Nonparametric likelihood inference for general autoregressive models

This paper shows how nonparametric likelihood inference for autoregressive models can be based on the family of “empirical” Cressie–Read statistics. The results of the paper apply to possibly nonstationary autoregressive models with innovations that form a martingale difference sequence, and can accommodate multiple and complex unit roots, as well as deterministic components. As an application, the paper considers nonparametric likelihood-based tests for seasonal unit roots and for double unit roots. Monte Carlo evidence seems to suggest that the proposed tests have competitive finite sample properties.

[1]  T. Lai,et al.  Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters , 1983 .

[2]  N. Haldrup.  Semiparametric Tests for Double Unit Roots , 1994 .

[3]  Eric Ghysels,et al.  Testing for unit roots in seasonal time series: Some theoretical extensions and a Monte Carlo investigation , 1994 .

[4]  Bartlett-type adjustments for empirical discrepancy test statistics , 2006 .

[5]  C. Z. Wei,et al.  Asymptotic Inference for Nearly Nonstationary AR(1) Processes , 1987 .

[6]  C. Z. Wei,et al.  Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes , 1988 .

[7]  P. Phillips.  Time series regression with a unit root , 1987 .

[8]  S. Pantula,et al.  Determining the Order of Differencing in Autoregressive Processes , 1987 .

[9]  Joseph P. Romano,et al.  Nonparametric confidence limits by resampling methods and least favorable families , 1990 .

[10]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[11]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[12]  Richard J. Smith.  GEL CRITERIA FOR MOMENT CONDITION MODELS , 2011, Econometric Theory.

[13]  Zacharias Psaradakis.  Bootstrap tests for unit roots in seasonal autoregressive models , 2000 .

[14]  Keith A. Baggerly,et al.  Empirical likelihood as a goodness-of-fit measure , 1998 .

[15]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

[16]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[17]  T. Lai,et al.  Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems , 1982 .

[18]  Richard J. Smith,et al.  Additional critical values and asymptotic representations for seasonal unit root tests , 1998 .

[19]  P. Jeganathan.  On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle , 1991, Econometric Theory.

[20]  Timothy R. C. Read,et al.  Multinomial goodness-of-fit tests , 1984 .

[21]  Yuichi Kitamura,et al.  Empirical likelihood methods with weakly dependent processes , 1997 .

[22]  N. E. Savin,et al.  The Level and Power of the Bootstrap t Test in the AR(1) Model With Trend , 1996 .

[23]  G. Imbens,et al.  Confidence intervals in generalized method of moments models , 2002 .

[24]  Wayne A. Fuller,et al.  Estimation for Autoregressive Processes with Unit Roots , 1979 .

[25]  THE LOCAL ASYMPTOTIC POWER OF CERTAIN TESTS FOR FRACTIONAL INTEGRATION , 1999, Econometric Theory.

[26]  P. Burridge,et al.  Bootstrapping the HEGY seasonal unit root tests , 2004 .

[27]  N. Chan,et al.  EMPIRICAL LIKELIHOOD FOR AUTOREGRESSIVE MODELS, WITH APPLICATIONS TO UNSTABLE TIME SERIES , 2002 .

[28]  G. A. Young,et al.  Nonparametric likelihood ratio confidence intervals , 1999 .

[29]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[30]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[31]  Yoosoon Chang,et al.  ON THE ASYMPTOTICS OF ADF TESTS FOR UNIT ROOTS , 2002 .