DIFFERENCING AS AN APPROXIMATE DE-TRENDING DEVICE Academic Article uri icon

abstract

  • Consider the model yj = f{hook}( j n) + j, j = 1,..., n, where the yj's are observed, f{hook} is a smooth but unknown function, and the j's are unobserved errors from a zero mean, strictly stationary process. The problem addressed is that of estimating the covariance function c(k) = E(0k) from the observations y1,..., yn without benefit of an initial estimate of f{hook}. It is shown that under appropriate conditions on f{hook} and the error process, n consistent estimators of c(k) can be constructed from second differences of the observed data. The estimators of c(k) utilize only periodogram ordinates at frequencies greater than some small positive number that tends to 0 as n . Tapering the differenced data plays a crucial role in constructing an efficient estimator of c(k). 1989.

published proceedings

  • STOCHASTIC PROCESSES AND THEIR APPLICATIONS

author list (cited authors)

  • HART, J. D.

citation count

  • 6

complete list of authors

  • HART, JD

publication date

  • January 1989