Testing the Order of Differencing in Time Series Regression

Saikkonen, Pentti; Luukkonen, Ritva

doi:10.1111/j.1467-9892.1996.tb00289.x

Cited by 2 publications

(1 citation statement)

References 35 publications

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“…For instance, seasonal intercept and conditional heteroskedasticity should be considered, as well as stationary linear models which are not ARMA. It seems also interesting to compare these results which other procedures which are known to be locally optimal under some simple ARMA speci…cation (see Saikkonen and Luukkonen (1996)).…”

Section: Discussionmentioning

confidence: 98%

Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II

Lacroix

1999

SSRN Journal

107

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Section: Discussionmentioning

confidence: 98%

Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II

Lacroix

1999

SSRN Journal

107

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Locally Optimal Tests Against Unit Roots in Seasonal Time Series Processes

Taylor

2003

Journal Time Series Analysis

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This paper builds on the existing literature on tests of the null hypothesis of deterministic seasonality in a univariate time-series process. Under the assumption of independent Gaussian errors, we derive the class of locally weighted mean most powerful invariant tests against unit roots at the zero and/or seasonal frequencies in a seasonally observed process. Representations for the limiting distributions of the proposed test statistics under sequences of local alternatives are derived, and the relationship with tests for corresponding moving average unit roots is explored. We also propose nonparametric modifications of these test statistics designed to have limit distributions which are free of nuisance parameters under weaker conditions on the errors. Our tests are shown to contain existing stationarity tests as special cases and to extend these tests in a number of useful directions. (LMMPI) tests, together with weighted versions thereof, against seasonal and/or zero frequency unit roots under the assumption of Gaussian white noise errors. The resulting tests maximize the slope of the power surface in any specified direction. By allowing for deterministic (seasonal) trend variables in our null regression model, we develop tests which are similar in cases where the true data generating process (DGP) contains either a deterministic linear trend or deterministic seasonal trends. In such cases, the tests of Canova and Hansen (1995) and Caner (1998), whose null model includes only seasonal dummy variables, are not based on a maximal invariant statistic and hence, in general, depend on nuisance parameters, even in the limit. The same applies to the tests of Tam andReinsel (1997, 1998) who also do not allow for seasonal trends. We also show that our LMMPI statistics coincide with statistics used to test for moving average unit roots, at the chosen frequencies, in integrated moving average models. The limiting distributions of the proposed statistics under relevant sequences of local alternatives are derived. We also demonstrate how our general framework may be employed to develop locally optimal tests against the class of non-stationary sub-annual processes discussed in Kunst (1997).In Section 3, we weaken our assumptions to allow for weakly dependent and heterogeneous errors. To obtain pivotal limiting null distributions in such cases, we modify our statistics with an extended variant of the HAC covariance matrix estimator used by Canova and Hansen (1995). Although the modified tests are no longer locally optimal in any formal sense, we show that the tests are consistent under the seasonal unit root alternative and give their asymptotic distributions under local alternatives. Furthermore, we show that, in certain special cases, the non-parametrically modified tests coincide with tests previously proposed by Kwiatkowski et al. (1992) and Canova and Hansen (1995), although the joint seasonal frequency tests proposed in the latter imply equal weighting to each subtest which we do not impose. Moreover, our framework a...

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Testing the Order of Differencing in Time Series Regression

Cited by 2 publications

References 35 publications

Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II

Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II

Locally Optimal Tests Against Unit Roots in Seasonal Time Series Processes

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