Comparing Time-Varying autoregressive Structures of Locally Stationary Processes

In this paper, a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modeling and function projections in adequate spaces. The covariance structure of the innovations may be also time-varying. In order to obtain function estimators for the time-varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefulness when applied to a financial time series.

[1]  R. Dahlhaus.  Fitting time series models to nonstationary processes , 1997 .

[2]  Jiin-Huarng Guo,et al.  Theory & Methods: A Nonparametric Test for the Parallelism of Two First‐Order Autoregressive Processes , 1999 .

[3]  D. Piccolo.  A DISTANCE MEASURE FOR CLASSIFYING ARIMA MODELS , 1990 .

[4]  W. Meredith,et al.  Statistics and Data Analysis , 1974 .

[5]  I. Daubechies,et al.  Wavelets on the Interval and Fast Wavelet Transforms , 1993 .

[6]  Elizabeth Ann Maharaj,et al.  Comparison and classification of stationary multivariate time series , 1999, Pattern Recognit..

[7]  Lynne Billard,et al.  Large-sample tests of homogeneity for time series models , 1984 .

[8]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[9]  R. Shumway.  Time-frequency clustering and discriminant analysis , 2003 .

[10]  Masanobu Taniguchi,et al.  Discriminant analysis for locally stationary processes , 2004 .

[11]  R. Dahlhaus.  On the Kullback-Leibler information divergence of locally stationary processes , 1996 .

[12]  Elizabeth Ann Maharaj.  Comparison of non-stationary time series in the frequency domain , 2002 .

[13]  Michael H. Neumann,et al.  Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes , 1999 .

[14]  Jorge Caiado,et al.  A periodogram-based metric for time series classification , 2006, Comput. Stat. Data Anal..

[15]  D. Cochrane,et al.  Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms , 1949 .

[16]  James D. Hamilton.  Time Series Analysis , 1994 .

[17]  Elizabeth Ann Maharaj.  Using Wavelets to Compare Time Series Patterns , 2005, Int. J. Wavelets Multiresolution Inf. Process..

[18]  Elizabeth Ann Maharaj,et al.  A SIGNIFICANCE TEST FOR CLASSIFYING ARMA MODELS , 1996 .

[19]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[20]  Hernando Ombao,et al.  Discrimination and Classification of Nonstationary Time Series Using the SLEX Model , 2004 .

[21]  P. J. Diggle,et al.  TESTS FOR COMPARING TWO ESTIMATED SPECTRAL DENSITIES , 1986 .

[22]  Peter J. Diggle,et al.  Nonparametric Comparison of Cumulative Periodograms , 1991 .

[23]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[24]  Elizabeth Ann Maharaj,et al.  Cluster of Time Series , 2000, J. Classif..