My data rejects unit root, but shows structural break, is this possible?
Solved – Can time series data have both unit root and structural break
hypothesis testingstationaritystructural-changetime seriesunit root
hypothesis testingstationaritystructural-changetime seriesunit root
My data rejects unit root, but shows structural break, is this possible?
Best Answer
Others have already answered about the wrong idea of hypothesis testing. Regarding your question : yes it is possible. Take for example this time series. It is the price series of a stock of the S&P 500 (therefore, real data) in a time span of more than 10 years. As you can see the series presents what seems to be a structural change. The ADF, with constant and constant plus trend, gives a p-value respectively of 0.003629 and 0.01257, therefore we can reject the null hypothesis of a unit root (if we assume a level of significance of 5%). Since we suspect the presence of a break, I run also a unit root test with an unknown breakpoint, which computed p-value is equal to 0.0239, once again we can reject the null of a unit root.
The second figure shows an OLS-based CUSUM test with alternative boundaries and alfa equals to 0.05 plotted with the R package "strucchange", which shows you the contemporaneous precence of a break.