# Estimation of latent factors for high-dimensional time series

Author(s) Lam, Clifford, Yao, Qiwei and Bathia, Neil

ISSN/ISBN 0006-3444

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+44 (0)20 7955 7636

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7636

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COL.6.09

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Tuesdays 11am - 12pm

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Clifford’s research are focused in 1) statistical leaning techniques, especially for high dimensional data, and 2) time series analysis. These include semiparametric modelling, variables and feature selection, regularization methods for high dimensional time series analysis, to name but a few areas. One particular area of interest is the estimation of a large covariance/precision matrix from data. With random matrix theories more developed over the past decade, it is a high time for further developments of theories and methodologies in the area of high dimensional matrix estimation and applications. This area is important in a wide variety of scientific fields, including portfolio allocation and risk assessment in finance, classification and large scale hypothesis testing in bioinformatics, forecasting in macroeconomics time series, or cosmological survey in astrophysics.

High dimensional time series modelling is needed nowadays for making sense of vast volume of data we can find everyday around us, including the internet. Clifford Lam’s one particular research interest about high dimensional time series analysis is to find “factors” that can explain/summarise a majority of time series dynamics, like market factors that explain the dynamics of most stock prices in FTSE 100. A goal is to incorporate large number of variables that we can observe, and then summarise these into factors for increasing the explanatory and predictive power of various time series models.

Another area of research is in spatial econometrics modelling. A commonly used model is the spatial lag/error model for a large spatial panel of time series. To be able to use such a model, a component called the spatial weight matrix, which is a square matrix of the same size as the dimension of the panel, has to be pre-specified. This matrix represents the underlying spatial interdependence structure of the data. Yet there are no universal rules in doing so, and most practitioner use certain distance metrics to specify such a matrix, which is at best a crude approximation to the said structure. Moreover, when the dimension of the panel increases, it becomes more difficult to specify this spatial weight matrix. There are in fact various ways to estimate the said matrix from data, and inference in the models with such a matrix estimated rather than pre-specified is also an important research element.

Prior to joining the LSE in 2008, Clifford was a PhD student in the department of Operations Research & Financial Engineering, Princeton University.

Author(s) Lam, Clifford, Yao, Qiwei and Bathia, Neil

ISSN/ISBN 0006-3444

Author(s) Lam, Clifford and Yao, Qiwei

ISSN/ISBN 0090-5364

Author(s) Lam, Clifford

ISSN/ISBN 0090-5364

Author(s) Lam, Clifford, Feng, Phoenix and Hu, Charlie

ISSN/ISBN 0006-3444

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