Working Paper: NBER ID: w21564
Authors: Ulrich K. Müller; Mark W. Watson
Abstract: 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.
Keywords: Low-frequency econometrics; Time series analysis; Long-run variability; Statistical inference
JEL Codes: C12; C22; C32
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| low-frequency variability in GDP growth rates (E39) | underlying economic phenomena (E26) |
| TFP growth (O49) | trend growth rate in GDP (O49) |
| persistence of inflation (E31) | long-run behavior of inflation (E31) |
| variations in TFP (F16) | GDP growth (O49) |
| long-run variance of GDP growth (O49) | long-run mean of GDP growth (O49) |
| long-run variance of inflation (E31) | long-run mean of inflation (E31) |