Risk Measure Estimation For Long Memory Time Series Based On Expectiles

In this thesis,we introduce the mathematical definitions of financial market risk measures including Value-at-risk and Expected shortfall and discuss the estimation method,especially semiparametric method based on expectile regression approach.First,we establish an expectile regression model for long memory time series.Then,we estimate parameters using asymmetric least squares regression method.Based on this,we show the method of calculating Value-at-Risk and Expected shortfall.Besides,since the weak convergency property of normalized partial sums of stationary Gaussian sequence with long memory,we investigate the consistency and asymptotic normality of ALS estimates when error terms are long memory stationary Gaussian sequence.In simulation studies,we discover that all estimates are located nearby and get closer to true parameters as the sample size increases when the regressors are inde-pendent of error terms.In contrast,for autoregression models,sample size makes no difference to accuracy of estimation.For both models,the bias and variance get larger as the long-memory parameter gets larger which means the long-memory properties of sequence can affect the ALS estimates.