Large sample properties of parameter least squares estimates for time‐varying arma models

Francq, Christian; Gautier, Antony

doi:10.1111/j.1467-9892.2004.02003.x

Cited by 19 publications

(13 citation statements)

References 16 publications

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“…Pesaran and Timmerman (2004) studied a linear time series model allowing for shift in variance for forecasting purposes. Francq and Gautier (2004) considered ARMA models with time varying parameters and allowing a finite number of regimes for the variance. Tsay (1988), Sanso et al (2004), among others proposed tests to detect volatility breaks in the residuals.…”

Section: Introductionmentioning

confidence: 99%

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Patilea

Raïssi

2012

Journal of Statistical Planning and Inference

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International audienceLinear vector autoregressive (VAR) models where the innovations could be unconditionally heteroscedastic are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose ordinary least squares (OLS), generalized least squares (GLS) and adaptive least squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residual vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a nonstationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations

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Section: Introductionmentioning

confidence: 99%

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Patilea

Raïssi

2012

Journal of Statistical Planning and Inference

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“…Basawa and Lund (2001) investigated maximum likelihood and least squares estimation of autoregressive and moving average (ARMA) models with periodically varying coefficients. Their models were extended recently by Francq and Gautier (2004) to consider ARMA models with nonperiodic time‐varying coefficients which are subject to irregular regime changes at known time points. In contrast, the present paper focuses on inference for autoregressive models with time‐varying innovation variances, while the autoregressive coefficients are constant over time.…”

Section: Introductionmentioning

confidence: 99%

Inference in Autoregression under Heteroskedasticity

Phillips

2005

Journal Time Series Analysis

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A scalar pth-order autoregression (AR(p)) is considered with heteroskedasticity of the unknown form delivered by a transition function of time. A limit theory is developed and three heteroskedasticity-robust test statistics are proposed for inference, one of which is based on the nonparametric estimation of the variance function. The performance of the resulting testing procedures in finite samples is compared in simulations and some suggestions for practical application are given. Copyright 2005 Blackwell Publishing Ltd.

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“…Lemma 2, which is an extension of Lem 1 in Francq and Gautier (2004a), will be used in the proof of Theorems 6 and 7. The proof is omitted for brevity but is available from the authors.…”

Section: Proofsmentioning

confidence: 99%

“…GARCH models with time‐varying coefficients have been considered by Polzehl and Spokoiny (2006). Time‐series models in which the coefficients are subordinated to an exogenous process have been recently proposed and analysed for the conditional mean by Bibi and Francq (2003) and Francq and Gautier (2004a,b). They consider ARMA models with time‐varying coefficients driven by an observed process and prove asymptotic properties for least squares and generalized least squares estimators.…”

Section: Introductionmentioning

confidence: 99%

Structure and estimation of a class of nonstationary yet nonexplosive GARCH models

Regnard

Zakoïan

2010

Journal of Time Series Analysis

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This article considers GARCH(1,1) models in which the time-varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi-maximum likelihood estimator are derived under mild assumptions. Copyright Copyright 2010 Blackwell Publishing Ltd

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Large sample properties of parameter least squares estimates for time‐varying arma models

Cited by 19 publications

References 16 publications

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Inference in Autoregression under Heteroskedasticity

Structure and estimation of a class of nonstationary yet nonexplosive GARCH models

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