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Computationally Efficient Gaussian Maximum Likelihood Methods for Vector ARFIMA Models

In this paper, we discuss two distinct multivariate time series models that extend the univariate ARFIMA model. We describe algorithms for computing the covariances of each model, for computing the quadratic form and approximating the determinant for maximum likelihood estimation, and for simulating from each model. We compare the speed and accuracy of each algorithm to existing methods and measure the performance of the maximum likelihood estimator compared to existing methods. We also fit models to data on unemployment and inflation in the United States, to data on goods and services inflation in the United States, and to data about precipitation in the Great Lakes.