Testing for parameter constancy in general causal time‐series models

Abstract

: We consider a process X = (X t ) t∈Z belonging to a large class of causal models including AR(∞), ARCH(∞), TARCH(∞),... models. We assume that the model depends on a parameter θ 0 ∈ IR d and consider the problem of testing for change in the parameter. Two statistics Q(1) n and Qn are constructed using quasi-likelihood estimator (QLME) of the parameter. Under the null hypothesis that there is no change, it is shown that each of these two statistics weakly converges to the supremum of the sum of the squares of independent Brownian bridges. Under the local alternative that there is one change, we show that the test statistic Q n = max Q (1) n , Q (2) n diverges to infinity. Some simulation results for AR(1), ARCH(1) and GARCH(1,1) models are reported to show the applicability and the performance of our procedure with comparisons to some other approaches.

Testing Parameter Change in General Integer‐Valued Time Series

“…We propose a change point test based on the MLE of the parameter of the model . Basing on Doukhan's and Kengne's () and Kengne's () idea, we will construct a test statistic that converges to a known distribution under H 0 and diverges to infinity under the alternative of change in the model. Throughout the sequel, the following notations will be used: for any ; for any function ; for any such as ; is the conditional log‐likelihood function computed on the observations where …”

“…On the other hand, as pointed out in numerous works, many real data often exhibit that structural change occurred during the data collecting processes. Ignoring these breaks can seriously affect any statistical inference on such data, as highlighted by Berkes et al (), Kengne (), Franke et al (), and Doukhan and Kengne (), just to name a few. Change point detection is now an important field in time series analysis given the large number of papers written in this direction during the last three decades.…”

Monitoring procedure for parameter change in causal time series

“…Many papers have been devoted to the problem of test for parameter changes in time series models when all data are available, see for instance Horváth [16], Inclan and Tiao [19], Kokoszka and Leipus [22], Kim et al [21], Horváth and Shao [18], Aue et al [3] or Kengne [20]. These papers consider "retrospective" (off-line) changes i.e.…”

“…Numerous classical time series (such as AR(∞), ARCH(∞), TARCH(∞), ARMA-GARCH or bilinear processes) are included in M Z (M, f ). The off-line change detection for such class of models has already been studied in Bardet et al [5] and Kengne [20].…”

Testing for white noise against locally stationary alternatives

“…Formal hypothesis tests for abrupt parameter changes can be found in ref. 12; to detect smooth changes in the covariance structure several tests switch to the frequency domain [13][14][15].…”