On the Extraction of a Common Persistent Component from Several Volatility Indicators

Measures of financial volatility exhibit clustering and persistence and can be jointly modeled as the element by element product of a vector of conditionally autoregressive scale factors and a multivariate i.i.d. innovation process (vector Multiplicative Error Model - vMEM). Since similar profiles are shared across measures, a restricted vMEM decomposes the conditional expected volatility into the sum of a common (persistent) component and a vector of measure specific components. With data on absolute returns, realized kernel volatility and daily range for the Dow Jones index, we show that indeed such a common component exists with the desired properties. The transitory components happen to have different features across volatility measures.