Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes

By Anestis Antoniadis, Theofanis Sapatinas. 2003

116 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/28c830af562e1bfa756a0baaf7771c74735c65e0

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Statistics and Probability

Citations in the corpus

Curve Forecasting by Functional Autoregression (2008, background): “Let H = L2[0, 1] be the real Hilbert space of the square-summable functions of x ∈ [0, 1].”
Determining the order of the functional autoregressive model (2013, methodology): “(2000), Damon and Guillas (2002), Antoniadis and Sapatinas (2003), Antoniadis et al. (2006), Kargin and Onatski (2008), Horváth et al. (2010) and Didericksen et al. (2012), among many others.”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, methodology): “Various nonparametric and prediction methods for the FAR(1) models have been developed, and numerous applications have been found; see Besse et al. (2000), Laukaitis and Rac̆kauskas (2002), Antoniadis and Sapatinas (2003), Fernández de Castroa et al. (2005), Kargin and Onatski (2008), among others.”
Fourier analysis of stationary time series in function space (2013, background): “Problems considered include that of the estimation of the second-order structure [e.g., Mas (2000), Bosq (2002), Dehling and Sharipov (2005)] and that of prediction [e.g., Antoniadis and Sapatinas (2003), Ferraty and Vieu (2004), Antoniadis, Paparoditis and Sapatinas (2006)].”
Weak convergence in the functional autoregressive model (2005, methodology): “Recently Mas and Menneteau [22] announced large and moderate deviations theorems for the process or its covariance sequence whereas Antoniadis and Sapatinas [3] implemented wavelet methods which considerably improved the prevision mean square error.”
An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves (2017, unknown): “The functional YW estimator however faces the inverse problem that violates the positive semidefiniteness of the covariance operator, as discussed in Antoniadis and Sapatinas (2003).”
Detecting changes in the mean of functional observations (2009, background): “To name a few recent applications of FDA which illustrate its advantages alluded to above, we cite Antoniadis and Sapatinas (2003), Fernández de Castro et al. (2005), Müller and Stadtmüller (2005), Yao et al.”
Testing stationarity of functional time series (2014, methodology): “The main model employed for such series has been the functional autoregressive model of order one, which has received a great deal of attention, see Bosq (2000), Antoniadis and Sapatinas (2003), Antoniadis et al. (2006) and Kargin and Onatski (2008), among many others. More recent research has consi”
Locally Stationary Functional Time Series (2016, background): “…flexibility as well as its simplicity, functional autoregressive processes have been found useful in numerous applications such as economics and medicine, especially for prediction purposes (see e.g., Damon and Guillas, 1982; Besse and Ramsay, 1986; Antoniadis and Sapatinas, 2003, for early work).”
Weakly dependent functional data (2010, unknown): “The Annals of Statistics 2010, Vol. 38, No. 3, 1845–1884 DOI: 10.1214/09-AOS768 © Institute of Mathematical Statistics, 2010”