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Advances on asymptotic normality in non-parametric functional time series analysis. (English) Zbl 1278.62052
Summary: We consider a stationary process and wish to predict future values from previous ones. Instead of considering the process in its discretized form, we choose to see it as a sample of dependent curves. Then, we cut the process into \(N\) successive curves. Obviously, the \(N\) curves are not independent. The prediction issue can be translated into a non-parametric functional regression problem from dependent functional variables. This paper aims to revisit and complete two recent works on this topic. This article extends recent literature and provides asymptotic law with explicit constants under \(\alpha\)-mixing assumptions. Then we establish pointwise confidence bands for the regression function. To conclude, we present how our results behave on a simulation and on a real time series.

MSC:
62G08 Nonparametric regression and quantile regression
60G10 Stationary stochastic processes
60G25 Prediction theory (aspects of stochastic processes)
62G20 Asymptotic properties of nonparametric inference
62M20 Inference from stochastic processes and prediction
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