Convergence of Heuristic-based Estimators of the GARCH Model
The GARCH econometric model is able to describe the volatility of financial data under realistic assumptions and the convergence of its theoretical estimators has been proven. However, when data is “unfriendly” maximum likelihood estimators need to be computed by stochastic optimization algorithms in order to avoid local optima attraction basins, and thus, a new source of uncertainty is introduced. A formal framework for joint convergence analysis of both, the estimators and the heuristic, has been previously described within the context of the GARCH(1,1) model. The aim of this contribution is to adapt and extend this research to asymmetric and multiple lagged GARCH models. Aspects of subset model selection are also investigated.
KeywordsBayesian Information Criterion GARCH Model Joint Convergence Model Selection Algorithm Smooth Transition Autoregressive
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