R Markdown

library(WDI)
issizlik <- WDI(country=c("US", "TR","JP"), indicator=c("SL.UEM.TOTL.ZS"), start=1990, end=2020)
names(issizlik) <- c("iso2c", "Ãœlke", "oran", "Sene")
head(issizlik)
##   iso2c  Ãœlke oran Sene
## 1    JP Japan  2.8 2020
## 2    JP Japan  2.4 2019
## 3    JP Japan  2.4 2018
## 4    JP Japan  2.8 2017
## 5    JP Japan  3.1 2016
## 6    JP Japan  3.4 2015
library(ggplot2)
ggplot(issizlik, aes(Sene, oran, color=Ãœlke, linetype=Ãœlke)) + geom_line()
## Warning: Removed 3 row(s) containing missing values (geom_path).

TR <- cbind(issizlik$oran[issizlik$Ãœlke == "Turkey"], issizlik$Sene[issizlik$Ãœlke == "Turkey"])
TR <- TR[order(TR[,2]),]
TR
##        [,1] [,2]
##  [1,]    NA 1990
##  [2,]  8.21 1991
##  [3,]  8.51 1992
##  [4,]  8.96 1993
##  [5,]  8.58 1994
##  [6,]  7.64 1995
##  [7,]  6.63 1996
##  [8,]  6.84 1997
##  [9,]  6.89 1998
## [10,]  7.69 1999
## [11,]  6.50 2000
## [12,]  8.38 2001
## [13,] 10.36 2002
## [14,] 10.54 2003
## [15,] 10.84 2004
## [16,] 10.64 2005
## [17,]  8.72 2006
## [18,]  8.87 2007
## [19,]  9.71 2008
## [20,] 12.55 2009
## [21,] 10.66 2010
## [22,]  8.80 2011
## [23,]  8.15 2012
## [24,]  8.73 2013
## [25,]  9.88 2014
## [26,] 10.24 2015
## [27,] 10.84 2016
## [28,] 10.82 2017
## [29,] 10.89 2018
## [30,] 13.67 2019
## [31,] 13.11 2020
TR <- ts(TR[,1], start=min(issizlik$Sene), end=max(issizlik$Sene))
plot(TR, ylab="İssizlik Oranı", xlab="Sene")

plot(TR, ylab="İssizlik Oranı", xlab="Sene")

library(dynlm)
## Zorunlu paket yükleniyor: 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 = 1992, End = 2020
## 
## Call:
## dynlm(formula = TR ~ L(TR, 1))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.86111 -0.60707  0.07293  0.34186  2.88144 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.7522     1.2326   1.422    0.167    
## L(TR, 1)      0.8298     0.1303   6.367  8.1e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.2 on 27 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.6002, Adjusted R-squared:  0.5854 
## F-statistic: 40.53 on 1 and 27 DF,  p-value: 8.102e-07
Ikincigecikme <- dynlm(TR ~ L(TR, 2))
summary(Ikincigecikme)
## 
## Time series regression with "ts" data:
## Start = 1993, End = 2020
## 
## Call:
## dynlm(formula = TR ~ L(TR, 2))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6422 -1.5442  0.1647  0.9234  3.2123 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   4.3002     1.9560   2.198   0.0370 *
## L(TR, 2)      0.5691     0.2110   2.697   0.0121 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.702 on 26 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.2187, Adjusted R-squared:  0.1886 
## F-statistic: 7.276 on 1 and 26 DF,  p-value: 0.0121
Ucuncugecikme <- dynlm(TR ~ L(TR, 3))
summary(Ucuncugecikme)
## 
## Time series regression with "ts" data:
## Start = 1994, End = 2020
## 
## Call:
## dynlm(formula = TR ~ L(TR, 3))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8500 -1.3634 -0.3321  1.2823  3.4925 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   6.1559     2.1894   2.812  0.00945 **
## L(TR, 3)      0.3710     0.2378   1.560  0.13134   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.871 on 25 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.0887, Adjusted R-squared:  0.05225 
## F-statistic: 2.433 on 1 and 25 DF,  p-value: 0.1313
AR10 <- dynlm(TR ~ L(TR, c(1:10)))
summary(AR10)
## 
## Time series regression with "ts" data:
## Start = 2001, End = 2020
## 
## Call:
## dynlm(formula = TR ~ L(TR, c(1:10)))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.42283 -0.70275  0.07598  0.43933  1.75770 
## 
## Coefficients:
##                                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)                            4.49907    3.09631   1.453   0.1802  
## L(TR, c(1:10))zoo(coredata(x), tt).1   0.72113    0.24521   2.941   0.0165 *
## L(TR, c(1:10))zoo(coredata(x), tt).2  -0.28303    0.36321  -0.779   0.4558  
## L(TR, c(1:10))zoo(coredata(x), tt).3  -0.10595    0.37493  -0.283   0.7839  
## L(TR, c(1:10))zoo(coredata(x), tt).4   0.04635    0.37561   0.123   0.9045  
## L(TR, c(1:10))zoo(coredata(x), tt).5   0.07820    0.37650   0.208   0.8401  
## L(TR, c(1:10))zoo(coredata(x), tt).6  -0.14423    0.38149  -0.378   0.7141  
## L(TR, c(1:10))zoo(coredata(x), tt).7   0.15156    0.37705   0.402   0.6971  
## L(TR, c(1:10))zoo(coredata(x), tt).8  -0.08407    0.37528  -0.224   0.8277  
## L(TR, c(1:10))zoo(coredata(x), tt).9  -0.31279    0.37508  -0.834   0.4259  
## L(TR, c(1:10))zoo(coredata(x), tt).10  0.52954    0.27715   1.911   0.0884 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.288 on 9 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.6602, Adjusted R-squared:  0.2826 
## F-statistic: 1.748 on 10 and 9 DF,  p-value: 0.207

