Identifying Common Long-range Dependence in a Vector Time Series

We propose a method to identify common persistent components in a k-dimensional time series. Assuming that the individual series of the vector process have long-range dependence, we apply canonical correlation analysis to the series and its lagged values. A zero canonical correlation implies the existence of a short-memory linear combination, hence the existence of common long-range dependence; its associated eigenvector provides an estimate of the combination. We illustrate the technique using several real examples, including squared returns of various stock prices. Power and size of the proposed method are investigated via simulation using series generated from fractionally integrated models and from long-memory stochastic volatility models.