On the errors-in-variables problem for time series

Abstract

The usual assumption in the classical errors-in-variables problem of independent measurement errors cannot necessarily be maintained when the data are time series; errors may be strongly serially correlated, possibly containing seasonal effects and trends. When it is possible to identify frequency bands over which the signal-to-noise ratio is large, an approximate solution to the errors-in-variables problem is to omit the remaining frequencies from a time series regression. We draw attention to the danger of “leakage” from the omitted frequencies, and show that the consequent bias can be reduced by means of tapering.