On periodic time-varying bilinear processes: structure and asymptotic inference

Bibi, Abdelouahab; Ghezal, Ahmed

doi:10.1007/s10260-015-0344-5

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…The BF approach has known several developments. In particular, it has been extended to time-dependent bilinear models [43], periodic bilinear models [44], periodic ARMA models (PARMA) with periodic bilinear innovations [45] and to GARCH models with time-varying coefficients [46,47]. More recent works on closely related models, such as weak ARMA models with regime changes [48], prefer to find a stationary and ergodic solution to the model equation.…”

Section: The Theory Of Cyclically Time-dependent Modelsmentioning

confidence: 99%

Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches

Azrak¹,

Mélard²

2022

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Autoregressive-moving average (ARMA) models with time-dependent (td) coefficients and marginally heteroscedastic innovations provide a natural alternative to stationary ARMA models. Several theories have been developed in the last 25 years for parametric estimations in that context. In this paper, we focus on time-dependent autoregressive (tdAR) models and consider one of the estimation theories in that case. We also provide an alternative theory for tdAR processes that relies on a -mixing property. We compare these theories to the Dahlhaus theory for locally stationary processes and the Bibi and Francq theory, made essentially for cyclically time-dependent models, with our own theory. Regarding existing theories, there are differences in the basic assumptions (e.g., on derivability with respect to time or with respect to parameters) that are better seen in specific cases such as the tdAR(1) process. There are also differences in terms of asymptotics, as shown by an example. Our opinion is that the field of application can play a role in choosing one of the theories. This paper is completed by simulation results that show that the asymptotic theory can be used even for short series (less than 50 observations).

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Section: The Theory Of Cyclically Time-dependent Modelsmentioning

confidence: 99%

Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches

Azrak¹,

Mélard²

2022

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“…The asymptotic properties of the (G) M M and (C) LS estimates have been also discussed under certain restrictions (see for example, Liu [28], Grahn [23], Wittwer [34] and among others). Recently, Bibi et al [8,11] have developed certain procedures for estimating some special bilinear processes with periodically time-varying parameters. In this section, we focus on the estimation of the parameter governing the following model…”

Section: Quasi-maximum Likelihood Estimation For Sp Blmentioning

confidence: 99%

“…The model (1.1) has been studied by Bibi et al { [5,7,8,9,10,11]}, more precisely, with respect to the probabilistic properties, Bibi [5], beside the motivations proposed to introduce the class of bilinear models with time-dependent coefficients, he also studied the L 2 −structure and some empirical properties of such models. In particular, with periodic coefficients, Bibi and Lessak [9] have established some sufficient conditions for the existence of causal, periodically correlated (P C) and β−mixing of the solution process for some specifications of (1.2) (see the subsection 2.2 for a definition of P C processes).…”

Section: Introductionmentioning

confidence: 99%