Computationally Efficient Methods for Two Multivariate Fractionally Integrated Models

21 Pages Posted: 20 Oct 2009

See all articles by Rebecca J. Sela

Rebecca J. Sela

New York University (NYU) - Leonard N. Stern School of Business; J.P. Morgan Chase & Co.

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: 0000

Abstract

We discuss two distinct multivariate time-series models that extend the univariate ARFIMA (autoregressive fractionally integrated moving average) model. We discuss the different implications of the two models and describe an extension to fractional cointegration. 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 with existing methods individually. Then, we measure the performance of the maximum likelihood estimator and of existing methods in a Monte Carlo. These algorithms are much more computationally efficient than the existing algorithms and are equally accurate, making it feasible to model multivariate long memory time series and to simulate from these models. We use maximum likelihood to fit models to data on goods and services inflation in the United States.

Suggested Citation

Sela, Rebecca J. and Hurvich, Clifford M., Computationally Efficient Methods for Two Multivariate Fractionally Integrated Models (0000). Journal of Time Series Analysis, Vol. 30, Issue 6, pp. 631-651, November 2009. Available at SSRN: https://ssrn.com/abstract=1490391 or http://dx.doi.org/10.1111/j.1467-9892.2009.00631.x

Rebecca J. Sela (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

J.P. Morgan Chase & Co. ( email )

60 Wall St.
New York, NY 10260
United States

Clifford M. Hurvich

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

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