Estimation and Prediction in Mis-specified Fractionally Integrated Models with an Unknown Mean

Music City Center 

This paper investigates how mis-specification of the short memory dynamics affects estimation and prediction in a fractionally integrated model with an unknown mean. We derive the limiting distributions of three parametric estimators, namely exact Whittle, time-domain maximum likelihood, and conditional sum of squares, under common mis-specification of the short memory dynamics. We show that, given a consistent estimator of the mean, these three estimators converge to the same pseudo-true value and their asymptotic distributions are identical to those of the frequency domain maximum likelihood and discrete Whittle estimators, which are mean invariant. We analyze the properties of a linear predictor under mis-specification, demonstrating that it is biased unless the true mean is zero and that mean squared forecast error depends on the true and pseudo-true fractional differencing parameter. To support our theoretical findings, we conduct an extensive numerical exploration of these estimation methods. Our simulations reveal that the DWH estimator performs best in terms of bias and mean squared error and provides superior forecast accuracy when combined with the sample mean.

conditional sum of squares



linear predictor

long memory model

maximum likelihood

mis-specification

pseudo-true value 

Business and Economic Statistics Section