Semiparametric Analysis of Stationary Fractional Cointegration and the Implied-Realized Volatility Relation

We consider semiparametric frequency domain analysis of cointegration between long memory processes, i.e. fractional cointegration, allowing derivation of useful long-run relations even among stationary processes. The approach uses a degenerating part of the periodogram near the origin to form a narrow band frequency domain least squares (FDLS) estimator of the cointegrating relation, which is consistent for arbitrary short-run dynamics. Our main theoretical contribution is to derive the asymptotic distribution theory for the FDLS estimator of the cointegration vector in the stationary long memory case. The motivating example is the relation between the volatility realized in the stock market and the associated implicit volatility derived from option prices. An application to high-frequency U.S. stock index and option data is offered