Nonparametric estimation of a periodic sequence in the presence of a smooth trend

Arbeitspapier

In this paper, we study a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates as well as the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study that investigates the small sample behaviour of our procedure. Finally, we illustrate our method by applying it to a series of global temperature anomalies.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP23/12

Classification and Topics

• Classification: Wirtschaft
• Subject: nonparametric estimation ; penalized least squares ; periodic sequence ; temperature anomaly data

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Vogt, Michael ; Linton, Oliver
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2012

Further information

• DOI: doi:10.1920/wp.cem.2012.2312
• Handle: http://hdl.handle.net/10419/64724
• Last update: 10.03.2025, 11:42 AM CET