Bayesian estimation of time-varying parameters in dynamic state space models in the presence of discounted evolution variance

O. O. Awe, A. A. Adepoju


Considerable attention has been devoted in literature to the estimation of linear models with constant location parameters. However, many phenomena in real life situations exhibit a non-linear time-varying pattern, indicating a need to adopt Bayesian dynamic models and deal with the complexity involved in estimating the resulting time-varying parameters. In this paper, we present a novel application involving the estimation of time-varying parameters in dynamic state space regression models in the presence of discounted evolution variance. A conceptual review of the derivation of the posterior distribution of the time-varying parameters was done with the application of the proposed technique examined with simulated and real data. The results showed substantial time-variation in the slopeĀ  parameters associated with the studied location parameters, thereby highlighting the empirical relevance and advantage of the discounting method as well as its computationally less intensive nature.

Full Text:



G. Petris, S. Petrone, and P. Campagnoli, Dynamic linear models with R. Springer, 2009.

J. Fuquene, M. Alvarez, and L. R. Pericchi, A robust bayesian dynamic linear model for latin-american economic time series: "the mexico and puerto rico cases"," Latin American Economic Review, vol. 24, no. 1, pp. 1-17, 2015.

R. Ravines, A. M Schmidt, and H. S Migon, "Revisiting distributed lag

models through a bayesian perspective," Applied Stochastic Models in

Business and Industry, vol. 22, no. 2, pp. 193-210, 2006.

G. U. Yule, Why do we sometimes get nonsense-correlations between

time-series? a study in sampling and the nature of time-series," Journal

of the royal statistical society, pp. 1-63, 1926.

J. Ojo, On time series models and prediction of deposits and loans of

rural branches of commercial banks in nigeria,"Journal of Science and

Multidisciplinary Research, vol. 5, no. 2, 2013.

S. Almon, The distributed lag between capital appropriations and expenditures, Econometrica: Journal of the Econometric Society, pp. 178{196, 1965.

H. Wold, A study in the analysis of stationary time series," 1938.

P. J. Harrison and C. F. Stevens, Bayesian forecasting," Journal of the

Royal Statistical Society. Series B (Methodological), pp. 205{247, 1976.

M. West and P. Harrison, Bayesian Forecasting and Dynamic Models,

nd ed. New York: Springer-Verlag, 1997.

J. Nakajima, M. Kasuya, and T. Watanabe, Bayesian analysis of time-varying parameter vector autoregressive model for the japanese economy and monetary policy," Journal of the Japanese and International

Economies, vol. 25, no. 3, pp. 225-245, 2011.

T. Doh and M. Connolly, The state space representation and estimation of a time-varying parameter VAR with stochastic volatility. Springer, 2013.

K. Cui and D. B. Dunson, Generalized dynamic factor models for mixed-measurement time series," Journal of Computational and Graphical Statistics, vol. 23, no. 1, pp. 169{191, 2014.

V. Soloviev, V. Saptsin, and D. Chabanenko, Markov chains application to the financial-economic time series prediction, arXiv preprint

arXiv:1111.5254, 2011.

G. E. Primiceri, Time varying structural vector autoregressions and monetary policy, The Review of Economic Studies, vol. 72, no. 3, pp. 821-852, 2005.

A. H. Sarris, A bayesian approach to estimation of time-varying regression coefficients," in Annals of Economic and Social Measurement, Volume 2, number 4. NBER, 1973, pp. 497-520.

L. A. Gil-Alana, R. Gupta, O. E. Olubusoye, and O. S. Yaya, Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, vol. 109, pp. 29{37, 2016.

O. O. Awe, D. M. Akinlana, O. S. Yaya, and A. O., Time series analysis

of the behaviour of import and export of agricultural and non-agricultural

goods in west africa: A case study of nigeria." Agris On-line Journal of

Economics and Informatics, vol. 10, no. 2, pp. 15{22, 2018.

B. Samson and O. Mercy, On the time series modelling of crude oil exportation in nigeria, European Journal of Academic Essays, vol. 2, no. 3,

pp. 1-11, 2015.

K. Ayinde and H. Abdulwahab, Modeling and forecasting nigerian crude oil exportation: Seasonal autoregressive integrated moving average approach," International Journal of Science and Research, vol. 2, no. 12, pp. 245-249, 2013.

J. M. Marin and C. Roberts, Bayesian Essentials with R. Springer-Verlag New York (Springer Texts in Statistics. 2nd Edition), 2014.

O. O. Awe, I. Crandell, and A. A. Adepoju, A time varying parameter

state-space model for analyzing money supply-economic growth nexus,

Journal of Statistical and Econometric Methods, vol. 4, no. 1, pp. 73{95,

A. Gelman, Parameterization and bayesian modeling, Journal of the

American Statistical Association, vol. 99, no. 466, 2004.

O. O. Awe and A. A. Adepoju, Modified recursive bayesian algorithm for estimating time-varying parameters in dynamic linear models, Statistics in Transition-New Series, vol. 19, no. 2, pp. 239-258, 2018.

J. Geweke, Bayesian treatment of the independent student-t linear

model," Journal of Applied Econometrics, vol. 8, no. S1, pp. S19-S40,

R. L. Brown, J. Durbin, and J. M. Evans, Techniques for testing the

constancy of regression relationships over time, Journal of the Royal Statistical Society. Series B (Methodological), pp. 149-192, 1975.


  • There are currently no refbacks.

Copyright (c) 2020 Journal of the Nigerian Mathematical Society

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.