Artifactual unit root behavior of Value at risk (VaR)

An effective model for time-varying quantiles of a time series is of considerable practical importance across various disciplines. In particular, in financial risk management, computation of Value-at-risk (VaR), one of the most popular risk measures, involves knowledge of quantiles of portfolio returns. This paper examines the random walk behavior of VaRs constructed under two most common approaches, viz. historical simulation and the parametric approach using GARCH models. We find that sequences of historical VaRs appear to follow a unit root model, which can be an artifact under some settings, whereas its counterpart constructed via the parametric approach does not follow a random walk model by default.