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.
Original language | English |
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Pages (from-to) | 957-971 |
Number of pages | 15 |
Journal | Journal of the American Statistical Association |
Volume | 115 |
Issue number | 530 |
Early online date | 30 May 2019 |
DOIs | |
Publication status | Published - 2 Apr 2020 |
Externally published | Yes |
Keywords
- Curve process
- Functional FARIMA
- Functional principal component analysis
- Limit theorems
- Long-range dependence