연세대학교 시계열분석 수업자료를 토대로한 복습 자료입니다.
Time Series
정상시계열과 random walk 자료생성
# A time series which contains no unit-root:
x = rnorm(1000)
# A time series which contains a unit-root:
y = cumsum(c(0, x))
par(mfrow=c(2,1))
plot.ts(x)
plot.ts(y)
단위근 검정 / 1차 차분 후 단위근 검정
adfTest(x)
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: -22.6036
## P VALUE:
## 0.01
##
## Description:
## Mon Jun 22 00:48:53 2020 by user: jay
adfTest(y)
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: -0.8042
## P VALUE:
## 0.36
##
## Description:
## Mon Jun 22 00:48:53 2020 by user: jay
#1차 차분 후
adfTest(diff(y))
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: -22.6036
## P VALUE:
## 0.01
##
## Description:
## Mon Jun 22 00:48:53 2020 by user: jay
plot.ts(diff(y))
PP Test
PP.test(x)
##
## Phillips-Perron Unit Root Test
##
## data: x
## Dickey-Fuller = -30.399, Truncation lag parameter = 7, p-value = 0.01
PP.test(y)
##
## Phillips-Perron Unit Root Test
##
## data: y
## Dickey-Fuller = -2.6131, Truncation lag parameter = 7, p-value = 0.3188
5장의 stock data를 이용하여 복습
data<-read.table("https://raw.githubusercontent.com/jaesanglee95/Jay_blog/master/stock.csv")
stock<-ts(data)
#stock data
plot.ts(stock)
adfTest(stock)
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: 1.373
## P VALUE:
## 0.9561
##
## Description:
## Mon Jun 22 00:48:54 2020 by user: jay
PP.test(stock)
##
## Phillips-Perron Unit Root Test
##
## data: stock
## Dickey-Fuller = -1.1877, Truncation lag parameter = 4, p-value = 0.9064
로그변환 후 결과 확인
logstock<-log(stock)
plot(logstock)
adfTest(logstock)
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: 2.6555
## P VALUE:
## 0.99
##
## Description:
## Mon Jun 22 00:48:54 2020 by user: jay
PP.test(logstock)
##
## Phillips-Perron Unit Root Test
##
## data: logstock
## Dickey-Fuller = -1.1894, Truncation lag parameter = 4, p-value = 0.9061
로그변환 후 1차 차분 후 결과 확인
diff_logstock<-diff(logstock, lag=1)
plot(diff_logstock)
adfTest(diff_logstock)
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 1
## STATISTIC:
## Dickey-Fuller: -8.6082
## P VALUE:
## 0.01
##
## Description:
## Mon Jun 22 00:48:54 2020 by user: jay
PP.test(diff_logstock)
##
## Phillips-Perron Unit Root Test
##
## data: diff_logstock
## Dickey-Fuller = -13.318, Truncation lag parameter = 4, p-value = 0.01
KPSS test
앞선 두 가지 검정 방법과 가설이 반대이다.
귀무가설: 정상이다 vs 대립가설: random walk
kpss.test(diff_logstock)
##
## KPSS Test for Level Stationarity
##
## data: diff_logstock
## KPSS Level = 0.1983, Truncation lag parameter = 4, p-value = 0.1