Detection of periodicity in functional time series

Abstract

We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a contaminating process which is weakly dependent. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully functional. Overall, for the functional series that motivate this research, the fully functional tests exhibit a superior balance of size and power. Asymptotic null distributions of all tests are derived and their consistency is established. Their finite sample performance is examined and compared by numerical studies and application to pollution data.

References in corpus (5)

• Weakly dependent functional data
• Nonstationary covariance models for global data
• Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
• Functional dynamic factor models with application to yield curve forecasting
• Prediction of functional ARMA processes with an application to traffic data

Cited by in corpus (4)

• A note on Herglotz's theorem for time series on function spaces
• Sparsely Observed Functional Time Series: Estimation and Prediction
• A note on quadratic forms of stationary functional time series under mild conditions
• Functional Lagged Regression with Sparse Noisy Observations