Abstract
Functional autoregressive models are popular for functional time series analysis, but the standard formulation fails to address seasonal behaviour in functional time series data. To overcome this shortcoming, we introduce seasonal functional autoregressive time series models. For the model of order one, we derive sufficient stationarity conditions and limiting behaviour, and provide estimation and prediction methods. Moreover, we consider a portmanteau test for testing the adequacy of this model, and we derive its asymptotic distribution. The merits of this model are demonstrated using simulation studies and via an application to hourly pedestrian counts.
Highlights
Improved acquisition techniques make it possible to collect a large amount of high-dimensional data, including data that can be considered functional (Ramsay, 1982)
B = 1000 trajectories are simulated from the Model (7.1) and the model parameter is estimated using the method of moments (MME), Unconditional Least Square (ULSE) and Kargin-Onatski (KOE) estimators
We have focused on seasonal functional autoregressive time series
Summary
Improved acquisition techniques make it possible to collect a large amount of high-dimensional data, including data that can be considered functional (Ramsay, 1982). A popular functional time series model is the functional autoregressive (FAR) process introduced by Bosq (2000), and further studied by Hörmann, Kokoszka, et al (2010), Horváth, Hušková & Kokoszka (2010), Horváth & Kokoszka (2012), Berkes, Horváth & Rice (2013), Hörmann, Horváth & Reeder (2013) and Aue, Norinho & Hörmann (2015). These models are applied in the analysis of various functional time series, they cannot handle seasonality adequately.
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