IMF Working Papers

A Closed Form Multivariate Linear Filter

By Francis Vitek

December 10, 2018

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Francis Vitek. A Closed Form Multivariate Linear Filter, (USA: International Monetary Fund, 2018) accessed November 23, 2024

Disclaimer: IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.

Summary

This paper considers the problem of jointly decomposing a set of time series variables into cyclical and trend components, subject to sets of stochastic linear restrictions among these cyclical and trend components. We derive a closed form solution to an ordinary problem featuring homogeneous penalty term difference orders and static restrictions, as well as to a generalized problem featuring heterogeneous penalty term difference orders and dynamic restrictions. We use our Generalized Multivariate Linear Filter to jointly estimate potential output, the natural rate of unemployment and the natural rate of interest, conditional on selected equilibrium conditions from a calibrated New Keynesian model.

Subject: Central bank policy rate, Economic theory, Financial services, Labor, Neoclassical theory, Output gap, Potential output, Production, Unemployment rate

Keywords: Central bank policy rate, Closed form, Equilibrium value, Estimates to parameter perturbation, Estimation Results, Gap estimate, Global, Inflation gap estimate, Interest rate gap, Maximization problem, Multivariate linear filter, Natural rate of interest, Natural rate of unemployment, Neoclassical theory, New Keynesian model, Objective function, Output gap, Parameter estimate, Potential output, Unemployment rate, WP

Publication Details

  • Pages:

    24

  • Volume:

    ---

  • DOI:

    ---

  • Issue:

    ---

  • Series:

    Working Paper No. 2018/275

  • Stock No:

    WPIEA2018275

  • ISBN:

    9781484388785

  • ISSN:

    1018-5941

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