Comparison of time series using subsampling

In this paper we propose a procedure based on the subsampling techniques for the comparison of stationary time series that are not necessarily independent. We study a test based on the Euclidean distance between the autocorrelation functions of two series. Consistency of the proposed method is established. We present a Monte Carlo study with the size and the power of the proposed test.

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

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

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

[4]  Julio Rodríguez,et al.  A Powerful Portmanteau Test of Lack of Fit for Time Series , 2002 .

[5]  J. Swanepoel,et al.  The comparison of two spectral density functions using the bootstrap , 1986 .

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

[7]  Joseph P. Romano,et al.  On the asymptotic theory of subsampling , 1999 .

[8]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[9]  Joseph P. Romano,et al.  Inference for Autocorrelations under Weak Assumptions , 1996 .

[10]  G. Box.  Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification , 1954 .

[11]  Jens Timmer,et al.  A test for a difference between spectral peak frequencies , 1999 .

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

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

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

[15]  Alan David Hutson,et al.  Resampling Methods for Dependent Data , 2004, Technometrics.