Stochastic integral convergence : A white noise calculus approach

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

View graph of relations



Original languageEnglish
Pages (from-to)2035-2057
Journal / PublicationElectronic Journal of Statistics
Issue number2
Publication statusPublished - 29 Sept 2015
Externally publishedYes


By virtue of long-memory time series, it is illustrated in this paper that white noise calculus can be used to handle subtle issues of stochastic integral convergence that often arise in the asymptotic theory of time series. A main difficulty of such an issue is that the limiting stochastic integral cannot be defined path-wise in general. As a result, continuous mapping theorem cannot be directly applied to deduce the convergence of stochastic integrals ∫10 Hn(s) dZn(s) to ∫10H(s) dZ(s) based on the convergence of (Hn, Zn) to (H,Z) in distribution. The white noise calculus, in particular the technique of S-transform, allows one to establish the asymptotic results directly.

Research Area(s)

  • Convergence, Fractional dickey-fuller statistic, S-transform, Stochastic integral, White noise calculus

Bibliographic Note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to