Estimating the system order by subspace methods

This paper discusses how to determine the order of a state-space model. To do so, we start by revising existing approaches and find in them three basic shortcomings: i) some of them have a poor performance in short samples, ii) most of them are not robust and iii) none of them can accommodate seasonality. We tackle the first two issues by proposing new and refined criteria. The third issue is dealt with by decomposing the system into regular and seasonal sub-systems. The performance of all the procedures considered is analyzed through Monte Carlo simulations

Unit Roots and Cointegrating Matrix Estimation using Subspace Methods

We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.State-space models, subspace methods, unit roots, cointegration.

Una metodología para el seguimiento de objetivos definidos sobre series históricas: el caso del control monetario en España

En este articulo se describe una metodología para efectuar el seguimiento de objetivos económicos, definidos sobre un vector de series históricas que' han sido observadas en el pasado. El procedimiento consiste en calcular utilizando un filtro de Kalman, una senda de objetivos a corto plazo compatible con el modelo econométrico que describe la evolucion de las series y con el objetivo final. De esta manera, se evitan algunos elementos arbitrarios característicos de los métodos que se utilizan en la actualidad. La aplicación del sistema se ilustra mediante un ejemplo relativo al objetivo monetario en España

ESTIMATING THE SYSTEM ORDER BY SUBSPACE METHODS

This paper discusses how to determine the order of a state-space model. To do so, we start by revising existing approaches and find in them three basic shortcomings: i) some of them have a poor performance in short samples, ii) most of them are not robust and iii) none of them can accommodate seasonality. We tackle the first two issues by proposing new and refined criteria. The third issue is dealt with by decomposing the system into regular and seasonal sub-systems. The performance of all the procedures considered is analyzed through Monte Carlo simulations.

Fast estimation methods for time series models in state-space form

We propose two fast, stable and consistent methods to estimate time series models expressed in their equivalent state-space form. They are useful both, to obtain adequate initial conditions for a maximum-likelihood iteration, or to provide final estimates when maximum-likelihood is considered inadequate or costly. The state-space foundation of these procedures implies that they can estimate any linear fixed-coefficients model, such as ARIMA, VARMAX or structural time series models. The computational and finitesample performance of both methods is very good, as a simulation exercise shows.State-space models, subspace methods, Kalman Filter, system identification.

From general State-Space to VARMAX models

Fixed coecients State-Space and VARMAX models are equivalent, meaning that they are able to represent the same linear dynamics, being indistinguishable in terms of overall fit. However, each representation can be specifically adequate for certain uses, so it is relevant to be able to choose between them. To this end, we propose two algorithms to go from general State-Space models to VARMAX forms. The first one computes the coeficients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coeficients of a VARMAX echelon. These procedures supplement the results already available in the literature allowing one to obtain the State-Space model matrices corresponding to any VARMAX. The paper also discusses some applications of these procedures by solving several theoretical and practical problems.State-Space, VARMAX models, Canonical forms, Echelon.

Decomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertising

This paper shows how to compute the in-sample effect of exogenous inputs on the endogenous variables in any linear model written in state-space form. Estimating this component may be, either interesting by itself, or a previous step before decomposing a time series into trend, cycle, seasonal and error components. The practical application and usefulness of this method is illustrated by estimating the effect of advertising on monthly sales of the Lydia Pinkham vegetable compound.State-space, Signal extraction, Time series decomposition, Seasonal adjustment, Advertising, Lydia Pinkham

A proposal to obtain a long quarterly chilean gdp series

An important limitation in order to specify and estimate a macroeconomic model that describes the Chilean economy resides in using variables with sufficient number of observations that allow for a reliable econometric estimation. Among these variables, the GDP constitutes a fundamental magnitude. Nevertheless, for this variable there is not quarterly information before 1980. This paper computes quarterly GDP series for the period 1966-1979 using the approach by Casals et al (2000). As result, the new series incorporates the cyclical dynamic in the quarterly series later to 1979 respecting, in addition, all the annual existing information before the above mentioned period

A Proposal to Obtain a Long Quarterly Chilean GDP Series

An important limitation in order to specify and estimate a macroeconomic model that describes the Chilean economy resides in using variables with sufficient number of observations that allow for a reliable econometric estimation. Among these variables, thSmoothing algorithm, arima model, transfer function model, chilean gdp

A PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES

An important limitation in order to specify and estimate a macroeconomic model that describes the Chilean economy resides in using variables with sufficient number of observations that allow for a reliable econometric estimation. Among these variables, the GDP constitutes a fundamental magnitude. Nevertheless, for this variable there is not quarterly information before 1980. This paper computes quarterly GDP series for the period 1966-1979 using the approach by Casals et al (2000). As result, the new series incorporates the cyclical dynamic in the quarterly series later to 1979 respecting, in addition, all the annual existing information before the above mentioned period.