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(a) Daily equity returns and posterior median of the conditional quantiles for (b) B-JSAV(1,1), and (c) B-JSSV(1,1) for IBM, S&P500, and WTI. We use different colours to depict the various quantiles for K = 10 and a = (0, 0.05, . . . , 0.45, 0.5).
Source publication
We consider jointly modelling a finite collection of quantiles over time. Formal Bayesian inference on quantiles is challenging since we need access to both the quantile function and the likelihood. We propose a flexible Bayesian time-varying transformation model, which allows the likelihood and the quantile function to be directly calculated. We d...
Contexts in source publication
Context 1
... IBM and S&P500 data were obtained from the Center for Research in Security Prices (CRSP), while the WTI data were obtained from the FRED data base (DCOILWTICO series). Figure 4(panel (a)) shows the evolution of each time series. ...
Context 2
... posterior medians of the conditional quantiles for the B-JSAV(1, 1) and B-JSSV(1, 1) models are shown in Figure 4. The results for B-JGJR(1, 1) and B-JAVL(1, 1) models are shown in Appendix D (supplementary materials). ...
Context 3
... IBM and S&P500 data were obtained from the Center for Research in Security Prices (CRSP), while the WTI data were obtained from the FRED data base (DCOILWTICO series). Figure 4 (panel (a)) shows the evolution of each time series. ...
Context 4
... posterior medians of the conditional quantiles for the B-JSAV(1,1) and B-JSSV(1,1) models are shown in Figure 4. The results for B-JGJR(1,1) and B-JAVL(1,1) models are shown in Appendix D. The B-JQTS model is able to describe the changing conditional distribution of returns (by construction, the model leads to no quantile crossings). ...
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Citations
... The (joint) quantile forecast is appealing in many economic applications (Ley and Steel, 2007), such as value at risk in the finance industry in order to develop a strategy for trading and/or hedging purposes. Recently, Griffin and Mitrodima (2022) proposed a Bayesian quantile time series model for asset returns which beautifully handled formal Bayesian inference on quantiles. It is an open question so far on how to incorporate the feature selection technique in joint quantile time series analysis, which is our goal of this paper. ...
... 7 The requirement of monotonicity follows from the definition of quantiles. Note that Griffin and Mitrodima (2022) or Wu and Narisetty (2021) propose frameworks to model a set of quantiles in a joint econometric framework. See also Chernozhukov et al. (2010) . ...
This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regressions (QRs) featuring conditional heteroskedasticity. I use data augmentation schemes to render the model conditionally Gaussian and develop an efficient sampling algorithm. Regularization of the high-dimensional parameter space is achieved via dynamic shrinkage priors. The merits of the proposed approach are illustrated in a simulation study, and a simple version of TVP-QR based on an unobserved components model is applied to dynamically trace the quantiles of inflation in the United States, the United Kingdom and the euro area. In an out-of-sample forecast exercise, I find the proposed model to be competitive and perform particularly well for higher-order and tail forecasts. A detailed analysis of the resulting predictive distributions reveals that they are sometimes skewed and occasionally feature heavy tails.
... Formal Bayesian inference on quantiles is challenging because the approach to both quantile function and probability is necessary. Griffin, and Mitrodima (2020) propose a flexible Bayesian time-varying transformation model, which enables the direct calculation of probability and quantile functions. The usefulness of the model is illustrated using MCMC methods. ...
Abstract
The objective of the paper was to evaluate the mutual relationship of
copper and zinc prices between 2011 and 2021 and to predict their
future prices until the year 2030. For this purpose, the following
methods were used: regression of neural structures in TIBCO's
Statistica software, version 13.0, time-series smoothing by means of
multilayer perceptron network, graphical representation, Pearson
correlation coefficient, and logical judgment. According to the
prediction, the copper price will decrease slightly compared to the
preceding years. In 2026, it is expected to stabilize at USD 610/t until
the year 2030. Zinc price is expected to increase slightly until the end
of the year 2030 when the resulting predicted price is USD 410/t.
Pearson correlation coefficient of copper and zinc achieves the
approximate value of 0.65. The results thus confirm the fact that these
commodities are not perfect complements. First, the mutual
relationship of the two commodities indicates that the price of zinc is
pushed up mainly by the copper price. On the contrary, the copper
price is pushed down by the price of zinc. There is a price
convergence between the two commodities. The future development
of copper and zinc prices is not subject to unpredictable events, such
as a political situation or the aforementioned COVID-19 pandemic.
Such a long-term prediction might thus not provide an objective
result.
Purpose
This study aims to introduce a tree-structured linear and quantile regression framework to the analysis and modeling of equity returns, within the context of asset pricing.
Design/Methodology/Approach
The approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The framework is applied on numerous U.S. asset pricing models, using alternative mimicking factor portfolios, frequency of data, market indices, and equity portfolios.
Findings
The findings reveal strong evidence that asset returns exhibit asymmetric effects and non- linear patterns to different common factors, but, more importantly, that there are multiple thresholds that create several partitions in the common factor space.
Originality/Value
To the best of the authors' knowledge, this paper is the first to explore and apply a tree-structured and quantile regression framework in an asset pricing context.
