) 0.96755 0.04325 22.371 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1277 on 56 degrees of freedom
## Multiple R-squared: 0.8994, Adjusted R-squared: 0.8976
## F-statistic: 500.4 on 1 and 56 DF, p-value: < 2.2e-16
AR10 <- dynlm(TR ~ L(TR, c(1:10)))
summary(AR10)
##
## Time series regression with "ts" data:
## Start = 1970, End = 2020
##
## Call:
## dynlm(formula = TR ~ L(TR, c(1:10)))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2124.75 -277.50 -56.73 337.91 1423.78
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 236.40345 158.63707 1.490 0.1440
## L(TR, c(1:10))1 1.03427 0.15747 6.568 7.53e-08 ***
## L(TR, c(1:10))2 0.06830 0.22724 0.301 0.7653
## L(TR, c(1:10))3 0.12906 0.22957 0.562 0.5771
## L(TR, c(1:10))4 -0.39876 0.23226 -1.717 0.0937 .
## L(TR, c(1:10))5 0.25626 0.24058 1.065 0.2932
## L(TR, c(1:10))6 0.01197 0.24336 0.049 0.9610
## L(TR, c(1:10))7 0.02645 0.23639 0.112 0.9115
## L(TR, c(1:10))8 -0.06448 0.24204 -0.266 0.7913
## L(TR, c(1:10))9 -0.02921 0.24118 -0.121 0.9042
## L(TR, c(1:10))10 -0.11036 0.19298 -0.572 0.5706
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 725 on 40 degrees of freedom
## Multiple R-squared: 0.9734, Adjusted R-squared: 0.9668
## F-statistic: 146.7 on 10 and 40 DF, p-value: < 2.2e-16
n<-200
u <- ts(rnorm(n))
v <- ts(rnorm(n))
y <- ts(rep(0,n))
for (t in 2:n){
y[t]<- y[t-1]+u[t]
}
x <- ts(rep(0,n))
for (t in 2:n){
x[t]<- x[t-1]+v[t]
}
plot(y,type='l', ylab="y[t-1]+u[t]")
plot(x,type='l', ylab="x[t-1]+v[t]")
Spurious <- lm(y~x)
summary(Spurious)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.861 -6.643 1.312 5.031 13.735
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.94583 0.54307 -20.156 <2e-16 ***
## x 0.03003 0.08357 0.359 0.72
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.745 on 198 degrees of freedom
## Multiple R-squared: 0.0006519, Adjusted R-squared: -0.004395
## F-statistic: 0.1292 on 1 and 198 DF, p-value: 0.7197
duragan <- dynlm(d(y) ~ d(x))
summary(duragan)
##
## Time series regression with "ts" data:
## Start = 2, End = 200
##
## Call:
## dynlm(formula = d(y) ~ d(x))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5943 -0.7889 -0.0064 0.6524 3.6270
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.05484 0.07464 -0.735 0.463
## d(x) -0.05699 0.07481 -0.762 0.447
##
## Residual standard error: 1.053 on 197 degrees of freedom
## Multiple R-squared: 0.002937, Adjusted R-squared: -0.002124
## F-statistic: 0.5803 on 1 and 197 DF, p-value: 0.4471
library(tseries)
## Warning: package 'tseries' was built under R version 4.1.2
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
adf.test(x)
##
## Augmented Dickey-Fuller Test
##
## data: x
## Dickey-Fuller = -2.3057, Lag order = 5, p-value = 0.4481
## alternative hypothesis: stationary
adf.test(y)
##
## Augmented Dickey-Fuller Test
##
## data: y
## Dickey-Fuller = -1.1648, Lag order = 5, p-value = 0.9099
## alternative hypothesis: stationary
adf.test(TR)
##
## Augmented Dickey-Fuller Test
##
## data: TR
## Dickey-Fuller = -2.316, Lag order = 3, p-value = 0.447
## alternative hypothesis: stationary
kpss.test(TR)
## Warning in kpss.test(TR): p-value smaller than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: TR
## KPSS Level = 1.348, Truncation lag parameter = 3, p-value = 0.01
Deltax <- diff(x)
adf.test(Deltax)
## Warning in adf.test(Deltax): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: Deltax
## Dickey-Fuller = -5.4382, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary