Re: AugmentedDickeyFuller and different result in R

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1. The p-value obtained in adf.test() is merely an approximation. It is calculated by using linear interpolation and the following table

which is taken from Table 4.2 of Banerjee et al. (1993), “Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data”. This actually corresponds to one of the three trend types (AugmentedDickeyFuller.TrendType CONSTANT_TIME) in SuanShu. Since the ADF distributions (either asymptotic or finite sample) are nonlinear, p-values in R are inaccurate, esp. if the value lies between 0.1 and 0.9.

2. In SuanShu, you are able to get the empirical distribution and hence the quantiles of the ADF distribution for any trend type/sample size. Accuracy can further be improved by increasing the number of simulations. It is more flexible than R and the result obtained is more trustworthy. For discussion on finite-sample critical values and lag orders, please see MacKinnon (1991) and Cheung and Lai (1995) for references.

3. A p-value of 0.36 (in R) or 0.2 (in SuanShu) shouldn’t affect your conclusion of the hypothesis test, since the null hypothesis would not be rejected (at 5% or 10%) in either case.