Publication: Contributions to time series factor modeling: model averaging and bias correction
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2017-03
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2017-05-12
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Abstract
Given the increasing availability of data and the evolution of computation,
there is a growing body of theory and applications taking advantage of multivariate
datasets. By including many variables in the analysis (even hundreds),
we can exploit more complete information as well as improve the
robustness of the estimators obtained (Stock and Watson, 2006).
In this dissertation, we work with multivariate time series. With the aim of
forecasting vectors of time series, well known approaches in time series literature
are AutoRegressive Integrated Moving Average (ARIMA, working with
each variable independently) and Vector AutoRegressive Integrated Moving
Average (VARIMA, working with a few variables at a time) models.
However, when there are many interrelated series, these approaches either
fail to include interconnections, or rapidly present methodological constraints
when more than few series are considered simultaneously. ARIMA models
fail to account for the variables’ mutual influence; while VARIMA models
can present an overwhelming complexity and possibly unfeasibility when
the number of time series is large. As a consequence of these limitations,
a large portion of research has focused on dimensionality reduction techniques.
These allow to exploit the relation between the series, as well as
their dynamic nature, and have the virtue of employing a reduced number of
parameters, thus circumventing the “curse of dimensionality” often associated
with multivariate data. In particular, in this thesis we focus on Factor
Models (FM).
The purpose of this dissertation is to improve the forecasts of high-dimensional
vectors of time series. Even with the expansion of research in this area, many
issues are still open. We explore some of the questions that arise with the
use of FM. In particular, we take an alternative approach for decisions regarding
the number of underlying common factors and what models these
factors follow (Chapter 2). On the other hand, even if the factors are accurately
estimated, and their estimation taken as observations in posterior
calculations, it is not unusual to deal with bias of the estimates of the parameters
for the model of the common factors, especially when the sample
size is small. Therefore, in Chapter 3 we work with techniques to correct
this bias and deal strictly with the effect of the time dimension, T.
Our discussion focuses on statistical and econometrical developments that
have been employed to address questions in the context of economics, business,
and demographics. For empirical examples we work with electricity
prices and industrial production indexes of European countries.
The rest of the dissertation is organized as follows. In Chapter 1 we introduce
the theory and challenges related to the estimation of factor models. We
address the reasons for employing dimensionality reduction, the techniques
that may be employed in the estimation of FM, the alternative criteria for
selecting the number of unobservable common factors, and what models are
usually employed for the common factors.
In Chapter 2 we work with the combination of forecasts, motivated by the
unsolved issues of selecting a number of common factors and selecting a
model for each of them. Instead of applying a particular criterion, we estimate
several specifications, with alternative numbers of common factors and
Summary 3 .alternative models for them. Afterwards, we evaluate the performance of five
easy to apply combination techniques in an application to electricity prices of
the Iberian and Italian markets. Even though the improvements that result
from the combinations are not big, it must be acknowledged that they are
maintained during a long period of time and are statistically significant for
some of the combinations considered, according to an Analysis of Variance
(ANOVA).
In Chapter 3 we propose two alternative techniques to correct the bias in AR
models for the estimated common factors, specifically when these are highly
persistent and the sample has a small time dimension (T is small). These
are the Bootstrap Bias-Correction methodology (Clements and Kim, 2007)
and Roy-Fuller’s methodology (Roy and Fuller, 2001). Though not originally
intended for factor models, these techniques contribute to reduce the bias of
AR coefficients, and by employing Monte Carlo simulations we show that the
improvement in the factors’ coefficients produces more accurate forecasts.
We obtain forecasting intervals, and present results in terms of coverage
and interval length. We apply these extensions to data of the Industrial
Production Index (IPI) for a group of European countries.
Finally, in Chapter 4 conclusions and further lines of research are summarized
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Keywords
Análisis multivariante, Análisis de series temporales, Modelo matemático, Previsión