Estimating the system order by subspace methods

Abstract

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 subsystems. The performance of all the procedures considered is analyzed through Monte Carlo simulations.

Forecasting linear dynamical systems using subspace methods

“…Note that the weighting matrix, W , and the system order, n , have to be specified. See Katayama (2005) for different W and García‐Hiernaux et al. (2007) to estimate n .…”

“…Regarding PROC A and PROC B, the range of values chosen for i was {3,12}, which means that 10 state‐space models where estimated and combined. The system order, n , required to estimate using subspace methods was computed with the MbC criterion described in García‐Hiernaux et al. (2007).…”

“…Consequently, I − i 0 +1 = 10 models are estimated and used in the prediction exercise. Estimating the system order with the MbC criterion (García‐Hiernaux et al. , 2007) returns .…”

“…Regarding PROC A and PROC B, the range of values chosen for i was f3,12g, which means that 10 state-space models where estimated and combined. The system order, n, required to estimate using subspace methods was computed with the MbC criterion described in García-Hiernaux et al (2007). Results show that PROC A generally offers better performance than PROC B, therefore I concentrate the discussion comparing PROC A, the non-combined subspace forecasts and the VAR predictions.…”

A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems

“…Modelling of linear dynamical systems leads to either a transfer function or a state space representation (Landau and Zito [2], Garcia-Hiernaux et al [3]). In case of transfer functions, autoregressive (AR), moving-average (MA), or autoregressive moving-average (ARMA) processes are the results of the modelling process of the physical and real-life problems (Wahlberg et al [4], AbdulRahim et al [5], and Dahlen [6]).…”