Using Vector Autoregression Methods to Study the Influence of Small Retail Business on Trade Dynamics

In this article, the authors implemented own ideas regarding applying methods of vector regression to the economic analysis using the example of the research of the influence of small retail business on trade dynamics. They’ve selected the components that reflect sectoral development tendencies of the small retail business and have high information capacity in measuring the intensity of economic development. The authors study the influence of composite indicators on the dynamics of an economic development aggregate - volume index of retail trade turnover.

The response of the retail trade volume index to some hypothetical parameters (artificial shocks) of time series of non-quantitative composite indicators illustrating business tendencies in small retail business was simulated. To perform such an analysis the authors used the impulse response function (IRF) for Vector Error Correction Model (VECM) based on modern vector autoregression (VAR) approaches.

The negative interrelation was established between the volume index of retail trade turnover and business potential of retail trade in the short term. Positive interrelations were established between the reviewer of volume index of retail trade turnover and economic situation of retail trade, as well as between volume index of retail trade turnover and competitive position of the small retail business.

The main objective was to select appropriate components for the model by means of preliminary analysis of time series with respect to the stationary process and by checking for co-integration. Vector Error Correction Model was constructed using impulse response function that estimates the spread of shocks over time for composite indicators and the reaction of volume index of retail trade turnover with such intermediate stages as determining the lag order, conducting the Granger test and decomposing volatility.

1. Sims Ch.A. Macroeconomics and Reality. Econometrica. 1980;(48):1-48.

2. Sims Ch.A., Zha T. Bayesian Methods for Dynamic Multivariate Models. International Economic Review. 1998;39(4):949-968.

3. Litterman R.B. Techniques of Forecasting Using Vector Autoregressions. Federal Reserve Bank of Minneapolis. Working Paper: 115, 1979.

4. Litterman R.B. Forecasting with Bayesian Vector Autoregressions - Five Years of Experience. Journal of Business and Economic Statistics. 1986;4(1):25-38.

5. Malakhovskaya O.A., Pekarskiy S.E. The Research of Cause-Effect Relationships in Macroeconomics: Nobel Prize in Economics 2011. The HSE Economic Journal. 2012;(1):3-30. (In Russ.)

6. Lutkepohl H. New Introduction to Multiple Time Series Analysis. Berlin: Springer; 2005.

7. Watson M.W. Vector Autoregressions and Cointegration. In: Engle R.F. and D.L. McFadden (eds.) Handbook of Econometrics, Vol. IV. Amsterdam: Elsevier Science Ltd.; 1994.

8. Hamilton J.D. Time Series Analysis. Princeton University Press; 1994.

9. Campbell J.Y., Lo A.W., MacKinlay A.C. The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press; 1997.

10. Tsay R.S. Analysis of Financial Time Series. John Wiley and Sons; 2002.

11. Johnson R.A., Wichern D.W. Applied Multivariate Statistical Analysis. Prentice Hall; 2007.

12. Greene W.H. Econometric Analysis. Prentice Hall; 1999.

13. Matveyev M.G. Parametric Identification of Models of Vectorial Autoregression. Sovremennaja jekonomika: problemy i reshenija. 2010;(5):133-142. (In Russ.)

14. Lola I.S. Measurement of Business Environment for Small Enterprises by Means of Composite Indicators. Voprosy statistiki. 2015;(10):26-38. (In Russ.)

15. Verbeek M. A Guide to Modern Econometrics. John Wiley & Sons, Ltd; 2000. (Russ. ed.: Aivazyan S.A. (ed.) Putevoditel’ po sovremennoi ekonometrike. Moscow: Nauchnaya kniga, «Biblioteka Solev»; 2008. 616 p.).

16. Engle R.F., Granger C.W.J. Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica. 1987;55(2):251-276.

17. Johansen S. Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica. 1991;59(6):1551-1580.

18. Kantorovich G.G. Lectures on «Time-series analysis» Course. The HSE Economic Journal. 2002;6(1):85-116, 2002;6(2):251-273, 2002;6(3):379-401, 2002;6(4):498-523, 2003;7(1):79-103. (In Russ.)

19. Brooks C., Tsolakos S. Real Estate Modeling and Forecasting. New York: Cambridge University Press; 2010.

20. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C. 2nd edition. Cambridge: Cambridge University Press.

21. Potter S.M. Nonlinear Impulse Response Function. Federal Reserve Bank of New York; 1998.