Time Series Prediction Of Per Capita GDP Based On Bayesian Theory

GDP per capita is an important reference index reflecting per capita income level and the level of living which takes the resident population of a country and the country of the accounting period into consideration. Although, GDP per capita can't accurately represent China's comprehensive national power like GDP. However, in some extent, it stands for a certain level and degree of national social development. Particularly, to populous country such as ours, GDP per capita is more accurate, deep and full of significance for reflecting national per capita income and living standards.Based on reading many literatures about the prediction of per capita GDP and bayesian statistical inference about parameter estimation, we take economic environment changes as time goes on and data with high correlation in the similar period into account, the model parameters will be changing, we decide to predict China's per capita GDP by combining these two models. Finally, we compare them with the traditional time series model to find it whether they have a higher accuracy or not. The specific study and content include: Firstly, introducing the traditional time series model: autoregressive moving average models ARIMA model. In addition, based on this study, we establish time series model of China's GDP per capital and forecast few future values; Secondly, we build roll time series ARIMA model for a certain length of China's per capita GDP and obtain the estimated parameters as prior information by studying the bayesian statistical inference. To test the sensitivity of the prior distribution method, we do simulation and prediction based on two prior distribution. Next, we predict China's per capita GDP by updating and calculate the parameters of Bayesian estimation with the sample data. Thirdly, we adapt MAPE and RMSE to evaluate different models.The result shows that prediction error of 2013 China's per capita GDP with first bayesian estimation is lower than traditional time series model(1978-2012), but higher than prediction error of 2014 China's per capita GDP. Two predictions effect with bayesian models are better than the traditional time series models(1985-2012).It proves that Bayesian parameter estimation has some scientific, and in order to obtain more accurate parameter estimation, we need assume reasonable priori distribution parameters. At the same time, shortcomings needs further study.