On change point test for ARMA–GARCH models: Bootstrap approach

The problem of testing for a parameter change has been a core issue in time series analysis. It is well known that the estimates-based CUSUM test often suffers from severe size distortions in general GARCH type models. The residual-based CUSUM test has been used as an alternative, which, however, has a defect not to detect the ARMA parameter changes in ARMA–GARCH models. As a remedy, one can employ the score vector-based CUSUM test in ARMA–GARCH models as in Oh and Lee (0000). However, it shows some size distortions for relatively small samples. Hence, we consider the bootstrap counterpart for obtaining a more stable test. Focus is made on the verification of the weak consistency of the proposed test. An empirical study is illustrated for its evaluation.     

Residual-based CUSUM of squares test for Poisson integer-valued GARCH models

This study considers the problem of testing for a parameter change in integer-valued time series models in which the conditional density of current observations is assumed to follow a Poisson distribution. As a test, we consider the CUSUM of the squares test based on the residuals from INGARCH models and find that the test converges weakly to the supremum of a Brownian bridge. A simulation study demonstrates its superiority to the residual and standardized residual-based CUSUM tests of Kang and Lee [Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152] and Lee and Lee [CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.] as well as the CUSUM of squares test based on standardized residuals.     

Covariance changes detection in multivariate time series

This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures based on the likelihood ratio test (LRT) statistic and on a cumulative sums (cusum) statistic are considered and compared in a simulation study. We conclude that for a single covariance change the cusum procedure is more powerful in small and medium samples, whereas the likelihood ratio test is more powerful in large samples. However, for several covariance changes the cusum procedure works clearly better. The procedures are illustrated in two real data examples.     

Finite sample distributions of statistics in change point analysis

This paper is concerned with derivation of finite sampling distributions of some statistics which appear frequently in change point analysis. The exact distribution of cusum test statistic is approximated by two methods. Approximations are presented and their accuracies are measured. We first consider the change point in mean problem and we study the exact distribution of change point estimator. Finally, we consider the change point in variance case.     

Test for Parameter Change in Linear Processes Based on Whittle's Estimator

In this article, we develop a cusum test for testing for parameter changes in linear processes based on Whittle's estimator. It is shown that under regularity conditions, the test statistic converges to the sup of a Brownian bridge. The result is particularly useful in handling the change point test in stationary ARMA processes. A simulation result is provided for illustration.     

On the Cusum test for parameter changes in garch(1,1) Models

This paper considers the problem of testing parameter constancy in GARCH(1,1) models. A cusum of squares test is propesed in analogy Of Incl´n and Tiao (1394)'s statistic. its limiting distribution is derived via using the invariance principle for mixingaie sequences obtained by McLeish(1975). Simulation results are illustrated to demonstrate the validity of the cusum test.     

Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes

In this paper we consider the problem of testing for a scale change in the infinite order moving average process X _j = _{i =0} a _{i j i} , where _j are i.i.d. r.v.s with E ₁ < for some > 0. In performing the test, a cusum of squares test statistic analogous to Inclan & Tiao's (1994) statistic is considered. It is well-known from the literature that outliers affect test procedures leading to false conclusions. In order to remedy this, a cusum of squares test based on trimmed observations is considered. It is demonstrated that this test is robust against outliers, is valid for infinite variance processes as well. Simulation results are given for illustration.     

The Multiple Outlier Problem in Time Series Analysis

In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.     

Change point detection in SCOMDY models

In this article, we consider the problem of testing for a copula parameter change in semiparametric copula-based multivariate dynamic models which cover ARMA-GARCH models. We construct the test statistics based on a pseudo MLE of the copula parameter and derive its limiting null distribution. Simulation results are provided for illustration.     

On CUSUM test for dynamic panel models

Statistical Methods & Applications - In this study, we consider the problem of testing for a parameter change in dynamic panel models with fixed effects. As a test, we suggest using the CUSUM...     

