A Review on Semiparametrically Nonlinear Time Series Modelling: Theory and Application

TOPIC: 

a review on Semiparametrically nonlinear time series modelling: theory and application 

ABSTRACT

Semiparametric methodologies have achieved quite a lot of success in nonlinear statistical and econometric modelling; see, for example, Fan and Gijbels (1996), Fan and Yao (2003) and Li and Racine (2007). Under various mixing stochastic processes (in particular the alpha--mixing, i.e., strong mixing, that covers many other mixings such as phi-mixing, beta-mixing as special cases), these techniques, including the popular local linear fitting, have been well studied in the literature by many researchers in time series modelling, c.f., Liebscher (1996), Masry (1996), Bosq (1998), Fan and Yao (2003), Gao (2007), Hansen (2008), Kristensen (2009), among others.

However, from a practical point of view, the mixing (e.g., alpha—mixing) processes suffer from many undesirable features. For example, for a lot of popular processes in econometrics such as an ARMA process mixed with ARCH or GARCH errors, it is still difficult to show whether they are alpha--mixing or not except in some very special cases. Even for a very simple linear AR(1) model with innovation being independent symmetric Bernoulli random variables taking on values of -1 and 1, the stationary solution to the model is not alpha--mixing (Andrews 1984).

In this talk, the speaker will first review some of the extensions of the stochastic processes beyond the mixings, in particular a class of generalised stable processes from mixings, or called near epoch dependence, which covers a variety of interesting stochastic processes in time series econometric modelling. The speaker will then report some recent developments on the local linear fitting and semiparametric model averaging techniques that his co-authors and himself have made under this kind of near epoch dependent processes. The results obtained include the pointwise asymptotic distributions for the probability density estimation and the local linear estimator of a nonparametric time series regression as well as their uniformly strong and weak consistencies with convergence rates under near epoch dependence. These results are showed to be useful for the study of a proposed semiparametric model averaging method with its empirical applications to an annual mean temperature anomaly series and high-frequency financial data presented.

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Presenter

Zudi Lu
The University of Adelaide 

Research Fields

Nonlinear Time Series Analysis, Nonlinear Spatial and Spatiotemporal Data Analysis, Semiparametric Data Analysis, Financial Econometrics, Environmental Risk Modelling, Computational Statistics and Econometrics.

Date:

26 April 2013 (Friday)

Time: 

3.45pm - 5.15pm 

Venue: 

Seminar Room 5.1, Level 5
School of Economics 
Singapore Management University
90 Stamford Road
Singapore 178903