Semi-Parametric Analysis And Risk Measure Based On Financial Time Series

In the financial markets, the risk of financial assets is due to the volatility of financial assets. So forecasting the volatility of financial time series has become a hot topic in theoretical and empirical financial fields. In this paper, we simulate and predicate the volatilities of The Shanghai index yields sequence with parametric models and semi-parametric methods. Parametric models contain ARCH model, GARCH model, EGARCH model, TGARCH model which base on t-distribution and normal distribution and GARCH-M model based on normal distribution, and semi-parametric methods include kernel density estimation, local polynomial estimation, spline function approximation and additive model. We choose the square of rates of return as true volatilities within the sample space, and calculate the true volatilities within the sample space using 5min high-frequency data. Introduce four error metrics, and compare the true volatilities with the simulated and predicted volatilities using the models. The results show that spline function approximation is the best method in volatility fitting within the sample space, T-EGARCH model is the best method and semi-parametric additive model rank only second to T-EGARCH model in volatility prediction outside the sample space.We can get the estimated and predicted volatilities through the models mentioned above, and calculate the risk of assets using VaR method. Under the given confidence level, we estimate and forecast the VaR of Shanghai composite index within and outside the sample space, compare to the true values, calculate the number of failures, and reach the conclusions by Kupiec failure test. Empirical results show that the simulating results of parametric models whose rates of return based on t-distribution are superior to that based on normal distribution and semi-parametric models are superior to parametric models within the sample space. In addition, the semi-parametric additive model is the most effective model in VaR prediction.From the Empirical analysis, we can come to the conclusions that semi-parametric additive model is the most effective model to describe the features of the financial data. It can be used as a supplement instead of parameter model to provide a powerful research tools to research subjects about forecasting and risk measurement of financial data.