The Application On Some Prediction With Markov Chain Model

Markov chain is a discrete time and discrete state stochastic process with the system'smemory. It's a common model to deal with the predicting problem. This paper makes predictionsabout per capita GDP of cities in Anhui, the Oriental 6+1 lottery tickets and the amount ofnational telecommunications business respectively based on Markov chains. This paper isdivided into the following parts:The first part is an introduction which mainly expounds on the research background andapplications of Markov chains at home and abroad.The second part mainly shows some knowledge about the definition and properties ofMarkov chain, the basic theory of predictive analysis . It contains the Chapman-Kolmogorovequation, the classification of states, the limiting probability and stationary distribution. Besides,the classification method of index values, the construction of transition probability matrix andthe inspection of "Markov property" are also mentioned.The third part introduces the optimized prediction method of Markov chain and weightedMarkov chain. The former was used to forecast and analyze per capita GDP of cities in Anhuithrough the optimized prediction method of Markov chain, and acquire the stationary distributionand the return period of each city's future state. It provides a new way for short-term predictionsof each city in Anhui. The latter can be applied to the prediction about the zodiac part of lottery6+1, and the predicted results are in line with the actual numbers, which indicated the feasibilityof Markov chain models in predicting.The fourth part discusses the gray Markov chain and its applications. First, we use the graymodel to predict the amount of national telecommunications services. Then correction thepredicted model by Markov chain, improved the predicted results and give out the intervalranges. Finally we point out some improved-model advantages which result from thecombination of the two above and the aspects we should pay attention to.