Abstract
A non-Gaussian state-space model is proposed to estimate a switching trend from serial data taken at equally spaced intervals. A procedure to detect structural changes in a linear trend is also proposed. The results of a simulation study conducted to check the performance of the detection procedure are shown. A numerical illustration is provided using economic time series data.
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References
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, Second International Symposium on Information Theory (eds. B. N.Petrov and F.Csaki), 267–281, Akademiai Kiado, Budapest.
Akaike, H. (1980). Likelihood and the Bayes procedure, Trabajos de Estadistica, 31, 143–166.
Bianchi, M. (1993). Infrequent shocks and signal extraction in economic time series, Ph.D. Thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
Broemeling, L. D. and Tsurumi, H. (1986). Econometrics and Structural Change, Marcel Dekker, New York.
Gordon, K. and Smith, A. F. M. (1990). Modeling and monitoring biomedical time series, J. Amer. Statist. Assoc., 85, 328–337.
Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting (with discussion), J. Roy. Statist. Soc. Ser. B, 38, 205–247.
Jacoby, S. L. S., Kowalik, J. S. and Pizzo, J. T. (1972). Iterative Methods for Nonlinear Optimization Problems, Prentice-Hall, New Jersey.
Kashiwagi, N. (1991). Bayesian detection of structural changes, Ann. Inst. Statist. Math., 43, 77–93.
Kashiwagi, N. (1993). On use of the Kalman filter for spatial smoothing, Ann. Inst. Statist. Math., 45, 21–34.
Kashiwagi, N. and Yanagimoto, T. (1992). Smoothing serial count data through a state-space model, Biometrics, 48, 1187–1194.
Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstatiionary time series (with discussion) J. Amer. Statist. Assoc., 82, 1032–1063.
Kohn, R. and Ansley, C. F. (1987). A new algorithm for spline smoothing based on smoothing a stochastic process, SIAM J. Sci. Statist. Comput., 8, 33–48.
Nelson, C. R. and Plosser, C. I. (1982). Trends and random walks in macroeconomic time series, Journal of Monetary Economics, 10, 139–162.
Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 1361–1401.
Quandt, R. E. (1958). The estimation of the parameters of a linear regression system obeying two separate regimes, J. Amer. Statist. Assoc., 53, 873–880.
Shumway, R. H. and Stoffer, D. S. (1991). Dynamic linear models with switching, J. Amer. Statist. Assoc., 86, 763–769.
Tsurumi, H. (1988). Survey of Bayesian and non-Bayesian testing of model stability in econometrics. Bayesian Analysis of Time Series and Dynamic Linear Models (ed. J. C.Spall), 75–100, Marcel Dekker, New York.
Wecker, E. W. and Ansley, C. F. (1983). The signal extraction approach to nonlinear regression and spline smoothing, J. Amer. Statist. Assoc. 78, 81–89.
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Kashiwagi, N. A state-space approach to polygonal line regression. Ann Inst Stat Math 48, 215–228 (1996). https://doi.org/10.1007/BF00054786
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DOI: https://doi.org/10.1007/BF00054786