Abstract
Dynamic factor models have a wide range of applications in econometrics and applied economics. The basic motivation resides in their capability of reducing a large set of time series to only few indicators (factors). If the number of time series is large compared to the available number of observations then most information may be conveyed to the factors. This way low dimension models may be estimated for explaining and forecasting one or more time series of interest. It is desirable that outlier free time series be available for estimation. In practice, outlying observations are likely to arise at unknown dates due, for instance, to external unusual events or gross data entry errors. Several methods for outlier detection in time series are available. Most methods, however, apply to univariate time series while even methods designed for handling the multivariate framework do not include dynamic factor models explicitly. A method for discovering outliers occurrences in a dynamic factor model is introduced that is based on linear transforms of the observed data. Some strategies to separate outliers that add to the model and outliers within the common component are discussed. Applications to simulated and real data sets are presented to check the effectiveness of the proposed method.
Highlights
Dynamic factor models have been introduced to explain and forecast time series of interest in the presence of a large set of explanatory time series
Since the distances of the estimated ζfrom the true values are generally small, we conclude that estimation of univariate outliers in the factors, or interaction between them and the estimates of the factor matrix A, are responsible for such a larger variability
We presented a method to discover outliers in multivariate time series generated by a dynamic factor model
Summary
Dynamic factor models have been introduced to explain and forecast time series of interest in the presence of a large set of explanatory time series. Where B is the back-shift operator and εi,t is uncorrelated white noise This leads to the dynamic factor model yt = Aθ (B)εt + ηt where θ (B) = diag (θ1(B), . Outliers in time series were introduced by (7) according to two different models, the additive outlier (or aberrant observation) and the innovation outlier (or aberrant innovation).
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