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1 results

  • Stochastic difference equations with non-integral differences

  • P. M. Robinson
  • Journal:
    Advances in Applied Probability / Volume 6 / Issue 3 / September 1974
    Published online by Cambridge University Press:
    01 July 2016, pp. 524-545
    Print publication:
    September 1974

  • As an alternative to conventional discrete time models for stochastic processes that fluctuate within the sampling interval, we propose difference equations containing non-integral lags. We discuss the problems of stability, identification and estimation, for which an approximate model is needed. Least squares applied to an approximate Fourier-transformed model yields estimators of the coefficients that are consistent with respect to the true model under some conditions. The conditions are weak when the model contains predetermined variables that obey an “aliasing condition”; estimators of the lags as well as coefficients can then be found that are consistent, efficient and satisfy a central limit theorem. Optimal estimators for stochastic difference-differential equations are also available.