Frequency domain estimation of temporally aggregated Gaussian cointegrated systems

This paper considers joint estimation of long run equilibrium coefficients and parameters governing the short run dynamics of a fully parametric Gaussian cointegrated system formulated in continuous time. The model allows the stationary disturbances to be generated by a stochastic differential equation system and for the variables to be a mixture of stocks and flows. We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain estimation of the unknown parameters using discrete time data. We formally establish the order of consistency and the asymptotic sampling properties of such an estimator. The estimator of the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that of the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.