Partial cross-quantilogram networks: Measuring quantile connectedness of financial institutions

We propose partial cross-quantilogram networks for measuring the connectedness of 30 China’s financial institutions at different quantiles. We find that networks at the extreme quantiles are more closely connected than those at the median quantile. The network density and centrality show that the systemically important financial institutions vary across different quantiles. We observe an asymmetric effect in quantile connectedness during the period of “2015–16 Chinese stock market turbulence;” that is, the network connectedness at the lower quantile (i.e., 0.05 quantile) is higher than that at the upper and median quantiles (i.e., 0.95 and 0.50 quantiles). By analyzing the similarity of networks across quantiles, we find that the similarity index is relatively high in the crisis period. Our study provides useful information on connectedness of financial institutions for regulators and investors.     

Forecasting value at risk and expected shortfall with mixed data sampling

I propose applying the Mixed Data Sampling (MIDAS) framework to forecast Value at Risk (VaR) and Expected shortfall (ES). The new methods exploit the serial dependence on short-horizon returns to directly forecast the tail dynamics of the desired horizon. I perform a comprehensive comparison of out-of-sample VaR and ES forecasts with established models for a wide range of financial assets and backtests. The MIDAS-based models significantly outperform traditional GARCH-based forecasts and alternative conditional quantile specifications, especially in terms of multi-day forecast horizons. My analysis advocates models that feature asymmetric conditional quantiles and the use of the Asymmetric Laplace density to jointly estimate VaR and ES.     

On downside risk predictability through liquidity and trading activity: A dynamic quantile approach

Most downside risk models implicitly assume that returns are a sufficient statistic with which to forecast the daily conditional distribution of a portfolio. In this paper, we analyze whether the variables that proxy for market-wide liquidity and trading conditions convey valid information for forecasting the quantiles of the conditional distribution of several representative market portfolios, including volume- and value-weighted market portfolios, and several Book-to-Market- and Size-sorted portfolios. Using dynamic quantile regression techniques, we report evidence of conditional tail predictability in terms of these variables. A comprehensive backtesting analysis shows that this link can be exploited in dynamic quantile modelling, in order to considerably improve the performances of day-ahead Value at Risk forecasts.     

Oil price shocks,geopolitical risks,and green bond market dynamics

This research explores the causal relation among oil price, geopolitical risks, and green bond index in the United States from December 2013 to January 2019. Unlike the conventional linear model specification used in earlier works, we evaluate causal relations based on Granger-causality in quantile analysis. Our empirical results reveal unidirectional Granger-causality from geopolitical risk to oil price at the extreme quantiles. We also observe a significant bi-directional causality from oil price to green bond index for the lower quantiles. Findings also reveal causality from geopolitical risk to green bond index in the lower quantiles of the distribution. Therefore, knowledge of these causal relationships can help policy makers to evaluate and implement effective policies to prevent sudden and substantial oil price shocks and geopolitical risk.     

Improved estimation of extreme quantiles in the multivariate Lomax (Pareto II) distribution

Estimation of a quantile of the common marginal distribution in a multivariate Lomax (Pareto II) distribution with unknown location and scale parameters is considered. For quadratic loss and specified extreme quantiles, it is established that the best affine equivariant procedure is inadmissible by constructing a better estimator.     

Evaluating quantile forecasts in the M5 uncertainty competition

Probabilistic forecasts are necessary for robust decisions in the face of uncertainty. The M5 Uncertainty competition required participating teams to forecast nine quantiles for unit sales of various products at various aggregation levels and for different time horizons. This paper evaluates the forecasting performance of the quantile forecasts at different aggregation levels and at different quantile levels. We contrast this with some theoretical predictions, and discuss potential implications and promising future research directions for the practice of probabilistic forecasting.     

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

Quantiles, expectiles and splines

A time-varying quantile can be fitted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions.     

Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market

Given the growing need for managing financial risk and the recent global crisis, risk prediction is a crucial issue in banking and finance. In this paper, we show how recent advances in the statistical analysis of extreme events can provide solid methodological fundamentals for modeling extreme events. Our approach uses self-exciting marked point processes for estimating the tail of loss distributions. The main result is that the time between extreme events plays an important role in the statistical analysis of these events and could therefore be useful to forecast the size and intensity of future extreme events in financial markets. We illustrate this point by measuring the impact of the subprime and global financial crisis on the German stock market in extenso, and briefly as a benchmark in the US stock market. With the help of our fitted models, we backtest the Value at Risk at various quantiles to assess the likeliness of different extreme movements on the DAX, S&P 500 and Nasdaq stock market indices during the crisis. The results show that the proposed models provide accurate risk measures according to the Basel Committee and make better use of the available information.     

Characterizing systems of distributions by quantile measures

Modelling an empirical distribution by means of a simple theoretical distribution is an interesting issue in applied statistics. A reasonable first step in this modelling process is to demand that measures for location, dispersion, skewness and kurtosis for the two distributions coincide. Up to now, the four measures used hereby were based on moments.
In this paper measures are considered which are based on quantiles. Of course, the four values of these quantile measures do not uniquely determine the modelling distribution. They do, however, within specific systems of distributions, like Pearson's or Johnson's; they share this property with the four moment-based measures.
This opens the possibility of modelling an empirical distribution—within a specific system—by means of quantile measures. Since moment-based measures are sensitive to outliers, this approach may lead to a better fit. Further, tests of fit—e.g. a test for normality—may be constructed based on quantile measures. In view of the robustness property, these tests may achieve higher power than the classical moment-based tests.
For both applications the limiting joint distribution of quantile measures will be needed; they are derived here as well.     

