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library(WDI)
enflasyon <- WDI(country=c("TR", "CN","CL"), indicator=c("FP.CPI.TOTL.ZG"), start=1960, end=2020)
names(enflasyon) <- c("iso2c", "Ulke", "enflasyonorani", "Sene")
head(enflasyon)
## iso2c Ulke enflasyonorani Sene
## 1 CL Chile 3.045491 2020
## 2 CL Chile 2.557545 2019
## 3 CL Chile 2.434890 2018
## 4 CL Chile 2.182718 2017
## 5 CL Chile 3.786194 2016
## 6 CL Chile 4.348774 2015
library(ggplot2)
ggplot(enflasyon, aes(Sene, enflasyonorani, color=Ulke, linetype=Ulke)) + geom_line()
## Warning: Removed 38 row(s) containing missing values (geom_path).
TR <- cbind(enflasyon$enflasyonorani[enflasyon$Ulke == "Turkey"], enflasyon$Sene[enflasyon$Ulke == "Turkey"])
TR <- TR[order(TR[,2]),]
TR
## [,1] [,2]
## [1,] 5.664740 1960
## [2,] 3.172857 1961
## [3,] 3.888320 1962
## [4,] 6.362707 1963
## [5,] 1.119638 1964
## [6,] 4.555534 1965
## [7,] 8.471996 1966
## [8,] 13.974893 1967
## [9,] 6.046240 1968
## [10,] 4.924194 1969
## [11,] 7.923952 1970
## [12,] 19.011409 1971
## [13,] 15.416456 1972
## [14,] 13.938165 1973
## [15,] 23.898162 1974
## [16,] 21.227355 1975
## [17,] 17.455689 1976
## [18,] 25.985338 1977
## [19,] 61.897044 1978
## [20,] 63.543108 1979
## [21,] 94.260860 1980
## [22,] 37.614783 1981
## [23,] 29.137515 1982
## [24,] 31.390271 1983
## [25,] 48.392323 1984
## [26,] 44.961730 1985
## [27,] 34.610076 1986
## [28,] 38.855843 1987
## [29,] 68.809643 1988
## [30,] 63.272552 1989
## [31,] 60.303869 1990
## [32,] 65.978568 1991
## [33,] 70.076104 1992
## [34,] 66.093843 1993
## [35,] 105.214986 1994
## [36,] 89.113317 1995
## [37,] 80.412151 1996
## [38,] 85.669362 1997
## [39,] 84.641343 1998
## [40,] 64.867488 1999
## [41,] 54.915371 2000
## [42,] 54.400189 2001
## [43,] 44.964121 2002
## [44,] 21.602438 2003
## [45,] 8.598262 2004
## [46,] 8.179160 2005
## [47,] 9.597242 2006
## [48,] 8.756181 2007
## [49,] 10.444128 2008
## [50,] 6.250977 2009
## [51,] 8.566444 2010
## [52,] 6.471880 2011
## [53,] 8.891570 2012
## [54,] 7.493090 2013
## [55,] 8.854573 2014
## [56,] 7.670854 2015
## [57,] 7.775134 2016
## [58,] 11.144311 2017
## [59,] 16.332464 2018
## [60,] 15.176822 2019
## [61,] 12.278957 2020
TR <- ts(TR[,1], start=min(enflasyon$Sene), end=max(enflasyon$Sene))
plot(TR, ylab="Enflayon Orani", xlab="Sene")
acf(TR)
pacf(TR)
plot(TR, ylab="Enflayon Orani", xlab="Sene")
library(dynlm)
## Loading required package: zoo
##
## 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
## -49.776 -4.939 -1.505 2.748 42.835
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.69314 2.55449 1.446 0.154
## L(TR, 1) 0.88793 0.05951 14.921 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.2 on 58 degrees of freedom
## Multiple R-squared: 0.7933, Adjusted R-squared: 0.7898
## F-statistic: 222.6 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
## -52.555 -7.680 -4.177 5.737 42.682
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.01786 3.41120 2.057 0.0442 *
## L(TR, 2) 0.79221 0.07888 10.043 3.21e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.45 on 57 degrees of freedom
## Multiple R-squared: 0.6389, Adjusted R-squared: 0.6326
## F-statistic: 100.9 on 1 and 57 DF, p-value: 3.212e-14
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
