An Alternative to Transfer Function Forecasting Based on Subspace Methods

Abstract

In the time series literature, recent interest has focused on the so-called subspace methods. These techniques use canonical correlations and linear regressions to estimate the system matrices of an ARMAX model expressed in state space form. In this article, we use subspace methods to forecast two series with the help of some exogenous variables related to them. We compare the results with those obtained using traditional transfer function models and find that the forecasts obtained with both methods are similar. This result is very encouraging because, in contrast to transfer function models, subspace methods can be considered as almost automatic.

Keywords:

• ARMAX
• Forecasting
• Kalman Filter
• State space model
• Subspace methods
• Transfer function

Mathematics Subject Classification:

• 62M10
• 93E12
• 91B82

Notes

¹⁾ and ²⁾ refer to Examples 1 and 2, respectively.

¹⁾ and ²⁾ refer to Examples 1 and 2, respectively.

¹⁾ and ²⁾ refer to Examples 1 and 2, respectively.