Estimation in Dynamic Linear Models (DLMs) with Fixed Parameters (FPs) has been faced with considerable limitations due to its inability to capture the dynamics of most time-varying phenomena in econometric studies. An attempt to address this limitation resulted in the use of Recursive Bayesian Algorithms (RBAs) which is also affected by increased computational problems in estimating the Evolution Variance (EV) of the time-varying parameters. In this paper, we propose a modified RBA for estimating TVPs in DLMs with reduced computational challenges.
discounted variance, dynamic models, granularity range, estimation algorithm.
ABREU, D., PEARCE, D., STACCHETTI, E., (1990). Toward a theory of dis counted repeated games with imperfect monitoring. Econometrica, Journal of the Econometric Society, pp. 1041–1063.
ATHANS, M., (1974). The importance of kalman filtering methods for economic systems, In Annals of Economic and Social Measurement, Vol. 3, No. 1, pp.49–64. NBER.
BELSLEY, D. A., KUTI, E., (1973). Time-varying parameter structures: An overview,In Annals of Economic and Social Measurement, Volume 2, number 4, pp.375–379. NBER.
BERTSEKAS, D. P., (1976). Dynamic programing and stochastic control, Mathe matics in Science and Engineering, Academic Press, New York.
BLANCHARD, O. J., FISCHER, S., (1989). Lectures on macroeconomics, MIT press.
CHETTY, V. K., (1971). Estimation of solowŠs distributed lag models, Economet rica: Journal of the Econometric Society, pp. 99–117.
COOLEY, T. F., PRESCOTT, E. C., (1973). Systematic (non-random) variation models: varying parameter regression: a theory and some applications, In Annals of Economic and Social Measurement, Vol. 2, No. 4, pp. 463–473.NBER.
COOLEY, T. F., PRESCOTT, E. C., (1976). Estimation in the presence of stochas tic parameter variation, Econometrica: journal of the Econometric Society, pp.167–184.
COOPER, R. L., (1972). The predictive performance of quarterly econometric models of the united states, In Econometric Models of Cyclical Behavior, Vol.1 and 2, pp. 813–947. NBER.
DOH, T., CONNOLLY, M., (2013). The state space representation and estimation of a time- varying parameter VAR with stochastic volatility, Springer.
FUQUENE, J., ALVAREZ, M., PERICCHI, L., (2013). A robust Bayesian dynamic linear model to detect abrupt changes in an economic time series: The case of Puerto Rico, arXiv preprint arXiv:1303.6073.
FÚQUENE, J., M. ÁLVAREZ, PERICCHI, L. R., (2015). A robust Bayesian dy namic linear model for Latin-American economic time series: ¸Sthe Mexico and Puerto Rico casesT, Latin American Economic Review 24 (1), pp. 1–17. ˇ
GALLANT, A. R., FULLER, W. A., (1973). Fitting segmented polynomial regres sion models whose join points have to be estimated, Journal of the American Statistical Associa- tion 68 (341), pp. 144–147.
GELFAND, A. E., HILLS, S. E., RACINE-POON, A., SMITH, A. F., (1990). Illus tration of Bayesian inference in normal data models using Gibbs sampling, Journal of the American Statistical Association 85 (412), pp. 972–985.
GELMAN, A., (2004). Parameterization and Bayesian modeling, Journal of the American Statistical Association 99 (466).
GEMAN, S., GEMAN, D., (1984). Stochastic relaxation, Gibbs distributions, and the bayesian restoration of images, Pattern Analysis and Machine Intelligence, IEEE Trans- actions on (6), pp. 721–741.
GEWEKE, J., (1993). Bayesian treatment of the independent student-t linear model, Journal of Applied Econometrics 8(S1), pp. 19–40.
GOLDFELD, S. M., QUANDT, R. E., (1973). A Markov model for switching regres sions, Journal of econometrics 1 (1), pp. 3–15.
HARVEY, A., PHILLIPS, G., (1982). The estimation of regression models with time varying parameters, In Games, economic dynamics, and time series analysis,pp. 306–321. Springer.
HASTINGS, W. K., (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57 (1), pp. 97–109.
HINKLEY, D. V., (1971). Inference in two-phase regression. Journal of the Ameri can Statistical Association 66 (336), 736–743.
KALABA, R., TESFATSION, L., (1980). A least-squares model specification test for a class of dynamic nonlinear economic models with systematically varying parameters, Journal of Optimization Theory and Applications 32 (4), pp. 537–567.
KALABA, R., TESFATSION, L., (1988). The flexible least squares approach to time-varying linear regression. Journal of Economic Dynamics and Control 12(1), 43–48.
MCZGEE, V. E., CARLETON, W. T., (1970). Piecewise regression. Journal of the American Statistical Association 65 (331), pp.1109–1124.
NAKAJIMA, J., KASUYA, M., WATANABE, T., (2011). Bayesian analysis of time varying parameter vector autoregressive model for the Japanese economy and monetary policy, Journal of the Japanese and International Economies 25 (3), pp. 225–245.
NG, C., YOUNG, P. C., (1990). Recursive estimation and forecasting of non stationary time series, Journal of Forecasting 9 (2), pp. 173–204.
PETRIS, G., (2010). An r package for dynamic linear models, Journal of Statistical Soft- ware 36(12), pp. 1–16.
POLLOCK, D., (2003). Recursive estimation in econometrics, Computational statis tics data analysis 44 (1), pp. 37–75.
PRIMICERI, G. E., (2005). Time varying structural vector autoregressions and monetary policy, The Review of Economic Studies 72 (3), pp. 821–852.
RAVINES, R., SCHMIDT, A. M, MIGON, H. S, (2006). Revisiting distributed lag models through a Bayesian perspective, Applied Stochastic Models in Busi ness and Industry 22 (2), pp. 193–210.
ROTHENBERG, T. J., (1973). Efficient estimation with a priori information, New Haven: Yale University Press.
SARRIS, A. H., (1973). A Bayesian approach to estimation of time-varying regres sion co-efficients, In Annals of Economic and Social Measurement, Vol. 2, No. 4, pp.497–520. NBER.
SOLOVIEV, V., SAPTSIN V., CHABANENKO, D., (2011). Markov chains application to the financial-economic time series prediction, arXiv preprint arXiv:1111.5254.
SPEAR, S. E., S. SRIVASTAVA, (1987). On repeated moral hazard with discount ing, The Review of Economic Studies 54 (4), pp. 599–617.
WEST, M., HARRISON, P., (1997). Bayesian Forecasting and Dynamic Models (2nd ed.), New York: Springer-verlag.
YOUNG, P. C., (2011). Recursive estimation and time-series analysis: An intro duction for the student and practitioner, Springer.
ZELLNER, A., (2009). Bayesian econometrics: past, present, and future. Ad vances in Econometrics 23, pp. 11–60.