##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Tingyi Zhu

#### UCSD

## Kernel Methods in Nonparametric Functional Time Series

##### Abstract:

Functional time series has become a recent focus of statistical research. In this talk, we will discuss the applications of kernel methods in the analysis of nonparametric functional time series. In the first half, we propose the kernel estimates for the autoregressor in a nonparametric functional autoregression model. It consistency is proved and a valid bootstrap procedure is provided to construct the prediction regions. In the second half of the talk, we propose a class of estimators for the spectral density kernel, which is a key element encapsulates the second-order dynamics of a functional time series. The new class of estimators employs the inverse Fourier transform of a flat-top function as the weight function employed to smooth the periodogram. It is shown that using a flat-top kernel yields a bias reduction and results in a higher-order accuracy in terms of optimizing the integrated mean square error (IMSE).

### October 16, 2017

### 10:30 AM

### AP&M 6402

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