Model selection and post selection to improve the estimation of the ARCH model

The Autoregressive Conditionally Heteroscedastic (ARCH) model is useful for handling volatilities in economical time series phenomena that ARIMA models are unable to handle. The ARCH model has been adopted in many applications that contain time series data such as financial market prices, options, commodity prices and the oil industry. In this paper, we propose an improved post-selection estimation strategy. We investigated and developed some asymptotic properties of the suggested strategies and compared with a benchmark estimator. Furthermore, we conducted a Monte Carlo simulation study to reappraise the relative characteristics of the listed estimators. Our numerical results corroborate with the analytical work of the study. We applied the proposed methods on the S&P500 stock market daily closing prices index to illustrate the usefulness of the developed methodologies.