Abstract
In this paper, a randomised pseudolikelihood ratio change point estimator for GARCH model is presented. Derivation of a randomised change point estimator for the GARCH model and its consistency are given. Simulation results that support the validity of the estimator are also presented. It was observed that the randomised estimator outperforms the ordinary CUSUM of squares test, and it is optimal with large variance change ratios.
Highlights
Volatility plays a very important role in financial derivatives; a good prediction of volatility will provide a more accurate pricing model for financial assets. e autoregressive integrated moving average (ARIMA) models developed by Box and Jenkins [1] assume a constant conditional variance of the errors; financial data do not obey this assumption
Lamoureux and Lastrapes and Hillebrand [6, 7] reported that the application of GARCH models to long time series of stock returns yields a high measure of persistence because of the presence of shifts in the data generating parameters of these models, leading to false results. e problem of structural changes prompted the idea of change point detection and estimation and has found applications in quality control, climate change, finance, etc
We study a randomised change point estimator in GARCH models, where we allow the test statistic to be data driven
Summary
Volatility plays a very important role in financial derivatives; a good prediction of volatility will provide a more accurate pricing model for financial assets. e autoregressive integrated moving average (ARIMA) models developed by Box and Jenkins [1] assume a constant conditional variance of the errors; financial data do not obey this assumption. E autoregressive integrated moving average (ARIMA) models developed by Box and Jenkins [1] assume a constant conditional variance of the errors; financial data do not obey this assumption For this reason, Engle [2] proposed the Autoregressive Conditional Heteroscedastic (ARCH) model; this model has found wide applications in finance modeling. Lee et al [16] studied variance change based on Inclan and Tiao [9] test for errors in AR(p) models and kernel-type estimator regression model. E change point problem for variance change has usually been viewed as deterministic Contrary to this notion, we study a randomised change point estimator in GARCH models, where we allow the test statistic to be data driven
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