A Modification of the CUSUM Test in the Linear Regression Model with Lagged Dependent Variables

Abstract

Abstract:We consider testing for structural change in a dynamic linear regression model, and show that the well known CUSUM test, which has been initially devised only for the standard static model, can easily be modified such as to remain asymptotically valid also in this nonstandard situation.

Empirical Likelihood for an Autoregressive Model with Explanatory Variables

“…Inference in model (1.1) has received considerable attention. When the errors are independent identically distribution, Durbin (1960) and Anderson and Taylor (1979) proposed the least-squares estimator of the regression coefficient; Ploberger et al (1989) investigated the well-known CUSUM test for structural change; Knight (1993) showed that under certain conditions, the M-estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n −1/2 rate; Dufour and Kiviet (1998) developed procedures for exact joint inference on the coefficient of the lagged dependent variable and linear transformations of the coefficients of the exogenous regressors. Furthermore, under martingale difference sequence, Crowder (1980) discussed consistency and asymptotic normality of least-squares estimators.…”

Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms

“…In this context, Brown et al (1975) and Jandhyala and MacNeill (1991) discussed general linear model, Lee et al (2004), Chihwa and Ross (1995), and Ploberger et al (1989) focused on detecting the linear model with different types of error terms. In this paper we propose methodology for detecting change in regression coefficients in the generalized linear model setting and the EF CUSUM scheme associated with it.…”

Asymptotically exact confidence intervals of cusum and cusumsq tests: a numerical derivation using simulation technique

“…There is a great amount of literature on use of recursive residuals, e.g., Brown, Durbin and Evans (1975), Galpin and Hawkins (1984), Harvey (1989), Johnston (1984), Ploberger (1989), Ploberger, Krämer and Alt (1989), and Westlund and Törnkvist (1989). Especially, Brown, Durbin and Evans (1975) described an important application of recursive residuals in testing for structural change over time.…”