A study on comparative analysis of heteroscedasticity tests used in nonlinear time series modelling

This study describes the methods to determine the non-linear behavior in financial time series and specifically to test for volatility using heteroscedastisity tests classified into three different groups - linearity tests, tests for autocorrelation and tests for the presence of ARCH or GARCH effects. The simulation study has been conducted in order to compare Park, Glejser, Breusch-Godfrey LM, White and ARCH LM test results by virtue of power of test. In accordance with the non-linear models with different combinations of parameter values, different number of data sets with different size was generated with the use of simulation methodology. Each of heteroscedastisity tests was applied to each of simulated non-linear time series data resulting in test statistics calculation. To make comparison, the power of tests was calculated and the advantages and disadvantages of tests were shown.Simulation results were verified using comparison of the heteroscedastisity tests applied on 11 real different non-linear data incorporating volatility by virtue of P - Value Method.As a result, simulation study showed the most powerful tests, whereas real-data study showed them to be with low p-value. This illustrates that real-data study have proved correctness of conclusions of simulation study.Key Words: ARCH, GARCH, Volatility, Test for Heteroskedasticity, Simulation, Power of Test.