Quadratic Prediction of Time Series via Auto-Cumulants

Tucker S. McElroy (), Dhrubajyoti Ghosh () and Soumendra Lahiri ()
Additional contact information
Tucker S. McElroy: U.S. Census Bureau
Dhrubajyoti Ghosh: Washington University in St. Louis
Soumendra Lahiri: Washington University in St. Louis

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 13, 463 pages

Abstract: Abstract Nonlinear prediction of time series can offer potential accuracy gains over linear methods when the process is nonlinear. As there are numerous examples of nonlinearity in time series data (e.g., finance, macroeconomics, image, and speech processing), there seems to be merit in developing a general theory and methodology. We explore the class of quadratic predictors, which directly generalize linear predictors, and show that they can be computed in terms of the second, third, and fourth auto-cumulant functions when the time series is stationary. The new formulas for quadratic predictors generalize the normal equations for linear prediction of stationary time series, and hence we obtain quadratic generalizations of the Yule-Walker equations; we explicitly quantify the prediction gains in quadratic over linear methods. We say a stochastic process is second order forecastable if quadratic prediction provides an advantage over linear prediction. One of the key results of the paper provides a characterization of second order forecastable processes in terms of the spectral and bi-spectral densities. We verify these conditions for some popular nonlinear time series models.

Keywords: Bi-spectral density; Nonlinear prediction; Nonlinear processes; Quadratic prediction; Polyspectra; 62M10; 62M20 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-023-00326-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00326-6

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-023-00326-6

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().