이상열 교수

Abstract. In this paper, we consider the problem of testing for parameter changes in time series models based on a cusum test. Although the test procedure is well established for the mean and variance in time series models, a general parameter case has not been discussed in the literature. Therefore, here we develop a cusum test for parameter change in a more general framework. As an example, we consider the change of the parameters in a random coeefficient autoregressive (1) model and that of t

In this paper we consider the problem of testing for a scale change in the infinite order moving average process X j =Σ ∞ i =0 a i ε j − i , where ε j are i.i.d. r.v.s with E ε 1 α < ∞ for some α > 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

ABSTRACT In this paper, we consider the problem of testing for a parameter change in Poisson autoregressive models. We suggest two types of cumulative sum (CUSUM) tests, namely, those based on estimates and residuals. We first demonstrate that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal and then construct the CMLE‐based CUSUM test. It is shown that under regularity conditions, its limiting null distribution is a function of independent Bro

In this paper we consider the problem of testing for a parameter change in regression models with ARCH errors based on the residual cusum test. It is shown that the limiting distribution of the residual cusum test statistic is the sup of a Brownian bridge. Through a simulation study, it is demonstrated that the proposed test circumvents the drawbacks of Kim et al.’s (2000) cusum test. For illustration, we apply the residual cusum test to the return of yen/dollar exchange rate data.

Motivated by Gaussian tests for a time series, we are led to investigate the asymptotic behavior of the residual empirical processes of stochastic regression models. These models cover the fixed design regression models as well as general AR$(q)$ models. Since the number of the regression coeffi-cients is allowed to grow as the sample size increases, the obtained results are also applicable to nonlinear regression and stationary AR$(\infty)$ models. In this paper, we first derive an oscillation-

Abstract. In this article, we study the quantile regression estimator for GARCH models. We formulate the quantile regression problem by a reparametrization method and verify that the obtained quantile regression estimator is strongly consistent and asymptotically normal under certain regularity conditions. We also present our simulation results and a real data analysis for illustration.

In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation

Abstract: In this paper, we have two asymptotic objectives: the LAN and the residual empirical process for a class of ARCH(1)-SM (stochastic mean) models, which covers nite-order ARCH and GARCH models. First, we establish the LAN for the ARCH(1)-SM model and, based on it, construct an asymptotically optimal test when the parameter vector contains a nuisance parameter. Also, we discuss asymptotically ecient estimators for unknown parameters when the innovation density is known and when it is unkn

This paper considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations. This family of INAR processes includes a broad class of INAR(1) processes with Poisson, negative binomial, and binomial innovations, respectively, featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated and the formula of the marginal mean and variance is provided. Further, a statistical process control procedure b