Cross-variety Arbitrage Strategy Research Based On Kalman Filtering Algorithm Under ARIMA Model

This paper mainly uses the theory of statistical arbitrage to study the arbitrage strategies of soybean meal futures and rapeseed meal futures.When conducting statistical arbitrage strategy research,three issues must be addressed:Choose the right matching futures,determine the hedge ratio,and choose the trading threshold.In view of futures selection,the test results show that there is a strong correlation between soybean meal futures and rapeseed meal futures and a relatively stable co-integration relationship,which ensures a long-term equilibrium relationship between the two futures,and is therefore suitable for cross-variety arbitrage research;For the hedge ratio problem,a fixed hedge ratio can be selected,but in practice,the actual value ratio between the two futures will change.If the matching ratio is kept constant,it will bring greater risks,so the core of this article is the need of building a time-varying parameter model,Kalman filtering can use strong and efficient recursive algorithms to solve this problem,The key of this algorithm is the establishment of state space expressions,This article uses the ARIMA model to establish the equation of state,The series of estimated coefficients obtained from the rolling window OLS regression of soybean meal futures and rapeseed meal futures is used as the data basis for establishing the ARIMA model,Finally build the ARIMA(2,1,0)model,the change rule of the matching ratio is obtained by analyzing the time series model,the expression of the state equation can then be transformed into,The expression of the measurement equation is determined by the cointegration relationship between soybean meal futures and rapeseed meal futures,Finally,the Kalman filter algorithm is used to iterate the equation to obtain the time-varying hedge ratio.Thereby,a dynamic co-integration relationship between two futures time series isobtained;Regarding the choice of transaction threshold,use a fixed multiple of standard deviation,when the spread sequence breaks through1 standard deviation,it returns to profit,when it reverts to the mean value,and closes,the stop loss when the spread breaks through the standard deviation of 4 times the standard deviation.This paper selects the five-minute high-frequency data of the main continuous contracts of soybean meal futures and rapeseed meal futures from January 1 to December 31,2019 as samples.The OLS model is used to obain a fixed hedge ratio,The Kalman filter algorithm based on ARIMA model is used to obtain the time-varying hedge ratio,then analyze the strategy.Backtesting inside and outside the sample found that:The annual rate of return,sharpe ratio and winning rate of strategy obtained by kalman filter algorithm under ARIMA model are all higher than that of the common co-integration model,and the maximum retracement is lower than that of the common co-integration model.Therefore,the model based on time-varying pairing ratio has higher returns and lower risks.Moreover,the performance of each performance evaluation index of the two strategies out of sample is better than that of the one in sample,indicating that both strategies can well adapt to the change of spread sequence,and the strategies have good stability.