Quasi-maximum likelihood estimation of periodic GARCH processes
نویسندگان
چکیده
This paper establishes the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution for the periodic GARCH (P -GARCH) equation. As a result, it is shown that the moment of some positive order of the P -GARCH solution is finite, under which we prove the strong consistency and asymptotic normality (CAN) of the QMLE without any condition on the moments of the underlying process.
منابع مشابه
Likelihood-Related Estimation Methods and Non-Gaussian GARCH Processes
This article discusses the finite distance properties of three likelihood-based estimation strategies for GARCH processes with non-Gaussian conditional distributions: (1) the maximum likelihood approach; (2) the Quasi Maximum Likelihood approach; (3) a multi-steps recursive estimation approach (REC). We first run a Monte Carlo test which shows that the recursive method may be the most relevant ...
متن کاملEffects of Outliers on the Identification and Estimation of Garch Models
This paper analyses how outliers affect the identification of conditional heteroscedasticity and the estimation of generalized autoregressive conditionally heteroscedastic (GARCH) models. First, we derive the asymptotic biases of the sample autocorrelations of squared observations generated by stationary processes and show that the properties of some conditional homoscedasticity tests can be di...
متن کاملThe Efficiency of the Estimators of the Parameters in Garch Processes
We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maxim...
متن کاملProperties and Estimation of GARCH(1,1) Model
We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...
متن کاملRank-Based Estimation for GARCH Processes
We consider a rank-based technique for estimating GARCH model parameters, some of which are scale transformations of conventional GARCH parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in Jaeckel (1972). They are useful for GARCH order selection and preliminary estimation. We give a limiting distribution for the rank estima...
متن کامل