\[ Random-Walk-Örneği \]

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 
## -7.4844 -1.9178  0.3547  1.9113  6.1274 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.48438    0.23238 -10.691  < 2e-16 ***
## x           -0.39140    0.05843  -6.698 2.13e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.986 on 198 degrees of freedom
## Multiple R-squared:  0.1847, Adjusted R-squared:  0.1806 
## F-statistic: 44.87 on 1 and 198 DF,  p-value: 2.132e-10
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 
## -3.3225 -0.6005  0.0542  0.6307  2.6028 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.008358   0.068834   0.121    0.903
## d(x)        -0.038071   0.066761  -0.570    0.569
## 
## Residual standard error: 0.9706 on 197 degrees of freedom
## Multiple R-squared:  0.001648,   Adjusted R-squared:  -0.00342 
## F-statistic: 0.3252 on 1 and 197 DF,  p-value: 0.5692
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 = -3.4123, Lag order = 5, p-value = 0.05409
## alternative hypothesis: stationary
adf.test(y)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  y
## Dickey-Fuller = -2.5721, Lag order = 5, p-value = 0.3365
## alternative hypothesis: stationary
kpss.test(TR)
## 
##  KPSS Test for Level Stationarity
## 
## data:  TR
## KPSS Level = 0.65122, Truncation lag parameter = 2, p-value = 0.01798
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 = -6.11, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary

\[ NÃœFUS-BÃœYÃœME-ORANI \]

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")

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 
## -9.517 -4.091  1.121  4.571  8.544 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.92903    0.61608  -8.001 1.02e-13 ***
## x           -0.06445    0.05331  -1.209    0.228    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.961 on 198 degrees of freedom
## Multiple R-squared:  0.007328,   Adjusted R-squared:  0.002315 
## F-statistic: 1.462 on 1 and 198 DF,  p-value: 0.2281
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 
## -2.43458 -0.70252 -0.03582  0.71794  2.58849 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.001492   0.072672  -0.021    0.984
## d(x)         0.013001   0.073656   0.177    0.860
## 
## Residual standard error: 1.018 on 197 degrees of freedom
## Multiple R-squared:  0.0001581,  Adjusted R-squared:  -0.004917 
## F-statistic: 0.03115 on 1 and 197 DF,  p-value: 0.8601
library(tseries)
adf.test(x)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  x
## Dickey-Fuller = -2.7486, Lag order = 5, p-value = 0.2626
## alternative hypothesis: stationary
adf.test(y)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  y
## Dickey-Fuller = -1.2932, Lag order = 5, p-value = 0.8721
## alternative hypothesis: stationary
kpss.test(TR)
## 
##  KPSS Test for Level Stationarity
## 
## data:  TR
## KPSS Level = 0.65122, Truncation lag parameter = 2, p-value = 0.01798
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 = -5.8536, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary