Improving Size and Power in the Unit Root Testing

Haldrup, Niels; Jansson, Michael

doi:10.2139/ssrn.1147594

Cited by 40 publications

(48 citation statements)

References 65 publications

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“…The results given in this section are also su¢ cient to determine corresponding results for the class of modi…ed unit root tests originally proposed in Stock (1999) and developed further in Perron and Ng (1996) and Ng and Perron (2001); see also Haldrup and Jansson (2006). Where these are based on semi-parameteric estimation of the serial correlation nuisance parameters, the limiting null distributions of these statistics are an immediate corollary of the results given in Phillips (1990).…”

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confidence: 69%

Unit Root Inference for Non-Stationary Linear Processes Driven by Infinite Variance Innovations

2016

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The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by in…nite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the in…nite variance process. These distributions are shown to coincide with the corresponding results for the case where the shocks follow a …nite autoregression, provided the lag length in the ADF regression satis…es the same o(T 1=3 ) rate condition as is required in the …nite variance case. In addition, we establish the rates of consistency and (where they exist) the asymptotic distributions of the ordinary least squares sieve estimates from the ADF regression. Given the dependence of their null distributions on the unknown tail index, our second contribution is to explore sieve wild bootstrap implementations of the ADF tests. Under the assumption of symmetry, we demonstrate the asymptotic validity (bootstrap consistency) of the wild bootstrap ADF tests. This is done by establishing that (conditional on the data) the wild bootstrap ADF statistics attain the same limiting distribution as that of the original ADF statistics taken conditional on the magnitude of the innovations.

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confidence: 69%

Unit Root Inference for Non-Stationary Linear Processes Driven by Infinite Variance Innovations

2016

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“…whereγ j is the sample autocovariance of order j computed from the OLS residuals from estimating ( It is well-known that semi-parametric unit root tests based on sums-of-covariances estimators can behave quite poorly in finite samples; see, for example, Haldrup and Jansson (2006).…”

Section: Phillips-perron-type Seasonal Unit Root Testsmentioning

confidence: 99%

Semi-Parametric Seasonal Unit Root Tests

2017

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It is well known that (seasonal) unit root tests can be seriously affected by the presence of weak dependence in the driving shocks when this is not accounted for. In the non-seasonal case both parametric (based around augmentation of the test regression with lagged dependent variables) and semi-parametric (based around an estimator of the long run variance of the shocks) unit root tests have been proposed. Of these, the M class of unit root tests introduced by Stock (1999), Perron and Ng (1996) and Ng and Perron (2001), appear to be particularly successful, showing good finite sample size control even in the most problematic (near-cancellation) case where the shocks contain a strong negative moving average component. The aim of this paper is threefold. First we show the implications that neglected weak dependence in the shocks has on lag un-augmented versions of the well known regressionbased seasonal unit root tests of Hylleberg et al. (1990). Second, in order to complement extant parametrically augmented versions of the tests of Hylleberg et al. (1990), we develop semi-parametric seasonal unit root test procedures, generalising the methods developed in the non-seasonal case to our setting. Third, we compare the finite sample size and power properties of the parametric and semi-parametric seasonal unit root tests considered. Our results suggest that the superior size/power trade-off offered by the M approach in the non-seasonal case carries over to the seasonal case.

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“…M GLS tests have become increasingly popular in the literature. For example, Haldrup and Jansson (2006) argue that practitioners should abandon the use of ADF tests altogether in favor of M GLS tests because of their excellent size properties and nearly optimal power properties. However, this note arrives at the opposite conclusion, suggesting that the choice of the most suitable testing method should be carefully assessed.…”

Section: Introductionmentioning

confidence: 99%

Selecting the Lag Length for the MGLS Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations

Quineche

Rodríguez

2017

Econometrics

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This is a simulation-based warning note for practitioners who use the M GLS unit root tests in the context of structural change using different selection lag length criteria. With T = 100, we find severe oversize problems when using some criteria, while other criteria produce an undersizing behavior. In view of this dilemma, we do not recommend using these tests. While such behavior tends to disappear when T = 250, it is important to note that most empirical applications use smaller sample sizes such as T = 100 or T = 150. The ADF GLS test does not present an oversizing or undersizing problem. The only disadvantage of the ADF GLS test arises in the presence of MA(1) negative correlation, in which case the M GLS tests are preferable, but in all other cases they are very undersized. When there is a break in the series, selecting the breakpoint using the Supremum method greatly improves the results relative to the Infimum method.

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Improving Size and Power in the Unit Root Testing

Cited by 40 publications

References 65 publications

Unit Root Inference for Non-Stationary Linear Processes Driven by Infinite Variance Innovations

Unit Root Inference for Non-Stationary Linear Processes Driven by Infinite Variance Innovations

Semi-Parametric Seasonal Unit Root Tests

Selecting the Lag Length for the MGLS Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations

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