Nonparametric High-Dimensional Time Series: Estimation and Prediction

This thesis introduces a new class of functional-coefficient time series models,
where the regressors consist of autoregressors and latent factor regressors,
and the coefficients are allowed to change with certain index variable. The
unobservable factor regressors are estimated through imposing an approximate
factor model on very high dimensional exogenous time series variables
and subsequently implementing the classical principal component analysis.
With the estimated factor regressors, a local linear smoothing method is used
to estimate the coefficient functions and obtain a one-step ahead nonlinear
forecast of the response variable, and then a wild bootstrap procedure is introduced
to construct the prediction interval. The developed methodology is
further extended to the case of multivariate response vectors and the model is
generalised to the factor-augmented vector time series model with functional
coefficients. The latter substantially generalises the linear factor-augmented
vector autoregressive model which has been extensively studied in the literature.
Under some regularity conditions, the asymptotic properties of the proposed methods are derived. In particular, we show that the local linear
estimator and the nonlinear forecast using the estimated factor regressors
are asymptotically equivalent to those using the true latent factor regressors.
The latter is not feasible in practical applications. This thesis also discusses
selection of the numbers of autoregressors and factor regressors and choice
of bandwidth in local linear estimation. Some simulation studies and an
empirical application to predict the UK inflation are given to investigate the
performance of our model and methodology in finite samples.