Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/56662
Authors: 
Song, Song
Härdle, Wolfgang K.
Ritov, Ya'acov
Year of Publication: 
2010
Series/Report no.: 
SFB 649 discussion paper 2010-039
Abstract: 
(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via functional factor analysis. We propose a two-step estimation procedure. At the first step, we detect the deterministic trends of the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under various situations extending current variable selection studies. At the second step, we obtain the detrended low dimensional stochastic process, but it also poses an important question: is it justified, from an inferential point of view, to base further statistical inference on the estimated stochastic time series? We show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible, which finally allows one to study the dynamics of the whole high-dimensional system with a low dimensional representation together with the deterministic trend. We apply the method to our motivating empirical problems: studies of the dynamic behavior of temperatures (further used for pricing weather derivatives), implied volatilities and risk patterns and correlated brain activities (neuro-economics related) using fMRI data, where a panel version model is also presented.
Subjects: 
semiparametric model
factor model
group lasso
seasonality
spectral analysis
periodic
asymptotic inference
weather
fMRI
implied volatility surface
JEL: 
C14
C32
G12
Document Type: 
Working Paper

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