Bias in the Estimation of Autocorrelations

Bias in the estimation of the mean reversion parameter in continuous time models

“…This result echoes the conjecture of Hurwicz (1950) about the bias in the autoregressive (AR) estimate in the discrete time AR(1) model. Second, we show that the bias formula, which mimics that of Marriott and Pope (1954) and Kendall (1954) for the discrete time model and that of Tang and Chen (2009) for continuous time models, is essentially linear in coe¢ cient. Consequently, the bias predicted by the formula does not disappear in the unit root case.…”

“…The simpler expression mimics the bias formula derived by Marriott and Pope (1954) for the discrete time AR model and corresponds to the bias formula derived independently by Tang and Chen (2009) for the same model but with unknown mean. The complicated one includes an additional term from the exact evaluation of the Cesaro sums.…”

“…The bias formula corresponds to that of Marriott and Pope (1954) and Kendall (1954) for the discrete time autoregressive (AR) model with an intercept. It was shown that the bias of the mean reversion estimator is of order T 1 but not of order n 1 , where T is the data span and n is the number of observations.…”

“…From the estimation equation (28), using the same notations as in Bao and Ullah (2004), we have H 1 = hV n , Q = 1=( h), H 1 = h, V = h(V n 1), H 2 = h 2 V n , H 2 = h 2 , H 3 = h 3 V n , W = h 2 (1 V n ), and H 3 = h 3 . Substituting all these expressions to the individual terms in the stochastic expansion of^ given by Equation (14), we obtain…”

Bartlett Correction in the Stable Ar(1) Model With Intercept and Trend

“…Marriot and Pope (1954), the Bartlett correction turns out to be independent of the AR (1) parameter ρ. Furthermore, the factor is always smaller than 1.…”