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Convergence theorems on the least square estimators of the structural parameters of a linear explosive model

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Summary

Linear explosive stochastic difference equations have been studied by White [6], Anderson [1], Rao [3] and the author [4], [5], leading to the derivation of limit distributions of certain sample functions bearing on structural estimation and goodness of fit tests. In this paper the author discusses certain results of similar interest on the structural parametric estimators of a linear explosive model generating a pair of related stochastic processes.

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References

  1. Anderson, T. W. (1959). On asymptotic distribution of estimators of parameters of stochastic difference equation,Ann. Math. Statist.,30, 676–687.

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  2. Diananda, P. H. (1953). Some probability limit theorems with statistical applications,Proc. Camb. Phil. Soc.,49, 239–246.

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  3. Rao, M. M. (1961). Consistency and limit distribution of parameters in explosive stochastic difference equations,Ann. Math. Statist.,32, 195–218.

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  4. Venkataraman, K. N. (1967). A note on the least square estimators of the parameters of a second order linear stochastic difference equations,Bull. Calcutta Statist. Ass.,16, 15–28.

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  5. Venkataraman, K. N. (1968). Some limit theorems on a linear explosive stochastic difference equation with a constant term, and their statistical applications,Sankhya, Ser. A,30, 51–74.

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  6. White, J. S. (1958). The limit distribution of serial correlation coefficient in the explosive case,Ann. Math. Statist.,29, 1188–1197.

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Authors and Affiliations

  1. University of Madras, Madras, India

    K. N. Venkataraman

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  1. K. N. Venkataraman
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Venkataraman, K.N. Convergence theorems on the least square estimators of the structural parameters of a linear explosive model. Ann Inst Stat Math 26, 61–85 (1974). https://doi.org/10.1007/BF02479804

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  • DOI: https://doi.org/10.1007/BF02479804

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