## -45.333 -10.116 -5.289 6.610 65.824
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.05948 3.99142 2.520 0.0146 *
## L(TR, 3) 0.70723 0.09162 7.719 2.25e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.22 on 56 degrees of freedom
## Multiple R-squared: 0.5155, Adjusted R-squared: 0.5068
## F-statistic: 59.58 on 1 and 56 DF, p-value: 2.247e-10
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
## -46.627 -5.646 -1.162 4.398 40.828
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.568378 4.017490 1.635 0.110
## L(TR, c(1:10))1 0.848343 0.157606 5.383 3.47e-06 ***
## L(TR, c(1:10))2 -0.009341 0.206809 -0.045 0.964
## L(TR, c(1:10))3 -0.052168 0.205972 -0.253 0.801
## L(TR, c(1:10))4 0.249136 0.203930 1.222 0.229
## L(TR, c(1:10))5 -0.140615 0.206982 -0.679 0.501
## L(TR, c(1:10))6 0.115712 0.206704 0.560 0.579
## L(TR, c(1:10))7 -0.195278 0.203437 -0.960 0.343
## L(TR, c(1:10))8 0.068556 0.205668 0.333 0.741
## L(TR, c(1:10))9 0.019648 0.205821 0.095 0.924
## L(TR, c(1:10))10 -0.080839 0.156152 -0.518 0.608
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.99 on 40 degrees of freedom
## Multiple R-squared: 0.7837, Adjusted R-squared: 0.7296
## F-statistic: 14.49 on 10 and 40 DF, p-value: 2.121e-10
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
## -8.4971 -3.7901 0.3893 3.2400 12.5618
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12.2802 0.3629 -33.84 <2e-16 ***
## x -0.9057 0.0542 -16.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.642 on 198 degrees of freedom
## Multiple R-squared: 0.5851, Adjusted R-squared: 0.583
## F-statistic: 279.2 on 1 and 198 DF, p-value: < 2.2e-16
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
## -3.08935 -0.69304 0.01772 0.62137 2.84283
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.11201 0.07315 -1.531 0.127
## d(x) -0.06684 0.08494 -0.787 0.432
##
## Residual standard error: 1.026 on 197 degrees of freedom
## Multiple R-squared: 0.003133, Adjusted R-squared: -0.001927
## F-statistic: 0.6191 on 1 and 197 DF, p-value: 0.4323
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
adf.test(x)
##
## Augmented Dickey-Fuller Test
##
## data: x
## Dickey-Fuller = -1.7185, Lag order = 5, p-value = 0.694
## alternative hypothesis: stationary
adf.test(y)
##
## Augmented Dickey-Fuller Test
##
## data: y
## Dickey-Fuller = -2.0785, Lag order = 5, p-value = 0.5432
## alternative hypothesis: stationary
adf.test(TR)
##
## Augmented Dickey-Fuller Test
##
## data: TR
## Dickey-Fuller = -1.3924, Lag order = 3, p-value = 0.8206
## alternative hypothesis: stationary
kpss.test(TR)
## Warning in kpss.test(TR): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: TR
## KPSS Level = 0.32137, Truncation lag parameter = 3, p-value = 0.1
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 = -5.1882, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
library(WDI)
nufus <- WDI(country=c("CN", "AF","SY"), indicator=c("SP.POP.GROW"), start=1960, end=2020)
names(nufus) <- c("iso2c", "Ulke", "NufusBuyumeOrani", "Sene")
head(nufus)
## iso2c Ulke NufusBuyumeOrani Sene
## 1 AF Afghanistan 2.303812 2020
## 2 AF Afghanistan 2.313073 2019
## 3 AF Afghanistan 2.384309 2018
## 4 AF Afghanistan 2.547833 2017
## 5 AF Afghanistan 2.778035 2016
## 6 AF Afghanistan 3.077054 2015
library(ggplot2)
ggplot(nufus, aes(Sene, NufusBuyumeOrani, color=Ulke, linetype=Ulke)) + geom_line()
