## Unobserved Components Models in Economics and Finance THE ROLE OF THE KALMAN FILTER IN TIME SERIES ECONOMETRICS

### BibTeX

@MISC{Harvey_unobservedcomponents,

author = {Andrew Harvey},

title = {Unobserved Components Models in Economics and Finance THE ROLE OF THE KALMAN FILTER IN TIME SERIES ECONOMETRICS},

year = {}

}

### OpenURL

### Abstract

Economic time series display features such as trend, seasonal, and cycle that we do not observe directly from the data. The cycle is of particular interest to economists as it is a measure of the fluctuations in economic activity. An unobserved components model attempts to capture the features of a time series by assuming that they follow stochastic processes that, when put together, yield the observations. The aim of this article is thus to illustrate the use of unobserved components models in economics and finance and to show how they can be used for forecasting and policy making. Setting up models in terms of components of interest helps in model building; see the discussions in [1] and [2] for a comparison with alternative approaches. A detailed treatment of unobserved components models is given in [3]. The statistical treatment of unobserved components models is based on the state-space form. The unobserved Digital Object Identifier 10.1109/MCS.2009.934465 components, which depend on the state vector, are related to the observations by a measurement equation. The Kalman filter is the basic recursion for estimating the state, and hence the unobserved components, in a linear state-space model (see “Kalman Filter”). The estimates, which are based on current and past observations, can be used to make predictions. Backward recursions yield smoothed estimates of components at each point in time based on past, current, and future observations. A set of one-step-ahead prediction errors, called innovations, is produced by the Kalman filter. In a Gaussian model, the innovations can be used to construct a likelihood function that can be maximized numerically with respect to unknown parameters in the system; see [4]. Once the parameters are estimated, the innovations can be used to construct test statistics that are designed to assess how well the model fits. The STAMP package [5] embodies a model-building procedure in which test statistics are produced as part of the output.

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Citation Context ...ks are developing dynamic stochastic general equilibrium models using state-space methods. These models are based on unobserved components, and estimation is by maximum likelihood or Bayesian methods =-=[21]-=-. AUTHOR INFORMATION Andrew Harvey (andrew.harvey@econ.cam.ac.uk) obtained the B.A. degree in economics and statistics from the University of York in 1968 and the M.Sc. in statistics from the London S... |

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Citation Context ... above trend is associated with an annual inflation rate that is 1% above the underlying trend in inflation. A multivariate unobserved components model linking inflation to unemployment is adopted in =-=[12]-=-. The motivation is similar to the motivation in (28) in that high unemployment implies underused resources and hence a gap between actual and potential output. The specification of the model differs ... |

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Citation Context ...c c ct21 c * t21 d 1 c kt d, (15) k* t * where kt and kt are N 3 1 vectors of Gaussian disturbances such that E1k tkr t2 5 E1k* t k* r t 2 5Sk, E(k tk* r t ) 5 0, and Sk is an N 3 N covariance matrix =-=[9]-=-, [10]. The operator # in (15) denotes the Kronecker matrix product. Since the parameters r and lc are the same in all N time series, the cycles have the same spectrum, and thus are referred to as sim... |

2 |
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Citation Context ...et series. Furthermore, the Kalman filter offers the flexibility needed for dealing with data irregularities, such as missing observations and observations at mixed frequencies. The study reported in =-=[13]-=- on the measurement of British unemployment provides an illustration. The challenge is to obtain timely estimates of the % Yearly Inflation 7.5 5.0 2.5 0.0 −2.5 Inflation Level Billion of US$ (Logged)... |

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