Abstract
This paper used cross-sectional aggregation as the inspiration for a model with long-range dependence that arises in actual data. One of the advantages of our model is that it is less brittle than fractionally integrated processes. In particular, we showed that the antipersistent phenomenon is not present for the cross-sectionally aggregated process. We proved that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for nonfractional long-range-dependent processes with negative degrees of persistence. As an application, we showed how we can approximate a fractionally differenced process using theoretically-motivated cross-sectional aggregated long-range-dependent processes. An example with temperature data showed that our framework provides a better fit to the data than the fractional difference operator.
Highlights
Long-range dependence has been a topic of interest in econometrics since Granger’s study on the shape of the spectrum of economic variables (Granger 1966)
Notwithstanding its popularity, Granger argued that processes generated by the fractional difference operator fall into the area of “empty boxes”, about theory—either economic or econometric—on topics that do not arise in the actual economy (Granger 1999)
Granger argued that fractionally integrated processes fall into the “empty box” category of theoretical developments that do not arise in the real economy
Summary
Long-range dependence has been a topic of interest in econometrics since Granger’s study on the shape of the spectrum of economic variables (Granger 1966). We present two algorithms to generate long-range dependence by cross-sectional aggregation with similar computational requirements as the fractional difference operator. We proved that cross-sectionally aggregated processes do not possess the antipersistent properties We argue that these are restrictions imposed by the fractional difference operator that may not hold in real data. We used temperature data to show that the model provides a better, theoretically supported, fit to real data than the fractional difference operator when the source of long-range dependence is crosssectional aggregation.
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