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Multivariate Series (multivariate + series)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting50%

Selected Abstracts

Wiener,Kolmogorov Filtering and Smoothing for Multivariate Series With State,Space Structure

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2007
Víctor Gómez
Abstract., Wiener,Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi-infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state,space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener,Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series. [source]

Forecast covariances in the linear multiregression dynamic model

JOURNAL OF FORECASTING, Issue 2 2008
Catriona M. Queen
Abstract The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Wiener,Kolmogorov Filtering and Smoothing for Multivariate Series With State,Space Structure

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2007
Víctor Gómez
Abstract., Wiener,Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi-infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state,space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener,Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series. [source]

Extracting Economic Cycles using Modified Autoregressions

THE MANCHESTER SCHOOL, Issue 5 2001
Alex S. Morton
We review a family of modified autoregressive models in both discrete- and continuous-time formulations. We present the case for these models by showing first how a standard discrete-time autoregressive model with orders selected by criteria such as the Akaike information criterion can fail to identify the correct periods of cyclical variations in a simulated example. We then show how the modified models can overcome this failure, and further illustrate this success with a real example of an unemployment series. A new extension of the continuous-time modified model to multivariate series is described. This is applied to a pair of series with mixed monthly, quarterly and annual sampling intervals. Common cyclical components of the two series are then extracted. [source]