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Quasi-maximum Likelihood Estimator (quasi-maximum + likelihood_estimator)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Estimation in nonstationary random coefficient autoregressive models

JOURNAL OF TIME SERIES ANALYSIS, Issue 4 2009
István Berkes
Primary 62F05; secondary 62M10 Abstract., We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model Xk = (, + bk)Xk,1 + ek, where (,, ,2, ,2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |, + b0| , 0 and show that ,2 cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for (,, ,2) is proven so that the unit root problem does not exist in the RCA model. [source]

Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes

JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2009
Abdelhakim Aknouche
Primary: 62F12; Secondary: 62M10, 91B84 Abstract., This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution of the periodic GARCH (PGARCH) equation. As a result, it is shown that the moment of some positive order of the PGARCH solution is finite, under which we prove the strong consistency and asymptotic normality of the QMLE for a PGARCH process without any condition on its moments and for a periodic ARMA-GARCH (PARMA-PGARCH) under mild conditions. [source]

A light-tailed conditionally heteroscedastic model with applications to river flows

JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2008
Péter Elek
Abstract., A conditionally heteroscedastic model, different from the more commonly used autoregressive moving average,generalized autoregressive conditionally heteroscedastic (ARMA-GARCH) processes, is established and analysed here. The time-dependent variance of innovations passing through an ARMA filter is conditioned on the lagged values of the generated process, rather than on the lagged innovations, and is defined to be asymptotically proportional to those past values. Designed this way, the model incorporates certain feedback from the modelled process, the innovation is no longer of GARCH type, and all moments of the modelled process are finite provided the same is true for the generating noise. The article gives the condition of stationarity, and proves consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator of the variance parameters, even though the estimated parameters of the linear filter contain an error. An analysis of six diurnal water discharge series observed along Rivers Danube and Tisza in Hungary demonstrates the usefulness of such a model. The effect of lagged river discharge turns out to be highly significant on the variance of innovations, and nonparametric estimation approves its approximate linearity. Simulations from the new model preserve well the probability distribution, the high quantiles, the tail behaviour and the high-level clustering of the original series, further justifying model choice. [source]

APPROXIMATING VOLATILITIES BY ASYMMETRIC POWER GARCH FUNCTIONS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
Jeremy Penzer
Summary ARCH/GARCH representations of financial series usually attempt to model the serial correlation structure of squared returns. Although it is undoubtedly true that squared returns are correlated, there is increasing empirical evidence of stronger correlation in the absolute returns than in squared returns. Rather than assuming an explicit form for volatility, we adopt an approximation approach; we approximate the ,th power of volatility by an asymmetric GARCH function with the power index , chosen so that the approximation is optimum. Asymptotic normality is established for both the quasi-maximum likelihood estimator (qMLE) and the least absolute deviations estimator (LADE) in our approximation setting. A consequence of our approach is a relaxation of the usual stationarity condition for GARCH models. In an application to real financial datasets, the estimated values for , are found to be close to one, consistent with the stylized fact that the strongest autocorrelation is found in the absolute returns. A simulation study illustrates that the qMLE is inefficient for models with heavy-tailed errors, whereas the LADE is more robust. [source]