Analysis Of Modeling High-dimensional Volatility

Volatility of financial assets is the conditional covariance matrix of the return on assets.It reflects not only the uncertainty of asset price dynamics,but also the risk level of financial assets.Therefore,the investigation on the volatility of financial market assets return sequencewill help us to recognize and protect against the risk of financial market.In practice,multiple assets should be considered simultaneously in actual investment process.Moreover,when the sample size(n)and dimension(d)go to infinity,the existing multivariate volatility model will not be able to apply.For the high-dimensional time series,dimension reduction method is used to build the high-dimensional volatility model in this study.First,we decompose the feature of sample covariance matrix based on lagging information.Then the two-step ratio of the eigenvalues method is used to determine the number of factors.And then,we establish a high-dimensional time series factor modelvia estimating the factor loading matrix by the eigenvectors of target matrix.Second,we create a multivariate volatility model of the factor sequence,which is built and compared to EWMA model,O-GARCH model,IC-GARCH model,GO-GARCH model and DCC-GARCH model respectively.Third,the estimated results are further used to construct the high-dimensional volatility.In addition,we also attempt to analyze and forecast the factor sequence by the VAR model,and complete the final prediction of the high-dimensional volatility model.Finally,we have an empirical analysis on the gem stocks data spanning the period of 2014-2015.The main research results of this paper are as follows:(1)We construct the volatility factor model according to the day logarithm yield data that contains 354 dimensions and 489 samples.Firstly,we use two-step ratio estimation method to estimate the factor number and select two factors(strong factor and weak factor).Secondly,by calculating the score sequence of the factor,we found that there is a negative immediate relevance between two factors and the correlation coefficient is-0.91.In addition,through the study of the linear dynamic dependency of factor score sequence inspection and cross correlation,we also found that there is a certain linear dynamic dependency between the two sequences.(2)We examine ARCH effect for the sequence of the sample and factor score sequence,and the results indicate that the sequence has significant ARCH effect.Hence,we use five different multivariate volatility models to analyze the factor score sequence in this paper.The final results demonstrate that the standard residual series have no ARCH effect,and the models fit well.From the view of the standard error,these five models have similar model accuracy.Among them,DCC-GARCH model works best while O-GARCH model works relativelypoor.Finally,thevolatilitymatrix is of the estimated factors is used into higher dimensional volatility model to complete the construction of high-dimensional volatility model.(3)We set up the VAR model to the estimated factor.Firstly,we select2 as the lag order of this modelto this data through Eviews 9.5.Then we predict the established VAR(2)model for 10 steps ahead,and the predicted value is used to forecast the high-dimensional volatility model.Finally,we execute impulse response analysis on the estimated factor,and the results show that the speed,whichreact to market information and return to a steady state,of strong factor is faster than the weak factor.