Journal
ANNALS OF APPLIED STATISTICS
Volume 13, Issue 3, Pages 1590-1616Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-AOAS1234
Keywords
Seasonal functional time series; warping function; Karcher mean
Categories
Funding
- Singapore Ministry of Education Academic Research Fund Tier 1
- Institute of Data Science at National University of Singapore
- Saw Swee Hock Visiting Professorship
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Electricity prices are high dimensional, serially dependent and have seasonal variations. We propose a Warping Functional AutoRegressive (WFAR) model that simultaneously accounts for the cross time-dependence and seasonal variations of the large dimensional data. In particular, electricity price curves are obtained by smoothing over the 24 discrete hourly prices on each day. In the functional domain, seasonal phase variations are separated from level amplitude changes in a warping process with the Fisher-Rao distance metric, and the aligned (season-adjusted) electricity price curves are modeled in the functional autoregression framework. In a real application, the WFAR model provides superior out-of-sample forecast accuracy in both a normal functioning market, Nord Pool, and an extreme situation, the California market. The forecast performance as well as the relative accuracy improvement are stable for different markets and different time periods.
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