Estimation of the intensity of non-homogeneous point processes via wavelets

• Published in: Annals of the Institute of Statistical Mathematics Vol. 63; no. 6; pp. 1221 - 1246
• Main Authors: de Miranda, José Carlos Simon, Morettin, Pedro A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-12-2011; Springer Nature B.V
• Subjects: Economics; Estimating techniques; Finance; Insurance; Management; Mathematical analysis; Mathematics; Mathematics and Statistics; Poisson distribution; Random variables; Statistics; Statistics for Business; Studies; Wavelet transforms; Point processes; Wavelets; Intensity; Non-internally correlated point processes; Poisson processes; Threshold
• ISSN: 0020-3157; 1572-9052
• DOI: 10.1007/s10463-010-0283-8

In this article we consider the problem of estimating the intensity of a non-homogeneous point process on the real line. The approach used is via wavelet expansions. Estimators of the intensity are proposed and their properties are studied, including the case of thresholded versions. Properties of the estimators for non-homogeneous Poisson processes follow as special cases. An application is given for the series of daily Dow Jones indices. Extensions to more general settings are also indicated.