The Analysis Of Integral Value Discrete Time Series Based On P-th Order Mixture Operator And Its Application

In the real life and economic fields,there are a large number of discrete time series.Simply using the continuous time series model to fit the discrete time series is insufficient to meet the needs of academic research.More and more scholars are investing in the study of discrete time series to explore the statistical laws behind discrete time series.From the perspective of ensuring the rationality,accuracy and convenience of the discrete time series,the INAR(p)model based on the Thinning operator is favored in the existing discrete time series modeling.Scholars have successively proposed INAR(p)models with different marginal distributions,and their parameter estimation methods,and have carried out active application research.Since the INAR(p)model has many similar properties with the continuous time series model,we choose to add the mixed operator based on the INAR(p)model,ie the Pegram mixed operator.The work of this paper is to combine the Pegram mixture operator with the mainstream Thinning operator model to form a new discrete time series application model.The model extends the smooth non-negative integer model and establishes the p-order nonnegative integer mixed operator(MPT(p))model.The MPT(p)model takes full account of the autocorrelation and dispersion of the data and uses simulation studies to prove the validity of the model.At the same time,the autocorrelation structure of the MPT(p)model is also given.The parameters are estimated using the Yule-Walker equation,and the parameter properties of the model are studied.Through simulation data,the model parameter estimation effect is shown,and the model is innovatively applied to the stock trading volume data.Through the data prediction results,the prediction of MPT(2)is better than the prediction of INAR(2)model model.This shows that the model proposed in this paper can achieve better short-term forecasting.The specific operations are as follows:First of all,in order to prove the excellent properties of the model,this paper proves that the model's auto-regression function is the same as the AR(p)model.This ensures that the model can easily use the Yule-walker equation to estimate the parameters in the parameter estimation.At the same time,it is proved that the prediction formula of MPT(p)model is the same as AR(p)model,and one-step transfer matrix and probability generation function are given,which lays a good foundation for the next numerical simulation.Secondly,using the cumulative distribution inversion of the model,the randomness of the model data is proved to be good,and then in order to prove that the Yule-walker equation estimation is effective,this paper selected three different combinations of parameters and selected different Monte Carlo.The amount of data is used to simulate the data.The simulation results prove that the Yule-walker equation can effectively estimate the parameters of the model and prove the reasonable validity of the model.In order to verify that the MPT(p)model presented in this paper has excellent application prospects in empirical modeling,this paper also carried out empirical simulations.Finally,in this paper,we use the autoregressive map and partial autocorrelation map to determine the order of the model and establish the MPT(2)model.The residual analysis shows that the model can effectively and effectively extract the effective information of the actual data,and compares and analyzes the predicted values and trends for the mainstream INAR(2)model,and gives the prediction of success rate.The excellent nature of the model.