Stationarity against integration in the autoregressive process with polynomial trend

• Autorzy: Proïa F.

Identyfikatory

DOI

10.19195/0208-4147.38.1.1

• Języki publikacji: EN

Abstrakty

EN

We tackle the stationarity issue of an autoregressive path with a polynomial trend, and generalize some aspects of the LMC test, the testing procedure of Leybourne and McCabe. First, we show that it is possible to get the asymptotic distribution of the test statistic under the null hypothesis of trend-stationarity as well as under the alternative of nonstationarity for any polynomial trend of order r. Then, we explain the reason why the LMC test, and by extension the KPSS test, does not reject the null hypothesis of trend-stationarity, mistakenly, when the random walk is generated by a unit root located at −1.We also observe it on simulated data and correct the procedure. Finally, we describe some useful stochastic processes that appear in our limiting distributions.

Słowa kluczowe

EN

LMC test; KPSS test; unit root; stationarity testing procedure; polynomial trend; stochastic nonstationarity; random walk; integrated process; ARIMA process; Donsker’s invariance principle; continuous mapping theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2018
• Tom: Vol. 38, Fasc. 1
• Strony: 1--26
• Opis fizyczny: Bibliogr. 25 poz., tab., wykr.

Twórcy

autor

Proïa F.

• Laboratoire Angevin de REcherche en MAthématiques (UMR 6093), Université d’Angers, Département de mathématiques, Faculté des Sciences, 2 Boulevard Lavoisier, 49045 Angers cedex, France

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).