Related Research And Application Of Homogeneous Markov Chain

Markov chain is an important tool for prediction,which is widely used in various fields,such as finance and hydrology.This paper mainly studies the generation,estimation and application of the one-step transition probability matrix of homogeneous Markov chain.The main work is as follows:(1)Discuss the stationarity of the homogeneous finite Markov chain.From the distribution of any Markov chain,combined with the method of contradiction,it is proved that any Markov chain is neither a strictly stationary process nor a wide stationary process.For stability state Markov chain,using time-shift invariance and the property of broad stationary to prove that it is both a strictly stationary process and a broad stationary process.(2)By studying two methods of generating Markov chains from different sampling methods: sampling generation based on Frequency-Distribution and generation based on Metropolis-Hastings sampling,and then use D-optimum criterion,A-optimum criterion,deviation and mean square error as comparison indicators to compare the pros and cons of the generation methods by generating the transition probability matrix of the Markov chain.The computer simulation results show that it is better to generate Markov chains based on Frequency-Distribution sampling.(3)Starting from the C-K equation method and the frequency instead of probability method,respectively,the Markov chain transition probability matrix is estimated,and the advantages and disadvantages of the estimation methods are compared based on the D-optimum criterion and the A-optimum criterion.The computer simulation results show the C-K equation method is better.(4)Aiming at the problem of the weight calculation of the weighted Markov chain prediction method that does not consider the stationarity of the Markov chain,an improved weighted Markov chain prediction method is proposed.And the improved method is analyzed from both hydrological and financial aspects.The weighted Markov chain prediction method is empirically analyzed,and it is verified that the weighted Markov chain prediction method improved based on the C-K equation method is better.