Maximum likelihood estimation of time series models: the Kalman filter and beyond

Tommaso Proietti and Luati Alessandra

MPRA Paper from University Library of Munich, Germany

Abstract: The purpose of this chapter is to provide a comprehensive treatment of likelihood inference for state space models. These are a class of time series models relating an observable time series to quantities called states, which are characterized by a simple temporal dependence structure, typically a first order Markov process. The states have sometimes substantial interpretation. Key estimation problems in economics concern latent variables, such as the output gap, potential output, the non-accelerating-inflation rate of unemployment, or NAIRU, core inflation, and so forth. Time-varying volatility, which is quintessential to finance, is an important feature also in macroeconomics. In the multivariate framework relevant features can be common to different series, meaning that the driving forces of a particular feature and/or the transmission mechanism are the same. The objective of this chapter is reviewing this algorithm and discussing maximum likelihood inference, starting from the linear Gaussian case and discussing the extensions to a nonlinear and non Gaussian framework.

Keywords: Time series models; Unobserved components (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2012-04-01
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-mac and nep-ore
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Related works:
Chapter: Maximum likelihood estimation of time series models: the Kalman filter and beyond (2013)
Working Paper: Maximum likelihood estimation of time series models: the Kalman filter and beyond (2012)
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