Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach
A Markov chain Monte Carlo (MCMC) approach, called a reversible jump MCMC, is employed in model selection and parameter estimation for possibly non-stationary and non-linear time series data. The non-linear structure is modelled by the asymmetric momentum threshold autoregressive process (MTAR) of Enders & Granger (1998) or by the asymmetric self-exciting threshold autoregressive process (SETAR) of Tong (1990). The non-stationary and non-linear feature is represented by the MTAR (or SETAR) model in which one ( „ 1 ) of the AR coefficients is greater than one, and the other ( „ 2 ) is smaller than one. The other non-stationary and linear, stationary and nonlinear, and stationary and linear features, represented respectively by ( „ 1 = „ 2 = 1 ), ( „ 1 p „ 2 < 1 ) and ( „ 1 = „ 2 < 1 ), are also considered as possible models. The reversible jump MCMC provides estimates of posterior probabilities for these four different models as well as estimates of the AR coefficients „ 1 and „ 2 . The proposed method is illustrated by analysing six series of US interest rates in terms of model selection, parameter estimation, and forecasting.
Volume (Year): 29 (2002)
Issue (Month): 5 ()
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koop, Gary & Potter, Simon M, 1999.
"Dynamic Asymmetries in U.S. Unemployment,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 17(3), pages 298-312, July.
- Daniel E. Sichel, 1989.
"Business cycle asymmetry: a deeper look,"
Working Paper Series / Economic Activity Section
93, Board of Governors of the Federal Reserve System (U.S.).
- Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
- Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S145-59, Supplemen.
- Enders, Walter & Granger, C. W. J., 1998.
"Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates,"
Staff General Research Papers
1388, Iowa State University, Department of Economics.
- Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
- Tom Doan, . "RATS programs to replicate Enders/Granger JBES(1998)on threshold unit roots," Statistical Software Components RTZ00054, Boston College Department of Economics.
- Balke, Nathan S & Fomby, Thomas B, 1997.
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
- Tom Doan, . "RATS programs to replicate Balke-Fomby threshold cointegration," Statistical Software Components RTZ00010, Boston College Department of Economics.
- Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
- Hansen, Bruce E, 1996.
"Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis,"
Econometric Society, vol. 64(2), pages 413-30, March.
- Tom Doan, . "TAR: RATS procedure to estimate a threshold autoregression, tests for threshold effect," Statistical Software Components RTS00209, Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate Hansen's threshold estimation and testing results," Statistical Software Components RTZ00091, Boston College Department of Economics.
- Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
- Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
- Oh, Man-Suk, 1999. "Estimation of posterior density functions from a posterior sample," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 411-427, February.
- Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
- Lee, Oesook & Shin, Dong Wan, 2001. "A note on stationarity of the MTAR process on the boundary of the stationarity region," Economics Letters, Elsevier, vol. 73(3), pages 263-268, December.
- Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-28, April.
- Shin, Dong Wan & Lee, Oesook, 2001. "Tests for Asymmetry in Possibly Nonstationary Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 233-44, April.
- Mehmet Caner & Bruce E. Hansen, 2001.
"Threshold Autoregression with a Unit Root,"
Econometric Society, vol. 69(6), pages 1555-1596, November.
- Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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