An optimization technique based on a vector autoregression model with state space representation: application to Ukrainian cargo transport data

Abstract

This paper proposes to forecast indicators of the Ukrainian cargo transport system, taking into account their relations with macroeconomic indicators. Increased forecast accuracy at a priori information uncertainty is attained through an optimization technique, starting with a Vector Autoregression (VAR) model of observed multiple time series, its state space representation and subsequent adaptive filtering. The adaptive filter, earlier proposed by the authors, minimizes forecasting errors. Under an optimization criterion, the information divergence of Kullback–Leibler between probability distributions of real values and their estimations is established. The main advantage of the proposed technique is connected with the opportunity to estimate future values of multiple time series even in presence of structural breaks (describing the changes of the status ‘before crisis’ / ‘after crisis’). The observations are available from 2003:1–2011:12, the analysis is performed for the period 2003:1–2011:9. In-sample forecasting of multiple time series of cargo volumes transferred by different transport modes and two macro indicators is compared with the forecast based on a VAR model. In-sample forecast is realized for the last three months 2011:10–2011:12.

Keywords:

• optimization
• vector autoregression
• adaptive filtering
• Kullback–Leibler information
• cargo transport

AMS Subject Classifications:

• 37M10
• 37N40
• 93E11
• 94A17

Acknowledgments

The authors express their deep gratitude to the Department of Quantitative Economics of the University of Fribourg, Switzerland, for the encouragement and support of this research, partially granted by the SNSF-SCOPES project Nr. 127 962.

Notes

1 Another important problem connected with the VAR model is the changing environment conditions. Recently, this is the world economic crisis. Note, that some economists consider the period September 2008 – December 2009 as its peak; others suppose that it is continuing and peak will be in the closest future. For Ukraine, the influence of financial crises does not seem to be important.