Abstract
Recently there has been a growing interest in joint estimation of the location and scale parameters using combined estimation functions. Combined estimating functions had been studied in Liang et al. (2011) for models with finite variance errors and in Thavaneswaran et al. (2013) for models with infinite variance<br />stable errors. In this paper, first a theorem on recursive estimation based on estimating functions is extended to multi-parameter setup and it is shown that the unified approach can be used to estimate the location parameter recursively for models with finite variance/infinite variance errors. The method is applied for the joint estimation of the location and scale parameters for regression models with ARCH errors and RCA models with GARCH errors.
Highlights
Estimating function theory is well suited to financial data (see Bera et al (2006))
Combined estimating functions had been studied in Liang et al (2011) for models with finite variance errors and in Thavaneswaran et al (2013) for models with infinite variance stable errors
First a theorem on recursive estimation based on estimating functions is extended to multi-parameter setup and it is shown that the unified approach can be used to estimate the location parameter recursively for models with finite variance/infinite variance errors
Summary
Ghahramani and Thavaneswaran (2009, 2011) have studied GARCH model identification and recursive estimation by combining least squares and least absolute deviation estimating functions and the method has been applied to identify several financial time series models. Thavaneswaran and Ravishanker (2015) studied recursive estimation for circular time series models using estimating functions. The following example motivates the use of estimating function theory for recursive estimation of the parameter in certain time series models with stable errors. In Thavaneswaran et al (2013) a fast, on-line, recursive parametric estimation for the location parameter based on transformed estimating functions is discussed using simulation studies, and a real financial time series is discussed in some detail.
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