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**A dynamic factor model for the analysis of multivariate time series.**
*(English)*
Zbl 0603.62099

In this paper, dynamic factor modelling of the lagged covariance structure of a vector-valued time series is considered. A dynamic factor analysis that yields a generalization of P-technique is presented in order to accomodate the lagged covariance structure of a multivariate time series. The proposed analysis is based upon a model in which the latent factors are conceived of as random time-dependent functions, called factor series. The analysis is applicable to a single relatively short trajectory of a multivariate time series.

In order to advance the use of dynamic factor analysis in psychology, a statistical methodology which is robust against small sample sizes is presented. In so doing, the dynamic factor model is set up as a simultaneous structural equation system. The problem of estimating the time course of a particular realization of the latent factor series is adressed. It is discussed that the estimation problem can be conceived of as the dynamic analogue of the estimation of factor scores in a traditional static factor model. It is shown that estimation using traditional methods of factor analysis leads to nonsensical results. This difficulty is alleviated by translating the dynamic factor model into a Markovian state model where the latent trajectory can be estimated by means of the Kalman filter.

The proposed dynamic factor analysis is applied to some real data and interpretation of a latent factor series is illustrated. It is shown that the considered model explicitly accounts for the entire lagged covariance function of an arbitrary second order stationary time series. Possible extensions of the dynamic factor model in order to accomodate time- varying trends are also discussed.

In order to advance the use of dynamic factor analysis in psychology, a statistical methodology which is robust against small sample sizes is presented. In so doing, the dynamic factor model is set up as a simultaneous structural equation system. The problem of estimating the time course of a particular realization of the latent factor series is adressed. It is discussed that the estimation problem can be conceived of as the dynamic analogue of the estimation of factor scores in a traditional static factor model. It is shown that estimation using traditional methods of factor analysis leads to nonsensical results. This difficulty is alleviated by translating the dynamic factor model into a Markovian state model where the latent trajectory can be estimated by means of the Kalman filter.

The proposed dynamic factor analysis is applied to some real data and interpretation of a latent factor series is illustrated. It is shown that the considered model explicitly accounts for the entire lagged covariance function of an arbitrary second order stationary time series. Possible extensions of the dynamic factor model in order to accomodate time- varying trends are also discussed.

Reviewer: R.Soyer

### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62H25 | Factor analysis and principal components; correspondence analysis |

62P25 | Applications of statistics to social sciences |

### Keywords:

dynamic factor modelling; lagged covariance structure; generalization of P-technique; multivariate time series; robust against small sample sizes; simultaneous structural equation system; latent factor series; estimation; Markovian state model; Kalman filter; second order stationary time series
Full Text:
DOI

### References:

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