The Spurious Regression Research Of Heavy-tailed Sequence In The Presence Of Structural Breaks

Since the1920s, the spurious regression has been one of the hot issues that be discussedextensively by the scholars coming from all over the world. Meanwhile, the problem of thestructural breaks also is the focus of the attention from economists in the economics and thespurious regression problem do not involve in the series which has infinite variance in thetraditional fields. Nowadays, more and more data obey heavy-tailed distribution, structuralbreaks often appears in the financial time series and spurious regression theory has importantguiding role for decision makers and investment Banks. So research about the spuriousregression model that has the structural breaks and heavy-tailed distribution is of greatsignificance. In view of this, this paper make systematic study for the model that has thestructural breaks, heavy-tailed distribution and the spurious regression. Innovation points ofmodels and methods are as follows: we derive the limit distribution of the statistic throughcombining Brown bridge theory and functional central limit theorem under constructing thethree spurious regression models that has the different structural breaks and heavy-tailedseries. In addition, we analyze the sensitivity of various factors that affected the rejection ratein order to validating correctness and rationality of theory using Monte Carlo simulation withthe help of a single variable method and rendering image of3-d.We find that regression parameters will present the regular changes with the increase ofsample size. Moreover, the models produce the phenomenon of spurious regression as long asthe sum of one over of the parameter of heavy-tail less than3/2whether the breaks locationare the same or not in the model with a level of item. The models with a level of item-a linearof trend and a differential of item-a linear of trend show that the test statistics of two modelsare divergent result in appearing respectively the phenomenon of spurious regression. The results of Monte Carlo simulation show that there is a close relationship betweenthe rejection rate and the divergence speed of the limit distribution of statistics. What’s more,the phenomenon of spurious regression not only is related to the position of the structuralbreaks, but it is sensitive to the regression coefficient, the parameter of heavy-tail.