Generalized Estimation of Missing Observations in Nonlinear Time Series Model Using State Space Representation
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 2, March 2013, Pages: 21-28
Received: Mar. 9, 2013;
Published: Apr. 2, 2013
Views 2755 Downloads 98
Biwott K. Daniel, Maseno University,Department of Statistics and Actuarial Science, Kenya
Odongo O. Leo, Kenyatta University,Department of Statistics, Kenya
The aim of the study was to formulate a Time Series Model to be used in obtaining optimal estimates of miss-ing observations. State space models and Kalman filter were used to handle irregularly spaced data. A non-Bayesian ap-proach where the missing values were treated as fixed parameters. Simulated AR (1) data and corresponding estimated missing values were generated using a computer programme. Values were withheld and then estimated as though they were missing. The results revealed that simple exposition of state space representation for commonly used Time Series Models can be formulated.
Biwott K. Daniel,
Odongo O. Leo,
Generalized Estimation of Missing Observations in Nonlinear Time Series Model Using State Space Representation, American Journal of Theoretical and Applied Statistics.
Vol. 2, No. 2,
2013, pp. 21-28.
Abraham B. and Thaveneswaran, A. (1991). A nonlinear Time Series model and estimation of missing observation. Ann. Inst. Stat.Math Vol 43, 422 – 528.
Abraham B.(1981) Missing observation in time series, Common Statistics A- Theory Methods, 10, 1645-1653.
Ansley, C.F and Kohn, R. (1883). Exact likelihood of vector autoregressive-moving average process with missing aggre-gated data. Biometrika 70, 275-278.
Jones, R.H (1985). Time series analysis with unequally space data. In:E.J. Hannan, P. R.Krishnaiah and M. M. Rao, Eds., Handbook of statistics, vol.5. North-Holland, Amsterdam, 157-177.
Penza, J. and Shea, B. (1997). The exact likelihood of an autoregressive-moving average model with incomplete data. Biometrika 84, 919-928.
Nassiuma. D. (1994). SymmetricStable Sequences with missing observations. J. Time Ser. Anal. 15, 313-323.
Palma, W. and Chan, N. H. (1997). Estimation and forecast-ing of long-memory processes. J. Forecasting 16, 395-410.
Chan,N. H and Palma, W. (1998). State space modeling of long memory process. Ann statist. 26, 719-740.
Palma, W. and Del Pino, G. (1999). Statistical analysis of incomplete long-range dependent data. Biometrika, 86, 4, 965-972.
Engle, R.F. (1982). Autoregressive conditional heterosce-dasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.
Harrison, P.J. and stevens, C.F. (1976). Bayesian forecasting (with discussion), J. Roy. Statist. Soc.Ser. B, 38, 205-248.
Tjostheim, D (1986). Estimation in nonlinear time series models, stochastic process. Appl. 21, 251-273.
Thavaneswaran, A and Abraham, B. (1988). Estimation for nonlinear timeseries models using estimating equations. J. Time Ser. Anal. 9, 99-108.
Nichols, D.F and B.G. Quinn (1982). Random coefficient Autoregressivemodels: An introduction lecture notes in sta-tistics no. 11. Springer-Verlag, New York.
Ozaki, T. (1985). Nonlinear time series models and dynamic systems, handbook of statistics, vol. 5 (eds, E.J. Hannan, P.R. Krishnaiah and M.M. Rao), 25-83, North Holland, Amster-dam.
Brockwel, P. J. and Davis, R. A. (1987). Time series: Theory and Methods, Springer, New York.
Shiryayev, A.N. (1984). Probability, Graduate test in Math., 95, Springer, New York.
Charbonnier, R., Barlaud, M., Alengrin, G. and Menez, J. (1987). Results on AR- modeling of nonstationary signals, Signal Process., 12, 143-1587.
Miller, R. B. and Ferreiro, O. (1984). A strategy to complete a time series with missing observations, Lecture Notes in statistics, 25, 251-275, Springer, New York.