Smoothing Methods for Histogram-Valued Time Series: An Application to Value-at-Risk

被引：12

作者：

Arroyo J. ^{[1
]}

González-Rivera G. ^{[2
]}

Maté C. ^{[3
]}

San Roque A.M. ^{[3
]}

机构：

[1] Departamento de Ingeniería del Software e Inteligencia Artificial, Universidad Complutense de Madrid

[2] Department of Economics, University of California, Riverside

[3] Instituto de Investigación Tecnológica, Universidad Pontificia Comillas

来源：

Statistical Analysis and Data Mining | 2011年 / 4卷 / 02期

关键词：

Barycenter; Exponential smoothing; High-frequency data; Symbolic data; Value-at-risk;

D O I：

10.1002/sam.10114

中图分类号：

学科分类号：

摘要：

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. Copyright © 2011 Wiley Periodicals, Inc., A Wiley Company.

引用

页码：216 / 228

页数：12

共 32 条

[1]

Billard L., Diday E., Symbolic Data Analysis: Conceptual Statistics and Data Mining, (2006)

[2]

Rodriguez O., Diday E., Winsberg S., (2000)

[3]

Nagabhushan P., Pradeep Kumar R., ISNN '07: Proceedings of the 4th International Symposium on Neural Networks, pp. 1012-1021, (2007)

[4]

Irpino A., Verde R., Data Science and Classification, Proceedings of the IFCS 2006, pp. 185-192, (2006)

[5]

Verde R., Irpino A., Brito P., Bertrand P., Cucumel G., de Carvalho F., Selected Contributions in Data Analysis and Classification, pp. 123-134, (2007)

[6]

Arroyo J., Mate C., Forecasting histogram time series with k-nearest neighbours methods, Int J Forecast, 25, pp. 192-207, (2009)

[7]

Arroyo J., Gonzalez-Rivera G., Mate C., Handbook of Empirical Economics & Finance, pp. 247-280, (2011)

[8]

Gonzalez-Rivera G., Arroyo J., Time series modeling of histogram-valued data. The daily histogram time series of SP500 intradaily returns,, Int J Forecast, (2011)

[9]

Colombo A., Jaarsma R., A powerful numerical method to combine random variables, IEEE Trans Reliab, 29, 2, pp. 126-129, (1980)

[10]

Billard L., Diday E., From the statistics of data to the statistics of knowledge: symbolic data analysis, J Am Stat Assoc, 98, 462, pp. 470-487, (2003)

← 1 2 3 4 →