A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test

Francq, Christian; Makarova, Svetlana; Zakoïan, Jean‐Michel

doi:10.1016/j.jeconom.2007.04.003

Cited by 12 publications

(9 citation statements)

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“…The problem has been studied in the MAR‐ARCH context by Carvallo and Skoulakis (2005) and Saikkonen (2007) under the first moment condition and in the pure bilinear case by Pham (1986) and Cline and Pu (2002), under the second moment assumption. Here, we establish geometric ergodicity without any moment requirements, just under the strict stationarity assumption similarly to Francq et al . (2008).…”

Section: Probabilistic Structure Of the Mixture Bilinear Mblk(10mentioning

confidence: 96%

On an independent and identically distributed mixture bilinear time-series model

Aknouche

Rabehi

2010

Journal of Time Series Analysis

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A class of nonlinear time-series models in which the underlying process follows a finite mixture of bilinear representations is proposed. The mixture feature appears in the conditional distribution of the process which is given as a finite mixture of distributions evaluated at the normed innovations of diagonal bilinear specifications. This class is aimed at capturing special characteristics exhibited by many observed time series such as tail heaviness, multimodality, asymmetry and change in regime. Some probabilistic properties of the proposed model, namely strict and second-order stationarity, geometric ergodicity, covariance structure, existence of higher order moments, tail behaviour and invertibility, are first studied. Parameter estimation is then performed through the EM algorithm, performance of which is shown via simulation experiments. Applications to some real-time-series data are proposed and through which it is shown how neglecting the mixture framework in a bilinear representation results in a loss in adequacy. Copyright Copyright 2010 Blackwell Publishing Ltd

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Section: Probabilistic Structure Of the Mixture Bilinear Mblk(10mentioning

confidence: 96%

On an independent and identically distributed mixture bilinear time-series model

Aknouche

Rabehi

2010

Journal of Time Series Analysis

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“…In this case, the process has short memory. As pointed in Francq et al (2008), existence and uniqueness of a strictly stationary solution of (2) hold under a less restrictive condition than p j=1 a 2 j < 1. Denote…”

Section: Application To An Autoregressive Process With Larch Errorsmentioning

confidence: 98%

“…Theorem 3.1 in Francq et al (2008) asserts that equation 2admits a strictly stationary solution if and only if…”

Section: Application To An Autoregressive Process With Larch Errorsmentioning

confidence: 99%

“…Then the model (2) is a special case of a more general quadratic ARCH model introduced by Sentana (1995). Stationarity conditions and mixing properties of LARCH( p) processes are studied by Francq, Makarova, and Zakoïan (2008). LARCH processes capture some classical stylized facts of financial time series but their volatility is in fact very atypical.…”

Section: Introductionmentioning

confidence: 99%

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On a Family of Contrasts for Parametric Inference in Degenerate Arch Models

Truquet

2014

Econom. Theory

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In this paper, we introduce a family of contrasts for parametric inference in ARCH models the volatility of which exhibits some degeneracy. We focus specifically on ARCH processes with a linear volatility (called LARCH processes), for which the Gaussian quasi-likelihood estimator may be inconsistent. Our approach generalizes that of Beran and Schützner (2009) and gives an interesting alternative to the WLSE used by Francq and Zakoïan (2010) for an autoregressive process with LARCH errors. The family of contrasts is indexed by a single parameter that controls the smoothness of an approximated quasi-likelihood function. Under mild conditions, the resulting estimators are shown to be strongly consistent and asymptotically normal. The optimal asymptotic variance is also given. For LARCH processes, an atypical result is obtained: under assumptions, we show that the limiting distribution of the estimators can be arbitrarily close to a Gaussian distribution supported on a line. Extensions to multivariate processes are also discussed.

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“…The Fisher-ADF test is the most reliable test and provides a basic model to test for a stochastic trend (Stock and Watson, 2003). The usefulness of the Fisher-PP test over the Fisher-ADF test is that it corrects for heteroscedasticity in error terms (Francq et al, 2008). In contrast, the Breitung test is powerful for testing the data series with fixed effects and small sample size (Kıran et al, 2009).…”

Section: Testing For Integration and Cointegrationmentioning

confidence: 99%

Regional analysis of the impact of inward foreign direct investment on economic growth in the Chinese electronic industry

Liu

Agbola

2014

Applied Economics

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This article empirically investigates the impact of inward foreign direct investment (FDI) on regional economic growth in the Chinese electronic industry (CEI). Utilizing a provincial-level panel data spanning the period 1989 to 2009, we specify and estimate an endogenous economic growth model for the CEI. Empirical results indicate that, for the coastal region, FDI inflows have been growth enhancing, while in the central and western regions the impact of FDI on economic growth is mixed, depending on the channel of capital flow. Results also indicate that exports, human capital, science and technology investment and fixed asset investment are growth enhancing, while unemployment and foreign R&D investment are growth impeding in the CEI.

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A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test

Cited by 12 publications

References 50 publications

On an independent and identically distributed mixture bilinear time-series model

On an independent and identically distributed mixture bilinear time-series model

On a Family of Contrasts for Parametric Inference in Degenerate Arch Models

Regional analysis of the impact of inward foreign direct investment on economic growth in the Chinese electronic industry

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