Research Of Stock Market Index Based On Markov Regime Switch Model

With the acceleration of my country's financial opening up,stock market transactions have become more frequent.The role of the stock market is twofold.Its role is to use its various functions to achieve people's expectations.It has both the positive side of promoting social and economic development and the negative side of increasing economic crisis and investment risk,but in general,it is still a new and vitality emerging from the process of socialized production.But the stock market is unpredictable,so the research on the stock market has practical significance.First,this article introduces several commonly used distributions and stochastic pro-cesses in the financial field,such as geometric Brownian motion,geometrically stable pro-cesses,etc.,and explains some of their properties.It also introduces the Markov mechanism conversion model,and focuses on the Markov mechanism conversion model(MSOU)of the OU process?uses the maximum likelihood estimation method to estimate the parameters of the MSOU,and refers to the forward algorithm of the neural network,The complete like-lihood function is improved to a compound likelihood function.Greatly reduce the amount of calculation.Assuming that the sequence length is T,the calculation time of the complete likelihood function is an exponential function of T,and the use of the coincidence likeli-hood function reduces the calculation time to a linear function of T,which greatly reduces the amount of calculation.Based on the improved composite likelihood function,the EM algorithm is used to estimate the parameters,and the convergence of the EM algorithm is proved.Secondly,this article implements all codes of two-state MSOU estimation under the assumption of normal distribution of residuals.The data was simulated ten times,and the ARMA and MSOU modeling were performed on them respectively.The results show that the MSOU model is more effective.The MSOU modeling results show a high state recogni-tion accuracy rate.In ten simulations,the minimum accuracy rate is 91.36%,the maximum accuracy is 97.67%,and the average of ten times is 95.81%.On the other hand,it is also found that if the probability of one state transitioning to another state is too high,that is,if p_iiis too large,the effect of its parameter estimation will be worse.Modeling of simulated data also shows that the use of BIC criteria can better select the number of parameters to be estimated in the model.Next,on the basis of the modeling conclusion of the simulation data,using the BIC criteria,the ARMA and MSOU modeling analysis of the Shanghai Stock Exchange Index from 2011 to 2020 is carried out.Also MSOU performed better.In the empirical analysis,the two-state model and the three-state MSOU model were tried respectively.In the three-state model,the p_iiof the two states are too large,and the jumps between states are too frequent,and it can be seen from the modeling conclusion of the simulation data that the effect of parameter estimation on them at this time Will get worse.Compared with the two-state model,p_iiare very small,and the jumps between states are not frequent,which is more suitable for actual investment analysis.The modeling of actual data found that the stable distribution is closer to the actual dis-tribution of residuals than the normal distribution.Therefore,the MSOU model is improved based on the assumption of stable residual distribution.The two-state MSOU model divides the hidden state of the stock market into two categories,which can be regarded as”bear mar-ket”and”bull market.”The duration of the bear market is longer than that of the bull market,which is consistent with the actual situation.And respectively estimate the daily average return rate of the bear market is-0.0114,and the daily average return rate of the bull market is 0.0311.In addition,this article also uses the Shanghai Stock Exchange Index from 2011 to 2012as an example.Combining the commonly used tool”MSOU”for stock investment with the MSOU model has better played the guiding role of the model in actual investment.