Some observations in testing for nonstandard mixtures

We consider optimal testing procedures for specific models of early and instantaneous failures in reliability studies. These models are typically used to accommodate lifetime data that have a higher concentration of failures near time zero. We show that it is possible to derive uniformly most powerful tests, for testing the mixing parameter in the instantaneous failure model, for general lifetime distributions. A novel procedure to test for early failures, which uses an invariance property of the maximum likelihood estimate of the nuisance parameter, is also presented.     

Monitoring parameter change in time series models

In this paper, we develop a monitoring procedure for an early detection of parameter changes in time series models. We design the monitoring procedure in general time series models and apply it to the changes for the autocovariances of linear processes, GARCH parameters, and underlying distributions. Simulation results are provided for illustration.     

A recursive approach to parameter estimation in regression and time series models

In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated with an example.     

Tests for Structural Changes in Time Series of Counts

We propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.     

Fractional integration versus level shifts: the case of realized asset correlations

Long memory has been widely documented for realized financial market volatility. As a novelty, we consider daily realized asset correlations and we investigate whether the observed persistence is (i) due to true long memory (i.e. fractional integration) or (ii) artificially generated by some structural break processes. These two phenomena are difficult to be distinguished in practice. Our empirical results strongly indicate that the hyperbolic decay of the autocorrelation functions of pair-wise realized correlation series is indeed not driven by a truly fractionally integrated process. This finding is robust against user specific parameter choices in the applied test statistic and holds for all 15 considered time series. As a next step, we apply simple models with deterministic level shifts. When selecting the number of breaks, estimating the breakpoints and the corresponding structural break models we find a substantial degree of co-movement between the realized correlation series hinting at co-breaking. The estimated structural break models are interpreted in the light of the historic economic and financial development.     

Statistical analysis of a class of factor time series models

For a class of factor time series models, which is called a multivariate time series variance component (MTV) models, we consider the problem of testing whether an observed time series belongs to this class. We propose the test statistic, and derive its symptotic null distribution. Asymptotic optimality of the proposed test is discussed in view of the local asymptotic normality. Also, numerical evaluation of the local power illuminates some interesting features of the test.     

Likelihood-based tests in zero-inflated power series models

We address the issue of performing testing inference in the class of zero-inflated power series models. These models provide a straightforward way of modelling count data and have been widely used in practical situations. The likelihood ratio, Wald and score statistics provide the basis for testing the parameter of inflation of zeros in this class of models. In this paper, in addition to the well-known test statistics, we also consider the recently proposed gradient statistic. We conduct Monte Carlo simulation experiments to evaluate the finite-sample performance of these tests for testing the parameter of inflation of zeros. The numerical results show that the new gradient test we propose is more reliable in finite samples than the usual likelihood ratio, Wald and score tests. An empirical application to real data is considered for illustrative purposes.     

A class of Stein‐rules in multivariate regression model with structural changes

In this paper, we consider an estimation problem of the matrix of the regression coefficients in multivariate regression models with unknown change‐points. More precisely, we consider the case where the target parameter satisfies an uncertain linear restriction. Under general conditions, we propose a class of estimators that includes as special cases shrinkage estimators (SEs) and both the unrestricted and restricted estimator. We also derive a more general condition for the SEs to dominate the unrestricted estimator. To this end, we extend some results underlying the multidimensional version of the mixingale central limit theorem as well as some important identities for deriving the risk function of SEs. Finally, we present some simulation studies that corroborate the theoretical findings.     

Improving the bandwidth-free inference methods by prewhitening

In this paper we consider inference of parameters in time series regression models. In the traditional inference approach, the heteroskedasticity and autocorrelation consistent (HAC) estimation is often involved to consistently estimate the asymptotic covariance matrix of regression parameter estimator. Since the bandwidth parameter in the HAC estimation is difficult to choose in practice, there has been a recent surge of interest in developing bandwidth-free inference methods. However, existing simulation studies show that these new methods suffer from severe size distortion in the presence of strong temporal dependence for a medium sample size. To remedy the problem, we propose to apply the prewhitening to the inconsistent long-run variance estimator in these methods to reduce the size distortion. The asymptotic distribution of the prewhitened Wald statistic is obtained and the general effectiveness of prewhitening is shown through simulations.