Temporal Aggregation of Stationary and Non-stationary Continuous-Time Processes
AbstractWe study the autocorrelation structure of aggregates from a continuous-time process. The underlying continuous-time process or some of its higher derivative is assumed to be a stationary continuous-time auto-regressive fractionally integrated moving-average (CARFIMA) process with Hurst parameter "H". We derive closed-form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. The limiting model of the aggregates, after appropriate number of differencing, is shown to be some functional of the standard fractional Brownian motion with the same Hurst parameter of the continuous-time process from which the aggregates are measured. These results are then used to assess the loss of forecasting efficiency due to aggregation. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..
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Bibliographic InfoArticle provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.
Volume (Year): 32 (2005)
Issue (Month): 4 ()
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898
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- Hassler, Uwe, 2011.
"Estimation of fractional integration under temporal aggregation,"
Journal of Econometrics,
Elsevier, vol. 162(2), pages 240-247, June.
- Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print peer-00815563, HAL.
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