Continuous time autoregressive models with common stochastic trends

Abstract

A multivariate continuous time model is presented in which a n-dimensional process is represented as the sum of k stochastic trends plus a n-dimensional stationary term, assumed to obey a system of higher-order autoregressive stochastic differential equations. When k < n, the variables are cointegrated and can be represented as linear combinations of a reduced number of common trends. An algorithm to estimate the parameters of the model is presented for the case that the trend and stationary disturbances are uncorrelated. This algorithm is used to extract a common (continuous time) stochastic trend from postwar U.S. GNP and consumption.