Application Of A High-order Markov Chain In Rainfall Forecasting

Rainfall forecasting is of great significance to the agricultural and economic de-velopment of our country.Rainfall could form a sample sequence in chronological order.Some researchers have found that they have Markov property by studying rainfall sequences,so a first-order Markov chain rainfall forecasting model was es-tablished.The characteristics of first-order Markov chains are that the next state is only related to the current state,and any other information about the past is irrelevant for forecasting.However,for some rainfall sequences with multi-period dependence,such as monthly and daily rainfall,their next state may depend on the information of past states.Since first-order Markov chains can not solve the multi-period dependence prob-lem,this paper proposes a high-order Markov chain rainfall forecasting model.First,we introduce a new tensor product of high-order Markov transition prob-ability tensor,and some properties and theorems similar to first-order Markov chains are obtained,we also prove some properties such as high-order strong Markov property.Second,based on the characteristics of rainfall sequences,we establish a state partition method which can identify outliers.According to the rainfall sequences,we construct a method for calculating the transition prob-ability tensor and generalizing the first-order Markov test to high-order case.Last,we forecasting the next state by calculating the weighted sum of multi-step transition probabilities.The monthly rainfall data from 1999 to 2017 in Fuzhou City are used to test the model.The forecasting interval and the true value obtained by our model are consistent.Our model has three advantages:1)the problem of multi-period dependence on monthly rainfall forecasting has been solved,2)our model is based on objective facts,3)the calculation of transition probability tensor are more efficient than classical high-order Markov chains.