## Warning: Removed 3 row(s) containing missing values (geom_path).
CN <- cbind(nufus$NufusBuyumeOrani[nufus$Ulke == "China"], nufus$Sene[nufus$Ulke == "China"])
CN <- CN[order(CN[,2]),]
CN
## [,1] [,2]
## [1,] NA 1960
## [2,] -1.0155278 1961
## [3,] 0.8204555 1962
## [4,] 2.4576474 1963
## [5,] 2.3206830 1964
## [6,] 2.3813681 1965
## [7,] 2.7873318 1966
## [8,] 2.5706976 1967
## [9,] 2.6109026 1968
## [10,] 2.7400021 1969
## [11,] 2.7616756 1970
## [12,] 2.7469155 1971
## [13,] 2.4573569 1972
## [14,] 2.2833954 1973
## [15,] 2.0659550 1974
## [16,] 1.7663918 1975
## [17,] 1.5473380 1976
## [18,] 1.3627795 1977
## [19,] 1.3381823 1978
## [20,] 1.3339280 1979
## [21,] 1.2542211 1980
## [22,] 1.2809523 1981
## [23,] 1.4726748 1982
## [24,] 1.4449497 1983
## [25,] 1.3120688 1984
## [26,] 1.3616991 1985
## [27,] 1.4873989 1986
## [28,] 1.6036051 1987
## [29,] 1.6100711 1988
## [30,] 1.5331700 1989
## [31,] 1.4673032 1990
## [32,] 1.3644340 1991
## [33,] 1.2255362 1992
## [34,] 1.1496194 1993
## [35,] 1.1302606 1994
## [36,] 1.0865092 1995
## [37,] 1.0481415 1996
## [38,] 1.0234500 1997
## [39,] 0.9595504 1998
## [40,] 0.8658514 1999
## [41,] 0.7879566 2000
## [42,] 0.7263806 2001
## [43,] 0.6699996 2002
## [44,] 0.6228609 2003
## [45,] 0.5939328 2004
## [46,] 0.5881250 2005
## [47,] 0.5583744 2006
## [48,] 0.5222719 2007
## [49,] 0.5123869 2008
## [50,] 0.4973814 2009
## [51,] 0.4829597 2010
## [52,] 0.5464576 2011
## [53,] 0.6783455 2012
## [54,] 0.6660730 2013
## [55,] 0.6303264 2014
## [56,] 0.5814561 2015
## [57,] 0.5730509 2016
## [58,] 0.6052450 2017
## [59,] 0.4676721 2018
## [60,] 0.3547409 2019
## [61,] 0.2259476 2020
CN <- ts(CN[,1], start=min(nufus$Sene), end=max(nufus$Sene))
plot(CN, ylab="Nufus Buyume Orani", xlab="Sene")
acf(TR)
pacf(TR)
library(dynlm)
Ilkgecikme <- dynlm(CN ~ L(CN, 1))
summary(Ilkgecikme)
##
## Time series regression with "ts" data:
## Start = 1962, End = 2020
##
## Call:
## dynlm(formula = CN ~ L(CN, 1))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29126 -0.15387 -0.08725 0.00153 1.54702
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.21753 0.08092 2.688 0.0094 **
## L(CN, 1) 0.84478 0.05451 15.498 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3247 on 57 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.8082, Adjusted R-squared: 0.8048
## F-statistic: 240.2 on 1 and 57 DF, p-value: < 2.2e-16
Ikincigecikme <- dynlm(CN ~ L(CN, 2))
summary(Ikincigecikme)
##
## Time series regression with "ts" data:
## Start = 1963, End = 2020
##
## Call:
## dynlm(formula = CN ~ L(CN, 2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49134 -0.25942 -0.12898 0.08636 2.79305
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.38536 0.12559 3.068 0.00331 **
## L(CN, 2) 0.70974 0.08393 8.457 1.38e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4939 on 56 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.5608, Adjusted R-squared: 0.553
## F-statistic: 71.52 on 1 and 56 DF, p-value: 1.378e-11
Ucuncugecikme <- dynlm(CN ~ L(CN, 3))
summary(Ucuncugecikme)
##
## Time series regression with "ts" data:
## Start = 1964, End = 2020
##
## Call:
## dynlm(formula = CN ~ L(CN, 3))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5790 -0.2733 -0.1402 0.1115 2.6177
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.39348 0.13073 3.010 0.00394 **
