The Spurious Regression Study Based On The Gradual Approximation Theory

Chinese economy and society develop rapidly, which leads to the research of stock returns prediction emerge in endlessly. Especially with the rapid development of the progress of economy, technology and the introduction of data mining technology, more and more companies, the Internet and large databases provide vast amounts of information to the public with the way of electronic data, and the research methods of stock are more and more, which have added spurious regression phenomenon.Therefore, in view of the high persistence of variables and plentiful noise of predictive return stock, it is particularly important and far-reaching significance to explain the spurious regression phenomenon.In this paper, controlling data information, noise and data size to study what factors and how much information and noise will affect stock returns prediction through theoretical study and the Monte Carlo simulation, which results a spurious regression.With the help of Monte Carlo simulation generating data of yield sequence and variable data, and using the regression forecasting and auto regression analysis get all the commonly used statistics, and using the research method of combining the statistics of the signal and noise, sample size, persistence and correlation study the asymptotic distribution of all statistics and the performance of the regression model. Finally, pick the Shanghai index returns and Shenzhen index returns as the research sample, and combining with the Monte Carlo simulation results of stock returns analyze spurious regression of yield sequence.Studies have found that increasing the observed data does not make the signal of data increase as the same ratio with the sample data increasing, which now increase more is noise but not the information to predict. In addition, the increasing observed data makes data easily have the same trend and produce spurious regression. In general,when the ratio of the signal to noise and sample size reaches a certain, the credibility of t test get small, and the fitting degree of regression get low, and slope coefficient exist spurious regression phenomenon. This article have also analyzed spurious regression phenomenon of the Shanghai index returns, and compared spurious regression predict phenomenon of the returns of Shanghai securities composite index and Shenzhen securities composite index with the high degree of trend sequences. Founding that it is insufficient to judge spurious regression phenomenon just referencing parametera, and predictors should combine the signal and noise ratio, the correlation coefficient of regression residuals and explanation variables’ auto regression residuals, the persistence of the stock returns and the persistence of the explanatory variables into account. On theother hand, for the low degree of trend of stock returns and prediction variables,forecasters can simply reference parameters a and signal to noise ratio statistics judging spurious regression phenomenon, and other statistics as auxiliary reference factors, which help to find out the real relationship between economic variables.