Non-stationary volatility with highly anti-persistent increments: evidence from range-based volatility
Abstract
We analyze range-based volatility of three highly capitalized companies to show that the volatility process is non-stationary and its logarithmic transformation together with logarithmic increments is approximately normally distributed. Further, the increments are shown to be highly anti-persistent.
Together with the assertion that logarithmic returns are normally distributed, and uncorrelated with time-varying volatility, we propose a new returns-generating process. The whole procedure is based on empirical observations without any limiting assumptions.
We reconstruct returns series which remarkably mimic the real-world series and posses the standard stylized facts - uncorrelated returns with heavy tails, strongly auto correlated absolute returns and volatility clustering.