Heavy-tailed Cointegration Tests Based On Statistical Sampling

Cointegration is a theory that describes a balanced relationship between economic time variables, the cointegration theory provides powerful theoretical tools and mathematical models to deal with complex macroeconomic issues. In the long-term empirical studies, statisticians found that most financial time series have shown pcak and heavy-tailed phenomenon. So heavy-tailed observations attract increasing attention. This paper studies cointegration tests in heavy-tailed observations. The asymptotic distributions of cointegration test statistic for heavy-tailed observations contain inestimable tail index parameter a, and the asymptotic results of cointegration test statistic are abstract. In the actual application process, the process of critical value selected is unstable because of singular value, it has only the- oretical significance. Therefore, some statistical algorithms are required to approximate asymptotic distribution of the test statistic. Subsampling algorithm and Sieve Bootstrap algorithm are constructed in this paper. Without the need to estimate the tail index parameter?, we calculate the critical value of the test statistic based on Phillips-Perron(PP) tests and Augmented Dickey-Fuller(ADF) tests. The validity of Sub- sampling algorithm and Sieve Bootstrap algorithm is proved in theory. At the same time, MonteCarlo simulations demonstrate that the proposed procedures are more effective. Finally, this paper makes an empirical analysis on the relationship between tax revenue and GDP in Shanghai, and illustrates the practicality and effectiveness of this method.