Some Convergence Theorems On Linear Models Generating A Pair Of Related Time Series
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AUTHOR(S)
Siddamsetty Upendra, R. Abbaiah
KEYWORDS
Time series definition, Stationary process, non-stationary process, assumptions of stationary, stochastic models for time series, some of the pivotal lemmas.
ABSTRACT
The main aim of this paper is to establish some convergence theorems on Linear Models Generating a Pair of Related Time Series of certain covariance type functions relating to the model specified. The estimates of residual are obtained on using the estimators defined under different placements of the roots ρ_1 and ρ_2 of P (z). This work is motivated by similar studies on linear stochastic difference equations for scalar time series. The pivotal lemmas concerned with the statements and proofs of some lemmas.
REFERENCES
[1] ANDERSON, T.W. (1971). THE STATISTICAL ANALYSIS OF TIME SERIES. John Wiley and Sons. Inc., New York.
[2] BARTLETT, M.S. (1966). AN INTRODUCTION TO STOCHASTIC PROCESSES WITH SPECIAL REFERENCE METHODS AND APPLICATIONS. (2/0) Cambridge University Press, Cambridge.
[3] DIANANDA, P.H. (1953). Some probability limit theorems with statistical applications. Proc. Cambridge Phil.
[4] FULLER, W.A. (1975). INTRODUCTION TO STATISTICAL TIME SERIES. John Wiley and Sons. Inc., New York.
[5] FULLER, W.A., HASZA, D.P. and GOEBEL, J.J. (1981). Estimation of the parameters of stochastic difference equations. Ann. Statist., 9, No.3, pp.531-543.
[6] HANNAN, E.J. (1960). TIME SERIES ANALYSIS, Methuen and Co., London.
[7] HANNAN, E.J. (1961). A central limit theorem for systems of regressions. Proc. Cambridge Phil.
[8] HANNAN, E.J. (1970). MULTIPLE TIME SERIES. John Wiley and Sons Inc., New York.
[9] LOEVE, M. (1963). PROBABILITY THEORY. D Van Nostrand Comp an., New York.
[10] VENKATARAMAN, K.N. (1972). Some limit theorems on linear stochastic models and their statistical applications, Sankhya, A 30, pp.51-74.
[11] VENKATARAMAN, K.N. (1974). Convergence theorems on the least square estimators of the structural parameters of a linear stochastic model. Ann. Inst. Statist. Math., 26, no.1, pp.61-85.
[12] VENKATARAMAN, K.N. (1980). Some theorems on a class of non-stationary linear stochastic processes. J. Ind. Statist. Assn., 18, pp.175-184.
[13] HANNAN, E.J. and NICHOLLS, D.F. (1972). The estimation of mixed regression, autoregression, moving averages and distributed lag models. Econometrica,40, pp.530-547.
[14] SCHMIDT, P. (1976). ECONOMETRICS, Marcel Dekker, Inc., New York.
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