Differencing as an approximate de-trending device Academic Article uri icon


  • Consider the model yj = f{hook}( j n) + εj, j = 1,..., n, where the yj's are observed, f{hook} is a smooth but unknown function, and the εj's are unobserved errors from a zero mean, strictly stationary process. The problem addressed is that of estimating the covariance function c(k) = E(ε0εk) 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 δ that tends to 0 as n → ∞. Tapering the differenced data plays a crucial role in constructing an efficient estimator of c(k). © 1989.

author list (cited authors)

  • Hart, J. D.

citation count

  • 6

publication date

  • April 1989