On the cusum of squares test for variance change in nonstationary and nonparametric time series models

Lee, Sangyeol; Na, Okyoung; Na, Seongryong

doi:10.1007/bf02517801

Cited by 33 publications

(18 citation statements)

References 22 publications

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“…An advantage of using the cusum test is that there are no assumptions imposed on the underlying distribution of observations unlike in the other methods, for instance, the parametric approach which is not suitable to the test a change in the autocorrelations of stationary time series. Lee et al [12], Lee and Na [14], and Lee et al [13] used the cusum test to overcome this problem and applied it to various cases such as the test for parameter changes in random coefficient autoregressive and autoregressive conditional heteroscedastic (ARCH) models.…”

Section: Introductionmentioning

confidence: 99%

Moving estimates test with time varying bandwidth

Lee

2007

Journal of Multivariate Analysis

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In this paper, we consider the problem of testing for parameter changes in time series models based on a moving estimates (ME) test. It is widely accepted that detecting some changes, for instance, those caused by temporary parameter shifts by the existing cusum test is difficult. A MV test with a fixed bandwidth has been developed to circumvent the defect, but the test still does not perform well under certain conditions. Motivated by this, we propose a MV test with a time varying bandwidth to outperform the original test. In order to illustrate our findings, we have provided simulation results.

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Section: Introductionmentioning

confidence: 99%

Moving estimates test with time varying bandwidth

Lee

2007

Journal of Multivariate Analysis

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“…Later, it was demonstrated that the same idea can be extended to a large class of time series models (cf., Lee et al (2003a)). Also, the variance change test has been studied in unstable AR models (cf., Lee et al (2003b)). …”

Section: Introductionmentioning

confidence: 99%

“…In fact, a significant improvement was observed in our simulation study. Despite the previous work of Lee et al (2003b) also considers a residual cusum test in time series models, the model of main concern was the autoregressive model with several unit roots. In fact, the mathematical analysis of the cusum test heavily relies on the probabilistic structure of the underlying time series model, and the arguments used for establishing the weak convergence result for unstable models are somewhat different from those for ARCH models.…”

Section: Introductionmentioning

confidence: 99%

The Cusum Test for Parameter Change in Regression Models with ARCH Errors

Lee

Tokutsu

Maekawa

2004

JJSS

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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.

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“…Some recent work considered structural change tests when some regressors are non‐stationary; see Lee et al. () and Nielsen and Sohkanen (). Extensions to these contexts need further investigation.…”

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Testing for structural change under non‐stationary variances

2015

The Econometrics Journal

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Non-stationarity of the volatility process reflects low-frequency volatility changes of an economic time series, and its theoretical and empirical relevance has been widely recognized. We investigate how it affects cumulative sum (CUSUM) related tests for structural change in regression coefficients. Non-stationary variances generally invalidate standard structural change tests by introducing an infinite-dimensional nuisance parameter in the limit distribution, and we propose robust alternatives. We also show that the practical relevance of the non-monotonic power issue, which is peculiarly associated with the test for changing mean, is mitigated (although the power against a small change is reduced) if there is comparable change in volatility levels. The results are useful to validate/modify a test to ensure monotonic power. Simulations and an empirical example provide finite-sample evidence of the theoretical findings.

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On the cusum of squares test for variance change in nonstationary and nonparametric time series models

Abstract: Cusum of squares test, variance change, autoregressive model with unit roots, nonparametric regression model, strong mixing process, weak convergence, Brownian bridge,

Cited by 33 publications

References 22 publications

Moving estimates test with time varying bandwidth

Moving estimates test with time varying bandwidth

The Cusum Test for Parameter Change in Regression Models with ARCH Errors

Testing for structural change under non‐stationary variances

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