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1 results

  • Asymptotic properties of time domain gaussian estimators

  • R. Kohn
  • Journal:
    Advances in Applied Probability / Volume 10 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    01 July 2016, pp. 339-359
    Print publication:
    June 1978

  • We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to non-linear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss–Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.