## L(CN, 3) 0.67991 0.08668 7.844 1.56e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5051 on 55 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.528, Adjusted R-squared: 0.5195
## F-statistic: 61.53 on 1 and 55 DF, p-value: 1.565e-10
AR10 <- dynlm(CN ~ L(CN, c(1:10)))
summary(AR10)
##
## Time series regression with "ts" data:
## Start = 1971, End = 2020
##
## Call:
## dynlm(formula = CN ~ L(CN, c(1:10)))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.153799 -0.026897 -0.003844 0.028790 0.151033
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0064475 0.0229402 0.281 0.780152
## L(CN, c(1:10))zoo(coredata(x), tt).1 1.7751671 0.1673650 10.607 4.7e-13
## L(CN, c(1:10))zoo(coredata(x), tt).2 -1.2474057 0.3328002 -3.748 0.000577
## L(CN, c(1:10))zoo(coredata(x), tt).3 0.8773870 0.3764456 2.331 0.025032
## L(CN, c(1:10))zoo(coredata(x), tt).4 -0.7368314 0.3704370 -1.989 0.053739
## L(CN, c(1:10))zoo(coredata(x), tt).5 0.5726644 0.3403353 1.683 0.100434
## L(CN, c(1:10))zoo(coredata(x), tt).6 -0.7134078 0.2835037 -2.516 0.016081
## L(CN, c(1:10))zoo(coredata(x), tt).7 0.5997102 0.2280475 2.630 0.012166
## L(CN, c(1:10))zoo(coredata(x), tt).8 -0.2021611 0.1831883 -1.104 0.276543
## L(CN, c(1:10))zoo(coredata(x), tt).9 0.0456964 0.1381970 0.331 0.742670
## L(CN, c(1:10))zoo(coredata(x), tt).10 -0.0004422 0.0541377 -0.008 0.993525
##
## (Intercept)
## L(CN, c(1:10))zoo(coredata(x), tt).1 ***
## L(CN, c(1:10))zoo(coredata(x), tt).2 ***
## L(CN, c(1:10))zoo(coredata(x), tt).3 *
## L(CN, c(1:10))zoo(coredata(x), tt).4 .
## L(CN, c(1:10))zoo(coredata(x), tt).5
## L(CN, c(1:10))zoo(coredata(x), tt).6 *
## L(CN, c(1:10))zoo(coredata(x), tt).7 *
## L(CN, c(1:10))zoo(coredata(x), tt).8
## L(CN, c(1:10))zoo(coredata(x), tt).9
## L(CN, c(1:10))zoo(coredata(x), tt).10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06345 on 39 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9899, Adjusted R-squared: 0.9873
## F-statistic: 383.1 on 10 and 39 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
## -6.8331 -2.9055 -0.5775 2.2306 10.1425
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.16623 0.29516 10.73 <2e-16 ***
## x -0.52251 0.04787 -10.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.892 on 198 degrees of freedom
## Multiple R-squared: 0.3757, Adjusted R-squared: 0.3725
## F-statistic: 119.1 on 1 and 198 DF, p-value: < 2.2e-16
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
## -2.48629 -0.65269 0.03276 0.69392 2.81807
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.03842 0.07160 0.537 0.592
## d(x) -0.06295 0.07157 -0.880 0.380
##
## Residual standard error: 1.009 on 197 degrees of freedom
## Multiple R-squared: 0.003911, Adjusted R-squared: -0.001145
## F-statistic: 0.7736 on 1 and 197 DF, p-value: 0.3802
library(tseries)
adf.test(x)
##
## Augmented Dickey-Fuller Test
##
## data: x
## Dickey-Fuller = -2.4068, Lag order = 5, p-value = 0.4057
## alternative hypothesis: stationary
adf.test(y)
##
## Augmented Dickey-Fuller Test
##
## data: y
## Dickey-Fuller = -2.2666, Lag order = 5, p-value = 0.4645
## alternative hypothesis: stationary
adf.test(TR)
##
## Augmented Dickey-Fuller Test
##
## data: TR
## Dickey-Fuller = -1.3924, Lag order = 3, p-value = 0.8206
## alternative hypothesis: stationary
kpss.test(TR)
## Warning in kpss.test(TR): p-value greater than printed p-value
##
## KPSS Test for Level Stationarity
##
## data: TR
## KPSS Level = 0.32137, Truncation lag parameter = 3, p-value = 0.1
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 = -5.3435, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary