A Random Weighted Linear Estimator Of The ARCH Parameters

The traditional econometrics is the mainstream tools of mathematical in our research and analysis, many model assumes that the selected samples meet homoskedastic conditions, however, with the development of financial theory and empirical work thorough, we have found this assumption is not reasonable. In 1982, the UK inflation study, Engel accurate measurement of how to real-time dynamic characterization income fluctuation, proposed heteroscedastic for the ARCH model to solve these problems effectively. ARCH family model become the main model in describing financial risks due to the of financial risk can more accurately than ever to the accurate model depict,. But the ARCH family model depends on the accuracy of the parameter estimation of accuracy, so the ARCH model parameters estimation method improvement become currently restrict its further application.For the traditional linear model, the main parameters estimation methods have least-square estimation, maximum likelihood estimation and moments estimate, suitable for different cases respectively the model parameters estimation. In recent years gradually become econometric model is relatively commonly used methods of parameter estimate. But the ARCH family model, so a typical nonlinear model for the maximum likelihood estimation, often restricted to optimal solution algorithm, could not find the optimal solution or the only solution. Even in estimation formula, reduce disturbance in to our research in the overall got too big, we can obtain under the influence of an approximate optimal solution, this regarding the non-normal randomized treatment effect is better. However accurate maximum likelihood method calculation is very difficult, and sample size is lesser, likelihood value tend to be flat. More importantly: when the estimate must parameters is strictly to restrain, this also the application. In the parameter equals to zero when significant test, we also can't get original hypothesis of the limiting distribution parameters. Some shortcomings are limiting the ARCH model application. Stochastic weighted method than previously linear estimator research methods improved certain precision, special is random weighting method for linear estimate methods in the ARCH model parameter estimation of parameters have no binding requirement. On the analysis of the sample data of financial markets, can get a more accurate results. The main theme of the more advanced lies in linear estimator random weighting method, method is applied to the ARCH model and the previous research the ARCH model parameters of maximum likelihood method must compare, concluded that random weighting method in the ARCH model of linear estimation method has better parameter estimation of applicability.