Asymptotic Theory for a Vector Arma-garch Model
نویسندگان
چکیده
This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment condition+ This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity ~ARCH! and GARCH models+ Moreover, the asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors+ Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models and also a consistent estimator of the asymptotic covariance+
منابع مشابه
On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations
This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standard...
متن کاملRecurrent Support and Relevance Vector Machines Based Model with Application to Forecasting Volatility of Financial Returns
In the recent years, the use of GARCH type (especially, ARMA-GARCH) models and computational-intelligence-based techniques—Support Vector Machine (SVM) and Relevance Vector Machine (RVM) have been successfully used for financial forecasting. This paper deals with the application of ARMA-GARCH, recurrent SVM (RSVM) and recurrent RVM (RRVM) in volatility forecasting. Based on RSVM and RRVM, two G...
متن کاملWind speed forecasting based on autoregressive moving average- exponential generalized autoregressive conditional heteroscedasticity-generalized error distribution (ARMA-EGARCH-GED) model
With the increase of wind power as a renewable energy source in many countries, wind speed forecasting has become more and more important to the planning of wind speed plants, the scheduling of dispatchable generation and tariffs in the day-ahead electricity market, and the operation of power systems. However, the uncertainty of wind speed makes troubles in them. For this reason, a wind speed f...
متن کاملEstimation in ARMA models based on signed ranks
In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performa...
متن کاملR-estimation for Arma Models
This paper is devoted to the R-estimation problem for the parameter of a stationary ARMA model. The asymptotic uniform linearity of a suitable vector of rank statistics leads to the asymptotic normality of √ n-consistent R-estimates resulting from the minimization of the norm of this vector. By using a discretized √ n-consistent preliminary estimate, we construct a new class of one-step R-estim...
متن کامل