Long-Range Dependent Curve Time Series

Degui Li, Peter M. Robinson and Han Lin Shang

Journal of the American Statistical Association, 2020, vol. 115, issue 530, 957-971

Abstract: We introduce methods and theory for functional or curve time series with long-range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the dominant subspace of the curves. In a semiparametric context, we propose an estimate of the memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications. The first of these finds a degree of stability and persistence in intraday stock returns. The second finds similarity in the extent of long memory in incremental age-specific fertility rates across some developed nations. Supplementary materials for this article are available online.

Date: 2020
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Citations: View citations in EconPapers (20)

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DOI: 10.1080/01621459.2019.1604362

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