A multivariate innovations state space Beveridge Nelson decomposition

de Silva, Ashton (2007): A multivariate innovations state space Beveridge Nelson decomposition.

Abstract

The Beveridge Nelson vector innovation structural time series framework is new formu- lation that decomposes a set of variables into their permanent and temporary components. The framework models inter-series relationships and common features in a simple man- ner. In particular, it is shown that this new speci¯cation is more simple than conventional state space and cointegration approaches. The approach is illustrated using a trivariate data set comprising the GD(N)P of Australia, America and the UK.

• Item Type: MPRA Paper
• Institution: RMIT University
• Language: English
• Keywords: vector innovation structural time series; multivariate time series; Bev- eridge Nelson; common components
• Subjects: E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

References

Anderson, H., Low, C. & Snyder, R. (2006), `Single source of error state space approach to Beveridge Nelson decomposition', Economics Letters 91, 104-109. Athanasopoulos, G. (2005), Essays on alternative methods of identification and estimation of vector autoregressive moving average models, PhD thesis, Department of Economet- rics and Business Statistics, Monash University, Australia. Barillas, F. & Schleicher, C. (2003), Common trends and common cycles in Canadian sectoral output, Working paper 2003-44, Bank of Canada. Beveridge, S. & Nelson, C. (1981), `A new approach to decomposition of economic times series into permanent and transitory components with particular attention to the mea- surement of the business cycle', Journal of Monetary Economics 7, 151-174. de Silva, A., Hyndman, R. & Snyder, R. (2007), The Vector Innovation Structural Time Series Framework: A Simple Approach to Multivariate Forecasting, Working Paper 03/2007, Department of Econometrics and Business Statistics, Monash University. Dufour, J.-M. & Pelletier, D. (2005), Practical methods for modelling weak VARMA pro- cesses: identification, estimation and specification with a macroeconomic application, Discussion paper, CIRANO and CIREQ, Universite de Montreal. Economic Cycle Research Institute (2007). url = http://www.businesscycle.com/. 21 Harvey, A. & Jaeger, A. (1993), `Detrending, stylised facts and the business cycle', Journal of Applied Econometrics 8, 231-247. King, R., Plosser, C., Stock, J. & Watson, M. (1987), Stochastic trends and economic fluctuations, NBER Working Paper 2229, NBER. Morley, J. C. (2002), `A state-space approach to calculating the Beveridge-Nelson decom- position', Economics Letters 75, 123-127. Morley, J. C., Nelson, C. R. & Zivot, E. (2003), `Why are the Beveridge-Nelson and unobserved-components decompositions of GDP so different?', The Review of Eco- nomics and Statistics 75(2), 235-243. Pagan, A. (1997), `Towards an understanding of some business cycle facts', The Australian Economic Review 30, 1-15. Proietti, T. (2002), Some reactions on trend-cycle decompositions with correlated com- ponents, Working Paper, Department of Economics, European University Institute. Schott, J. (1997), Matrix Analysis for Statistics, John Wiley & Sons. Sinclair, T. (2005), Permanent and transitory movements in output and unemployment: Okun's law persists, Working Paper, Department of Economics, Washington University. Stock, J. & Watson, M. (1988), `Testing for common trends', Journal of the American Statistical Association 83(404), 1097-1107. Tiao, G. & Tsay, R. (1989), `Model speci¯cation in multivariate time series', Journal of the Royal Statistical Society 51, 157-213. Vahid, F. & Engle, R. (1993), `Common trends and common cycles', Journal of Applied Econometrics 8(4), 341-360. Vahid, F. & Engle, R. (1997), `Codependent cycles', Journal of Econometrics 80, 199{221. Watson, M. (1994), Vector Autoregressions and Cointegration, Vol. IV, Elsevier, chap- ter 47, pp. 2843-2915.