In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes whic...In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years.So,the L_(2)-structure of the process is studied and its covariance function is given.These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process.Finite sample properties are also considered through Monte Carlo experiments.In end,the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar.展开更多
In this paper,I propose a natural extension of time-invariant coefficients threshold GARCH(TGARCH)processes to time-varying one,in which the associated volatility switch between different regimes due to dependency of ...In this paper,I propose a natural extension of time-invariant coefficients threshold GARCH(TGARCH)processes to time-varying one,in which the associated volatility switch between different regimes due to dependency of its coefficients on unobservable(latent)time homogeneous Markov chain with finite state space(MS-TGARCH).These models are showed to be capable to capture some phenomena observed for most financial time series,among others,the asymmetric patterns,leverage effects,dependency without correlation and tail heaviness.So,some theoretical probabilistic properties of such models are discussed,in particular,we establish firstly necessary and sufficient conditions ensuring the strict stationarity and ergodicity for solution process of MS-TGARCH.Secondary,we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator(QMLE)for estimating the unknown parameters involved in model and we examine thus the strong consistency of such estimates.The finite-sample properties of QMLE are illustrated by a Monte Carlo study.Our proposed model is applied to model the exchange rates of the Algerian Dinar against the single European currency(Euro).展开更多
文摘In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years.So,the L_(2)-structure of the process is studied and its covariance function is given.These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process.Finite sample properties are also considered through Monte Carlo experiments.In end,the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar.
文摘In this paper,I propose a natural extension of time-invariant coefficients threshold GARCH(TGARCH)processes to time-varying one,in which the associated volatility switch between different regimes due to dependency of its coefficients on unobservable(latent)time homogeneous Markov chain with finite state space(MS-TGARCH).These models are showed to be capable to capture some phenomena observed for most financial time series,among others,the asymmetric patterns,leverage effects,dependency without correlation and tail heaviness.So,some theoretical probabilistic properties of such models are discussed,in particular,we establish firstly necessary and sufficient conditions ensuring the strict stationarity and ergodicity for solution process of MS-TGARCH.Secondary,we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator(QMLE)for estimating the unknown parameters involved in model and we examine thus the strong consistency of such estimates.The finite-sample properties of QMLE are illustrated by a Monte Carlo study.Our proposed model is applied to model the exchange rates of the Algerian Dinar against the single European currency(Euro).
