Time series analysis via rank order theory: Signed-rank tests for ARMA models (original) (raw)

A goodness-of-fit test based on ranks for arma models

Communications in Statistics-theory and Methods, 1995

In this paper we introduce a goodness-of-fit test based on ranks for ARMA models. The classical portmanteau statistic is generalized to a class of estimators based on ranks. The asymptotic distributions of the proposed statistics are derived. Simulation results suggest that the proposed statistics have good robustness properties for an adequate choice of the score functions.

A goodnes-of-fit test based on ranks for arma models

RePEc: Research Papers in Economics, 1992

Multivariate Signed-Rank Tests in Vector Autoregressive Order Identification

Statistical Science, 2004

The classical theory of rank-based inference is essentially limited to univariate linear models with independent observations. The objective of this paper is to illustrate some recent extensions of this theory to time-series problems (serially dependent observations) in a multivariate setting (multivariate observations) under very mild distributional assumptions (mainly, elliptical symmetry; for some of the testing problems treated below, even second-order moments are not required). After a brief presentation of the invariance principles that underlie the concepts of ranks to be considered, we concentrate on two examples of practical relevance: (1) the multivariate Durbin-Watson problem (testing against autocorrelated noise in a linear model context) and (2) the problem of testing the order of a vector autoregressive model, testing VAR(p 0) against VAR(p 0 + 1) dependence. These two testing procedures are the building blocks of classical autoregressive order-identification methods. Based either on pseudo-Mahalanobis (Tyler) or on hyperplane-based (Oja and Paindaveine) signs and ranks, three classes of test statistics are considered for each problem: (1) statistics of the sign-test type, (2) Spearman statistics and (3) van der Waerden (normal score) statistics. Simulations confirm theoretical results about the power of the proposed rank-based methods and establish their good robustness properties.

Estimation in ARMA models based on signed ranks

2003

In this paper we develop an asymptotic theory for estima- tion based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and

Estimation in Arma Models Based on Signedv Ranks

Journal of the Iranian Statistical Society, 2003

Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test

Journal of The American Statistical Association, 2007

This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions. Several test statistics are derived from these processes; the classical Brock, Dechert, and Scheinkman statistic and a rank-based analog are included as special cases. Because the limiting distributions of the rank-based test statistics are marginfree, their finite-sample p values can be easily calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several classes of alternatives.

Rank Tests for Serial Dependence

Journal of Time Series Analysis, 1981

A family of linear rank statistics is proposed in order to test the independence of a time series, under the assumption that the random variables involved have symmetric distributions with zero medians, without the standard assumptions of normality or identical distributions. The family considered includes analogues of the sign, Wilcoxon signed-rank and van der Waerden tests for symmetry about zero and tables constructed for these tests remain applicable in the present context. The tests proposed are exact and may be applied to assess serial dependence at lag one or greater. The procedures developed are illustrated by a test of the efficiency of forward exhange rates as predictors of future spot rates during the German hyperinflation.

Kolmogorov-Smirnov Tests for AR Models Based on Autoregression Rank Scores

Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2001

Tests of the Kolmogorov-Smirnov type are constructed for the parameter of an autoregressive model of order p. These tests are based on autoregression rank scores, and extend to the time-series context a method proposed by Jureckova (1991) for regression rank scores and regression models with independent observations. Their asymptotic distributions are derived, and they are shown to coincide with those of classical Kolmogorov-Smirnov statistics, under null hypotheses as well as under contiguous alternatives. Local asymptotic efficiencies are investigated. A Monte Carlo experiment is carried out to illustrate the performance of the proposed tests.

Rank-Based Extensions of the BDS Test for Serial Dependence

2006

This paper proposes new tests of randomness for innovations of a large class of time series models. These tests are based on functionals of empirical processes constructed either from the model residuals or from their associated ranks. The asymptotic behavior of these empirical processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors when appropriate regularity conditions hold. Several test statistics are derived from these processes; the classical BDS statistic and a rank-based analogue thereof are included as special cases. Since the limiting distributions of the rank-based test statistics are margin-free, their finite-sample P -values can easily be calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several alternatives.

Time series analysis via rank order theory: Signed-rank tests for ARMA models (original) (raw)

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