High-Dimensional Time Series, Common Factors, and Nonstationarity

In this modern information age, with increasing computing power it has become commonplace to access and to analyze data of unprecedented size and complexity. In many important statistical applications, the number of variables or parameters is now as large as or even much larger than the number of observations. Inference under such a circumstance is generally acknowledged as an important challenge in contemporary statistics, and has been a focus point for active research lately. The Newton Institute in Cambridge has staged a large scale research programme on Statistical Theory and Methods for Complex, High-Dimensional Data in January -- June 2008. Against this background, the proposed project is devoted to the research on both theory and methodology for analyzing ultra-high dimensional time series which arise from various practical problems. For example, in portfolio optimization and risk management the number of assets concerned is typically in the order of hundreds or thousands. The so-called panel data, collected for various applications, consist of p time series of length n with, typically, p is larger or much larger than n.For analyzing those large scale multiple time series, dimension-reduction is a key for success. In this project we propose an innovative factor modelling technique which is statistically versatile and computationally effective. In particular, we will conduct the research in several interlocking areas including: (i) modelling high-dimensional time series with nonstationary factors, (ii) establishing high-dimensional volatility dynamics based on factors, including high-dimensional daily volatilities using high-frequency data; and (iii) identify finite dimensionality of curve time series. The results from (i) will be useful for modelling and forecasting panels of time series arising from economics, business, marketing, sociology, biology and ecology etc. (ii) addresses directly the important issues in modern finance such as asset pricing, portfolio allocation and risk management. Curve time series analysis (iii) will find applications in, for example, environment studies (annual weather record charts, annual pollution charts), finance (daily volatility curves, yield curves), marketing (sales charts). The freely-available softwares will be developed to implement the new methods.High-dimensional data analysis is clearly one of the most vibrant research areas in statistics (including biostatistics) and econometrics (including financial econometrics) these days. The novelty of this proposal lies mainly on the new estimation procedure which transfers the problem of estimating latent factors, which may be nonstationary, into a standard eigenanalysis, and therefore is applicable to the cases with the dimensionalities in the order of thousands. The idea of handling nonstationarity in the framework of curve time series is also new.