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

  • K. N. Venkataraman


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.


Basic Assumption Convergence Theorem Asymptotic Property Limit Distribution Generic Symbol 
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  1. [1]
    Anderson, T. W. (1959). On asymptotic distribution of estimators of parameters of stochastic difference equation,Ann. Math. Statist.,30, 676–687.MATHMathSciNetGoogle Scholar
  2. [2]
    Diananda, P. H. (1953). Some probability limit theorems with statistical applications,Proc. Camb. Phil. Soc.,49, 239–246.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Rao, M. M. (1961). Consistency and limit distribution of parameters in explosive stochastic difference equations,Ann. Math. Statist.,32, 195–218.MATHMathSciNetGoogle Scholar
  4. [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.MATHMathSciNetGoogle Scholar
  5. [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.MATHMathSciNetGoogle Scholar
  6. [6]
    White, J. S. (1958). The limit distribution of serial correlation coefficient in the explosive case,Ann. Math. Statist.,29, 1188–1197.MATHMathSciNetGoogle Scholar

Copyright information

© Institute of Statistical Mathematics 1974

Authors and Affiliations

  • K. N. Venkataraman
    • 1
  1. 1.University of MadrasMadrasIndia

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