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Smoothing methods for histogram‐valued time series: an application to value‐at‐risk
Author(s) -
Arroyo Javier,
GonzálezRivera Gloria,
Maté Carlos,
San Roque Antonio Muñoz
Publication year - 2011
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.10114
Subject(s) - exponential smoothing , histogram , smoothing , barycentric coordinate system , computer science , autoregressive model , series (stratigraphy) , exponential function , econometrics , value (mathematics) , moving average , algorithm , mathematics , artificial intelligence , machine learning , statistics , image (mathematics) , paleontology , mathematical analysis , geometry , biology
We adapt smoothing methods to histogram‐valued time series (HTS) by introducing a barycentric histogram that emulates the “average” operation, which is the key to any smoothing filter. We show that, due to its linear properties, only the Mallows‐barycenter is acceptable if we wish to preserve the essence of any smoothing mechanism. We implement a barycentric exponential smoothing to forecast the HTS of daily histograms of intradaily returns to both the SP500 and the IBEX 35 indexes. We construct a one‐step‐ahead histogram forecast, from which we retrieve a desired γ ‐value‐at‐risk (VaR) forecast. In the case of the SP500 index, a barycentric exponential smoothing delivers a better forecast, in the MSE sense, than those derived from vector autoregression models, especially for the 5% VaR. In the case of IBEX35, the forecasts from both methods are equally good. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 216–228, 2011