bug in auto.arima?

[Apratimguha]

Using the dataset "strikes" from the package "fma", kpss.test gives a p.value of 0.0585. So it does not reject the null of stationarity. Yet, the best model fitted by auto.arima is ARIMA(0,1,0). I wonder what is the reason for this inconsistency. [Output is given below]

kpss.test(strikes)

KPSS Test for Level Stationarity

data: strikes KPSS Level = 0.44329, Truncation lag parameter = 2, p-value = 0.0585

auto.arima(strikes) Series: strikes ARIMA(0,1,0)

sigma^2 estimated as 359750: log likelihood=-226.65 AIC=455.3 AICc=455.45 BIC=456.67

[mitchelloharawild]

The forecast package's ndiffs() function uses urca for the tests with legacy tseries default arguments.

library(urca)
kpss_result <- ur.kpss(fma::strikes, use.lag = trunc(3*sqrt(length(fma::strikes))/13))
summary(kpss_result)
#> 
#> ####################### 
#> # KPSS Unit Root Test # 
#> ####################### 
#> 
#> Test is of type: mu with 1 lags. 
#> 
#> Value of test-statistic is: 0.6186 
#> 
#> Critical value for a significance level of: 
#>                 10pct  5pct 2.5pct  1pct
#> critical values 0.347 0.463  0.574 0.739

^{Created on 2019-11-09 by the reprex package (v0.2.1)}

[Apratimguha]

Hi, the two packages seem to give very different p-values for the same calculated test statistic. Is there any further reading available on it?

[mitchelloharawild]

The two packages give the same test statistic:

tseries::kpss.test(fma::strikes)
#>  KPSS Test for Level Stationarity
#> 
#> data:  fma::strikes
#> KPSS Level = 0.44329, Truncation lag parameter = 2, p-value =
#> 0.0585
urca::ur.kpss(fma::strikes)
#> 
#> ####################################### 
#> # KPSS Unit Root / Cointegration Test # 
#> ####################################### 
#> 
#> The value of the test statistic is: 0.4433

^{Created on 2019-11-09 by the reprex package (v0.2.1)}

The truncation lag parameter used in forecast is the legacy short lag value of tseries::kpss.test which was trunc(3*sqrt(length(fma::strikes))/13)

[Apratimguha]

My concern was more with the p-values. But now I see the source of the difference: the two defaults are different.

Is there a way to change the options in the functions called by auto.arima?

[mitchelloharawild]

It is possible to specify a particular d and D for auto.arima() by setting their arguments to the desired number of differences. This allows you to write your own options for the test.

The fable package allows you to more directly modify the test used for selecting differences via unitroot_spec = unitroot_options().