Does VAR Estimate Have a Unit Root ? Application Of the Phillips-Perron Test

The Value at Risk (VaR) model is widely applied to estimate firms' exposure to market risks. However, when one investigates the relationship between VaR measure and any other tested variables in a standard regression procedure, the analysis may be invalid if VaR estimates are not a stationary process. This paper employs the Phillips-Perron test to examine VaR stationarity for the stock indexes from 10 countries. The empirical evidence indicates that the stationarity hypothesis is quite questionable, because it can be either accepted or rejected simply depending on which specific VaR estimation model is used. This finding is robust and highly consistent across countries, holding periods of different lengths, and confidence levels. Our result strongly suggests that any study using VaR measure in a standard regression may suffer from potentially serious bias and could thus lead to incorrect conclusions