The Effect of Level Shift in the Unconditional Variance on Predicting Conditional Volatility

We evaluate out-of-sample forecasting performance of different pre-diction models using different estimation windows to account for a variety of statistical characteristics such as the long range dependence and the structural breaks of the process. We identify the timing of the deterministic shifts in the unconditional variance and evaluate the impact of accounting for the level shifts in the unconditional variance on out-of-sample volatility forecasting. The mod-ified iterated cumulative sums of squares algorithm identifies two shifts in the unconditional variance for the KOSPI (Korea Composite Stock Price Index) re-turns. For the KOSPI returns process, the full sample performance of the re-cursive GARCH(1,1) model is worse than the competing models, which is un-surprising given two structural breaks in the process. The superiority of the competing models in forecasting performance can be attributed to the capability of the model which accommodates both the long range dependence by giving a slow hyperbolic rate of decaying weights on the past observations in forming the likelihood and the structural changes in the variance by discarding observations beyond a rolling window length distance in the past which may have come from a different regime. Although we try to improve the forecasting performance by incorporating statistical characteristics of the process into a prediction model, the out-of-sample performance of the prediction model can be tainted with un-certainties related to statistical tests and estimation methodologies.