On the properties of the Dickey-Pantula test against fractional alternatives

Dolado, Juan J.; Marmol, Francesc

doi:10.1016/s0165-1765(97)81873-3

Cited by 5 publications

(8 citation statements)

References 9 publications

(9 reference statements)

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“…This recommended sequence of testing will lead to similar test statistics and, hence, will have a size that can be controlled by choice of the significance level. (Dolado and Marmol (1997) study this testing sequence when the underlying series is fractionally integrated. However, fractional integration is beyond the assumptions of the present study wherein integer orders of integration are assumed.…”

Section: Introductionmentioning

confidence: 99%

On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

Haldrup¹,

Lildholdt²

2002

Journal Time Series Analysis

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We examine some of the consequences on commonly used unit root tests when the underlying series is integrated of order two rather than of order one. It turns out that standard augmented Dickey–Fuller type of tests for a single unit root have excessive density in the explosive region of the distribution. The lower (stationary) tail, however, will be virtually unaffected in the presence of double unit roots. On the other hand, the Phillips–Perron class of semi‐parametric tests is shown to diverge to plus infinity asymptotically and thus favouring the explosive alternative. Numerical simulations are used to demonstrate the analytical results and some of the implications in finite samples.

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Section: Introductionmentioning

confidence: 99%

On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

Haldrup¹,

Lildholdt²

2002

Journal Time Series Analysis

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“…the autocorrelations of the approximate rate of return, are all them small. Nonetheless, an alternative potential explanation for the high persistence of the exchange rate is the possibility that the memory parameters of these series may be fractional, since it is well known that standard integer order unit root tests have low power against fractional alternatives (cf., e.g., Hassler and Walter, 1994;Dolado and Marmol, 1997).…”

Section: Exchange Rate Dynamicsmentioning

confidence: 99%

Residual log-periodogram inference for long-run relationships

Hassler

Marmol

Velasco

2006

Journal of Econometrics

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We assume that some consistent estimator b b of an equilibrium relation between non-stationary series integrated of order d 2 ð0:5; 1:5Þ is used to compute residualsû t ¼ y t b bx t (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence d of the equilibrium deviation u t : Provided b b converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of d: At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on d: This requires that d d40:5 for superconsistent b b; so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0pdo0:5; as well as for non-stationary but transitory equilibrium errors, 0:5odo1: In particular, if x t contains several series we consider the joint estimation of d and d: Wald statistics to test for parameter restrictions of the system have a limiting w 2 distribution. We also analyse the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics. r 2005 Elsevier B.V. All rights reserved.JEL classification: C14; C22

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“…Finally, its applications by using the energy series, Bitcoin exchange rate and financial data in are presented in Section 6. Dolado and Marmol (1997) named the Data Generating Process (DGP) of 𝑦 to be Nonstationary Fractionally Integrated (NFI) process and defined it as:…”

Section: Introductionmentioning

confidence: 99%

ARFURIMA models: simulations of their properties and application

Jibrin

Rahman

2022

Statistics in Transition New Series

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This article defines the Autoregressive Fractional Unit Root Integrated Moving Average (ARFURIMA) model for modelling ILM time series with fractional difference value in the interval of 1 < d < 2. The performance of the ARFURIMA model is examined through a Monte Carlo simulation. Also, some applications were presented using the energy series, bitcoin exchange rates and some financial data to compare the performance of the ARFURIMA and the Semiparametric Fractional Autoregressive Moving Average (SEMIFARMA) models. Findings showed that the ARFURIMA outperformed the SEMIFARMA model. The study’s conclusion provides another perspective in analysing large time series data for modelling and forecasting, and the findings suggest that the ARFURIMA model should be applied if the studied data show a type of ILM process with a degree of fractional difference in the interval of 1 < d < 2.

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On the properties of the Dickey-Pantula test against fractional alternatives

Abstract: The limit properties of the testing sequence underlying the Dickey-Pantula test for a double unit root in a time series are derived when the true data generating process is assumed to be nonstationary fractionally integrated. © 1997 Elsevier Science S.A.

Cited by 5 publications

References 9 publications

On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

On the Robustness of Unit Root Tests in the Presence of Double Unit Roots

Residual log-periodogram inference for long-run relationships

ARFURIMA models: simulations of their properties and application

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