Why would Augmented Dickey-Fuller Test fail to reject in this case? (Which implies a unit root exists and non-stationary series) when
Box-Ljung also fails to reject, which implies white noise? and,
KPSS test fails to reject, which implies stationary.
Data:
999300000
1020000000
1036547048
1034600000
1069910054
1047200000
990700000
1070000000
1161500000
1191100000
1219200000
1225400000
1336807261
1390300000
1373900000
1355700000
1503400000
1505600000
1503000000
1541800000
1689600000
1716400000
1640500000
1550800000
1627400000
1683100000
1666500000
1551700000
1631800000
1602100000
1670900000
1609200000
1723600000
After a seasonal and non-seasonal difference :
diff( diff ( data, lag = 4) )
Adf test won't reject null => unit root exists & non-stationary :
adf.test(diff(diff(data), lag=4))
Augmented Dickey-Fuller Test
data: diff(diff(data), lag = 4)
Dickey-Fuller = -3.174, Lag order = 3, p-value = 0.1234
alternative hypothesis: stationary
Box test shows white noise though :
Box.test(diff(diff(data), lag=4),type='Ljung',lag=min(T, h))
Box-Ljung test
data: diff(diff(data), lag = 4)
X-squared = 6.4625, df = 6.6, p-value = 0.4416
KPSS test doesn't reject showing stationary
kpss.test(diff(diff(data, lag=4)))
KPSS Test for Level Stationarity
data: diff(diff(data, lag = 4))
KPSS Level = 0.080543, Truncation lag parameter = 2, p-value = 0.1
acf plot shows no significant autocorrellation
So why does Dickey-Fuller fail to reject?