Abstract:In recent years, quantile regression has achieved
increasing prominence as a quantitative method of choice in applied
econometric research. The methodology focuses on how the quantile
of the dependent...In recent years, quantile regression has achieved
increasing prominence as a quantitative method of choice in applied
econometric research. The methodology focuses on how the quantile
of the dependent variable is influenced by the regressors, thus
providing the researcher with much information about variations in
the relationship between the covariates. In this dissertation, I
consider two quantile regression models where the information set
may contain quantiles of the regressors. Such frameworks thus
capture the dependence between quantiles - the quantile of the
dependent variable and the quantile of the regressors - which I
call models of quantile dependence. These models are very useful
from the applied researcher's perspective as they are able to
further uncover complex dependence behavior and can be easily
implemented using statistical packages meant for standard quantile
regressions. The first chapter considers an application of the
quantile dependence model in empirical finance. One of the most
important parameter of interest in risk management is the
correlation coefficient between stock returns. Knowing how
correlation behaves is especially important in bear markets as
correlations become unstable and increase quickly so that the
benefits of diversification are diminished especially when they are
needed most. In this chapter, I argue that it remains a challenge
to estimate variations in correlations. In the literature, either a
regime-switching model is used, which can only estimate correlation
in a finite number of states, or a model based on extreme-value
theory is used, which can only estimate correlation between the
tails of the returns series. Interpreting the quantile of the stock
return as having information about the state of the financial
market, this chapter proposes to model the correlation between
quantiles of stock returns. For instance, the correlation between
the 10th percentiles of stock returns, say the U.S. and the U.K.
returns, reflects correlation when the U.S. and U.K. are in the
bearish state. One can also model the correlation between the 60th
percentile of one series and the 40th percentile of another, which
is not possible using existing tools in the literature. For this
purpose, I propose a nonlinear quantile regression where the
regressor is a conditional quantile itself, so that the
left-hand-side variable is a quantile of one stock return and the
regressor is a quantile of the other return. The conditional
quantile regressor is an unknown object, hence feasible estimation
entails replacing it with the fitted counterpart, which then gives
rise to problems in inference. In particular, inference in the
presence of generated quantile regressors will be invalid when
conventional standard errors are used. However, validity is
restored when a correction term is introduced into the regression
model. In the empirical section, I investigate the dependence
between the quantile of U.S. MSCI returns and the quantile of MSCI
returns to eight other countries including Canada and major equity…Read More
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: article
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Cited By Count: 1
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