A Study Of The Theory And Application Of Endogenous Structural Break

The study of the theory and application of endogenous structure break is a hotspot in the field of time series analysis among the last decades. In the analysis of time series, the basic assumption is the stationarity and ergodicity of the seires. The classic unit root theory only consider the stationarity of the siries, when there is no structural breaks in the series the ergodicity assumption can be satisfied, but when there is structural breaks the ergodicity assumption cann’t be satisfied, so the classic unit root theory needs to be extended to cover structural breaks that might exist.This article begins with the estimation method and assumption of the theory of endogenous structure break, focuses on the testing method of one or more structure break points, the unit root test of trend stationary process with structural break and the limiting distribution of the other parameters of the AOADF test of unit root process with structural break, combined with specific macroeconomic and financial data on how to execute the testing of endogenous structure breaks and unit root test with structural break.In theoretical research, the main contribution of this article is as follows:(1) Deriving the limit distribution of the intercept, the trend and the break magnitude term under four situations such as intercept break without drift, intercept with drift, trend break without drift and trend break with drift. Under any data generating process, the parameter’s t statistic need to be divided by T to get limiting distribution. Scaled by the sample size:(a) Under intercept break without drift, the critical values of the t ststistic of the intercept decreases as the break position shift to the end of the sample, the critical values of the t ststistio of the break magnitude d1reaches maximum at the intermediate then decrease to the ends.(b) Under intercept break with drift, the critical values of the t ststistic of the intercept doesn’t show any regular character as the break position shifts, the critical values of the t ststistic of the break magnitude d1increases as the break position lying [0.3,0.7] move to the middle of the sample, the critical values of the t ststistic of the trend reaches maximum at the intermediate then decrease to the ends.(c) Under trend break without drift, the critical values of the t ststistic of the intercept and the trend term share the similar character, which decreases as the break position shifts to its end, the critical values of the t ststistic of the break magnitude d2reaches maximum at the intermediate then decrease to the ends.(d) Under trend break with drift, the critical values of the t ststistic of the intercept decreases as the break position shift to the end; the critical values of the t ststistic of the break magnitude d1reaches minimum at the intermediate then increases to the ends; the critical values of the t ststistic of the break magnitude d2reaches maximum at the intermediate then decrease to the ends; the critical values of the t ststistic of the trend term increases as the break position shift to the ends.(2) Study the effect of structural break on the ADF unit root test under three processes such as intercept break without trend, intercept break with trend and trend break. When the data generating process is intercept break stationary or trend stationary process, the autoregressive coefficient estimates α converges to1with the speed of f T1/2, the limit distribution of α and ta contains the position parameter of the structural break, the magnitude of the break and the standard deviation of the error term, shift to right when the magnitude increases and left when the standard deviation increases. When the data generating process is trend stationary process with trend break, α converges to1with the speed of T3/2, the limit distribution of α contains the position parameter of the structural break, the magnitude of the break and the standard deviation of the error tenn while t(?) don’t contain the standard deviation of the error tenn.(3) Combined the optimal test statistic Exp-LM of endogenous structural break with the AOADF test statistic of structural break, such that in the case of unknown break position parameter, we can make advantage of the Exp-LM statistic to determine whether there is a break point, if there does exist one, then can get the consist estimate of the break location parameter and the type of structural break. Based on the estimated break position parameter, the AOADF test can be used.In application study, the main contribution is(1) Investigate the stock market with the structural break GARCH (1,1) model, the result suggests that there is no structural break in the GARCH (1,1) model of Shanghai Composite Index return series, but there is an ARCH term break in the GARCH(1,1) model of the Shenzhen Component Index return series, which could explain the persistence in the volatility and the high excess kurtosis;(2) Take advantage of the test of endogenous structural break to analysis the series of GDP, inflation and the exchange rate. It is suggested that there is a trend break in the GDP series, the potential data generating process is unit root with trend break; there is intercept breaks in the inflation series, the potential data generating process is stationary process with intercept break; there is no structural break in the exchange rate, the potential data generating process is unit root.