Prediction of functional ARMA processes with an application to traffic data

By Johannes Klepsch, Claudia Kl¨uppelberg, Taoran Wei. 2016

102 citations recorded by the source corpus.

For a functional ARMA(p, q) process an approximating vector model, based on functional PCA, is presented. Sufficient conditions are given for the existence of a stationary solution to both the functional and the vector model equations, and the structure of the approximating vector model is investigated. The stationary vector process is used to predict the functional process, where bounds for the difference between vector and functional best linear predictor are given. Finally, functional ARMA processes are applied for the modeling and prediction of highway traffic data.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/141d62fe734e9be270de45163563fa3a77482f8d

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In Applied Mathematics

In Control and Systems Engineering

Citations in the corpus

Wasserstein autoregressive models for density time series (2020, background): “Simpler sufficient conditions in Hilbert spaces are given in [5] (AR(p) case) and [16] (ARMA(p, q) case).”
Forecasting Functional Time Series with a New Hilbertian ARMAX Model: Application to Electricity Price Forecasting (2018, background): “[33]–[35] propose using vector time series models to estimate all the scores jointly.”
Long-Range Dependent Curve Time Series (2020, background): “When d = 0, (4.1) becomes the functional ARMA(p, q) of Klepsch, Klüppelberg, and Wei (2017), while when q = 0, it further reduces to the functional AR(p) model of Bosq (2000) and Liu, Xiao, and Chen (2016), and when p = 0, it reduces to the functional MA(q) model of Chen, Lei, and Tu (2016) and Aue…”