Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models

Eric Hillebrand, Marcelo C. Medeiros

Research output: Contribution to journalArticlepeer-review


We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in time series models and apply our modeling framework to daily realized measures of integrated variance. We develop asymptotic theory for parameter estimation and propose two model-building procedures. The methodology is applied to stocks of the Dow Jones Industrial Average during the period 2000 to 2009. We find strong evidence of nonlinear effects in financial volatility. An out-of-sample analysis shows that modeling these effects can improve forecast performance. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)23-41
Number of pages19
JournalJournal of Business and Economic Statistics
Issue number1
StatePublished - Jan 2 2016
Externally publishedYes


  • Forecasting
  • Long memory
  • Realized variance
  • Smooth transitions

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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