  We establish theoretical and analytical results about the low frequency
contamination induced by general nonstationarity for estimates such as the
sample autocovariance and the periodogram, and deduce consequences for
heteroskedasticity and autocorrelation robust (HAR) inference. We show that for
short memory nonstationarity data these estimates exhibit features akin to long
memory. We present explicit expressions for the asymptotic bias of these
estimates. This bias increases with the degree of heterogeneity. in the data
and is responsible for generating low frequency contamination or simply making
the time series exhibiting long memory features. The sample autocovariances
display hyperbolic rather than exponential decay while the periodogram becomes
unbounded near the origin. We distinguish cases where this contamination only
occurs as a small-sample problem and cases where the contamination continues to
hold asymptotically. We show theoretically that nonparametric smoothing over
time is robust to low frequency contamination.in that the sample local
autocovariance and the local periodogram are unlikely to exhibit long memory
features. Simulations confirm that our theory provides useful approximations.
Since the autocovariances and the periodogram are key elements for HAR
inference, our results provide new insights on the debate between consistent
versus inconsistent small versus long/fixed-b bandwidths for long-run variance
(LRV) estimation-based inference.
