Statistical Arbitrage Analysis In Financial Markets Based On The Chebyshev Polynomials Of Time-Varying Co-Integration

Variable coefficient model is widely applied in econometrics and biomedical,due to the fact that the model has good robustness and easy to explain,etc.At present,the time-varying coefficients co-integration model has attracted attentions from some scholars,especially the discussion of the time-varying in co-integration relation between variables is very active,but the application of statistical arbitrage strategy is very rare.This paper will study time-varying coefficients co-integration model of statistical arbitrage strategy problem in different financial markets.Compared with the classical ECM model,time-varying ECM model established by Chebyshev polynomials has certain difficulty on the theoretical research,such as time-varying,the term?_t?=??_t?of parameter estimation and estimation of asymptotic distribution,etc.Because the time-varying coefficients co-integration model in this paper takes into account the standard co-integration model,though the problem is more difficult,the results are more affluent.Firstly,the paper makes a theoretical analysis of standard co-integration model and time-varying co-integration model.The standard co-integration model assumes that coefficient is fixed,considering the co-integration vector with time-varying characteristics,the paper introduces the Chebyshev polynomials approximation method to establish time-varying coefficients of co-integration model.This model transforms coefficient into a function of time variable,to improve the prediction ability of model.Secondly,the paper uses daily data of the northeast securities and GF negotiable securities in the brokerage business to make statistical arbitrage analysis on the basis of the standard co-integration model.Considering time-varying co-integration relationship,this paper improves the structure mutation point of financial time series of detection methods.Using the new model to detect change points,and uses these change points to set up variable structure co-integration model.Further,the paper operates statistical arbitrage performance analysis again under the different Chebyshev polynomials order situation.Next,this paper selects China CYTS Tours and LJG Tours two stocks in the tourism sector to arbitrage analysis and performance comparison of the above two models.Considering the application of time-varying co-integration model in different financial markets,this paper selects the daily data of Swiss francs/yen and euro/yen in the foreign exchange market to statistical arbitrage analysis of standard co-integration and time-varying co-integration.Considering the influence of high frequency data on statistical arbitrage strategy,this paper selects one minute trading data of the futures market IF1706 and IF1707for arbitrage analysis.The above results show that the application of time-varying co-integration model in the stock market,foreign exchange market and futures market are effective.The statistical arbitrage performance that based on the time-varying coefficients co-integration model to detect variable structure point is superior to the standard co-integration model of arbitrage performance.At the same time,the number of change point is equal to the order of Chebyshev time polynomials.The number of mutation point is not the more the better in the situation of statistical arbitrage.