On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation

Variance ratio tests of the seasonal unit root hypothesis

“…Focusing on the case where the shocks follow a ÿnite-order autoregressive process of order p [AR(p)], Burridge and Taylor (2001a) (BTa) show that lag augmentation, along the lines of the augmented Dickey-Fuller (ADF) test, provides only a partial solution with the limiting null distributions of certain of the harmonic frequency unit root tests still depending, in general, on the parameters of the AR(p) polynomial. Moreover, BTa did not cover the case where the shocks have an AR(∞) representation, as would be needed to allow for stationary and invertible ARMA shocks.…”

Measurement errors and outliers in seasonal unit root testing

“…Because in practice the complex paired roots are typically tested jointly, only the joint F-test is reported for this case. As suggested by Burridge and Taylor (2001), when HEGY tests are considered using lag augmentation to account for serial correlation, the t statistics associated with the harmonic frequencies are no longer pivotal whereas the joint F-test is, and this is a separate argument for reporting the result for this case only.…”

“…Burridge and Taylor (2001) in a study of the influence of lagaugmentation in the presence of higher order serial correlation. Since the joint test is pivotal it is preferable to use this test when the harmonic frequencies are addressed.…”

Efficient tests of the seasonal unit root hypothesis

“…However, it is straightforward to show that this does not hold for general fðzÞ, with the limiting distributions oft k andt à k depending on the functions a k and b k of cðzÞ defined in Lemma B.1; cf. Burridge and Taylor (2001) and Rodrigues and Taylor (2004a). As is standard in the literature on HEGY tests, Theorem 5.1 imposes the condition that v Snþs is a finite-order stationary ARðpÞ process, with a lag truncation of p à Xp in (5.1).…”