A0186
Title: Detection of periodicity in functional time series
Authors: Gilles Nisol - ULB (Belgium) [presenting]
Abstract: Determining whether the dynamics of certain phenomena has a periodic pattern is essential in many fields, notably in climatology, finance or environmental sciences. For example, a weekly pattern in pollution level curves may be associated with an anthropogenic influence. The aim is to extend the range of application of existing periodicity tests to time series of functional data. We will investigate two approaches for testing whether observations are stationary, against the alternative hypothesis that there is a fixed periodic trend inherent. First, we will consider the projection of the time series onto a finite subspace and derive the likelihood ratio test statistic for the projected series. Second, we will define a purely functional test, in the sense that it does not require any projection on a subspace. To start with, our theory is derived in an i.i.d. Gaussian framework with a simple sinusoidal alternative, and then it is generalized to stationary observations and some arbitrary periodicity pattern. We will then conduct a simulation study in order to assess the power functions of our tests. Finally, we apply our procedure to intraday volatility curves of SP100 which are shown to exhibit a weekly periodicity.
