NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Low-Frequency Econometrics

Ulrich K. Müller, Mark W. Watson

NBER Working Paper No. 21564
Issued in September 2015
NBER Program(s):Technical Working Papers

Many questions in economics involve long-run or trend variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of low-frequency trigonometric weighted averages, which in turn can be used to conduct inference about long-run variability and covariability. Because the low-frequency weighted averages have large sample normal distributions, large sample valid inference can often be conducted using familiar small sample normal inference procedures. Moreover, the general approach is applicable for a wide range of persistent stochastic processes that go beyond the familiar I(0) and I(1) models.

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Document Object Identifier (DOI): 10.3386/w21564

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