Long Memory Mixing GAS Copula Models And Its Application In Portfolio

The correlation between financial assets has always been the focus of scholars’ research.With the increasing trend of international economic integration,the geographical correlation of various financial assets has also increased,which has given birth to an important topic of modern financial market analysis,namely,the interdependent structure and time-varying characteristics of financial assets.Due to the long memory nature of correlations between assets,the study of correlations between assets can be used to more accurately predict future asset correlations using information that exists about these assets.This helps investors to more accurately grasp the correlation structure of assets in the long memory phase and optimize asset allocation to maximize returns.Regarding the study of asset volatility,scholars have gradually evolved from the initial ARCH model to the Generalized Autoregressive Score(GAS)model using scoredriven parameter updates to explore the forecasting methods of the series from multiple perspectives.Later,as the research on high-frequency data continued,scholars found that the realized measures calculated from high-frequency data could effectively capture linear correlations and improve the predictive power of variance and covariance.Ghysels,Santa-Clara and Valkanov(2004)formally proposed the Mixed Data Sampling(MIDAS)model,which incorporates data of different frequencies into the model to jointly fit the data and forecast,so as not to corrupt the data,but also to efficiently mine the information of the sample data.Therefore,this paper constructs a long-memory mixed-frequency dynamic GAS Copula model based on the mixed-frequency data sampling method with high-frequency achieved measures as the driving factor,and explores its application in stock portfolios.In summary,the thesis builds on the Mixed Data Sampling-Generalized Autoregressive Score(MIDAS-GAS)model based on the generalized autoregressive score proposed by Gorgia,Koopman,and Li(2019),with reference to the Melo Mendes(2008)proposed FIGARCH(Fractional Integrated Generalized Autoregressive Conditional Heteroskedasticity)model incorporates long memory fractional integer coefficients,adds realized volatility as a covariate,and combines Copula function,the MIDAS-FIGRAS(Mixed Data Sampling Fractional Realized Integrated Generalized Autoregressive Score)Copula model is introduced to study the time-varying characteristics of correlation between asset series to improve the fit and prediction accuracy.In the Monte Carlo simulation section,five different dynamic processes are simulated,and the Bayesian Information Criterion(BIC),Mean Absolute Error(MAE),and Mean Square Error(MSE)are used for GAS,GRAS,FIGRAS,and FIGRAS.GRAS,FIGRAS and MIDAS-FIGRAS models were compared and analyzed for their fitting and prediction ability.It is found that FIGRAS with the addition of long memory fractional integer coefficients has a better performance,and MIDAS-FIGRAS also has a good performance in some specific cases.In this part of the empirical analysis,six stocks,Alibaba,Tencent Holdings,Qixing,Starnet,CITIC Heavy Industries and Huashu Media,are classified into high,medium and low correlation portfolios based on their daily return correlation coefficients,and descriptive statistics are performed on the daily return series of each stock to model the marginal distribution and combine with Copula function to describe the change in the correlation structure of each portfolio,using log-likelihood function values,The predictive ability of the MIDAS-FIGRAS model was compared using the rolling predictive density function and the conditional predictive ability(CPA)test.FIGRAS model performs better than other models in terms of predictive ability.Finally,the optimal investment weight is obtained by combining the Coefficient of Relative Risk Aversion(CRRA)function,and the performance of each model is compared in the form of management fee for portfolio application.The conclusions are as follows: the improved long-memory mixed-frequency Copula model has some improvement in in-sample fitting effect and out-of-sample prediction ability,and it is more obvious in t-distribution with thick-tailed characteristics.It shows that based on the Copula correlation structure,adding the fractional integer coefficient and considering the long memory nature of time series can fully exploit the information of data with multiple lags.Secondly,adding high-frequency realized measures is helpful to improve the model’s ability to portray and predict dynamic correlations,in addition to the asset closing prices,and to change new information when supplementing the driving dependence parameters.Finally,based on the utility function transformed management fee,it is found that investors are more willing to pay a fee to move from the base model to the relatively complex but more capable long-memory mixed-frequency Copula model,which can avoid market risk to a greater extent and improve portfolio returns.