Non‐parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

Within the inferential context of predicting a distribution of potential outcomes P[y(t)] under a uniform treatment assignment t ∈ T, this paper deals with partial identification of the α‐quantile of the distribution of interest Q_α[y(t)] under relatively weak and credible monotonicity‐type assumptions on the individual response functions and the population selection process. On the theoretical side, the paper adds to the existing results on non‐parametric bounds on quantiles with no prior information and under monotone treatment response (MTR) by introducing and studying the identifying properties of α‐quantile monotone treatment selection (α‐QMTS), α‐quantile monotone instrumental variables (α‐QMIV) and their combinations. The main result parallels that for the mean; MTR and α‐QMTS aid identification in a complementary fashion, so that combining them greatly increases identification power. The theoretical results are illustrated through an empirical application on the Italian returns to educational qualifications. Bounds on several quantiles of ln(wage) under different qualifications and on quantile treatments effects (QTE) are estimated and compared with parametric quantile regression (α‐QR) and α‐IVQR estimates from the same sample. Remarkably, the α‐QMTS & MTR upper bounds on the α‐QTE of a college degree versus elementary education imply smaller year‐by‐year returns than the corresponding α‐IVQR point estimates. Copyright © 2010 John Wiley & Sons, Ltd.     

Markov switching quantile autoregression

This paper considers the location‐scale quantile autoregression in which the location and scale parameters are subject to regime shifts. The regime changes in lower and upper tails are determined by the outcome of a latent, discrete‐state Markov process. The new method provides direct inference and estimate for different parts of a non‐stationary time series distribution. Bayesian inference for switching regimes within a quantile, via a three‐parameter asymmetric Laplace distribution, is adapted and designed for parameter estimation. Using the Bayesian output, the marginal likelihood is readily available for testing the presence and the number of regimes. The simulation study shows that the predictability of regimes and conditional quantiles by using asymmetric Laplace distribution as the likelihood is fairly comparable with the true model distributions. However, ignoring that autoregressive coefficients might be quantile dependent leads to substantial bias in both regime inference and quantile prediction. The potential of this new approach is illustrated in the empirical applications to the US inflation and real exchange rates for asymmetric dynamics and the S&P 500 index returns of different frequencies for financial market risk assessment.     

How does investor attention matter for crude oil prices and returns? Evidence from time-frequency quantile causality analysis

This paper studies the time–frequency, nonlinear quantile relationship between investor attention (GSVI) and crude oil over the period from January 2000 to April 2020. To do so, the wavelet coherency, wavelet-based causality-in-quantiles test and quantile-on-quantile method are employed. The results indicate that first, the correlation between investor attention and crude oil is relatively high, and the highly correlated regions are concentrated from 8 to 16 months. In most cases, the GSVI is negatively correlated with the crude oil market. Additionally, under extreme market conditions, the explanatory ability is stronger than in the normal market, and it is greater in the low-frequency domain than in the high-frequency domain. Finally, investor attention has an apparent asymmetric impact on crude oil prices and returns at each scale, displaying a positive effect on the low quantiles of crude oil but a negative effect on the high quantiles across all quantiles of the GSVI. In the short term, when crude oil prices and returns are in a bear market, the larger volume of the GSVI has a greater impact on them. Moreover, the impact becomes greatest under extreme market conditions.     

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting,incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.     

Semiparametric quantile averaging in the presence of high-dimensional predictors

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the “true” structure of the underlying conditional quantile function, and in addition, we may have a large number of predictors. Focusing on such cases, we introduce a flexible and practical framework based on penalized high-dimensional quantile averaging. In addition to prediction, we show that the proposed method can also serve as a predictor selector. We conduct extensive simulation experiments to asses its prediction and variable selection performances for nonlinear and linear time series model designs. In terms of predictor selection, the approach tends to select the true set of predictors with minimal false positives. With respect to prediction accuracy, the method competes well even with the benchmark/oracle methods that know one or more aspects of the underlying quantile regression model. We further illustrate the merit of the proposed method by providing an application to the out-of-sample forecasting of U.S. core inflation using a large set of monthly macroeconomic variables based on FRED-MD database. The application offers several empirical findings.     

Does transaction activity predict Bitcoin returns? Evidence from quantile-on-quantile analysis

This paper uses the quantile-on-quantile regression to examine the predictive power of transaction activity for Bitcoin returns over the period from January 2013 to December 2018. We measure the Bitcoin transaction activity using trading volumes, the number of unique Bitcoin transactions, and the number of unique Bitcoin addresses. Considering the onset of structural breaks, we identify considerable effects of the heterogeneity concerning the quantiles of transaction activity, which cannot be depicted fully by the traditional quantile regression method. The empirical results show that higher transaction activity tends to predict higher/lower Bitcoin returns when the market is in a bullish/bearish state. We find that the nexus is asymmetric across quantiles, depending on the sign and size of the transaction activity, and the predictive relationship intensifies in the upper or lower quantiles of the conditional distribution. In addition, this empirical evidence is in line with the volume-return association in the equity market due to private informative and noninformative trading actions. Overall, our findings suggest that transaction activity-based strategies should be made with respect to Bitcoin market performance, specifically during extreme conditions.     

The relationship between carbon dioxide emissions and economic growth: quantile panel-type analysis

This paper samples the data of 138 countries during the 1971–2007 period, and performs an empirical test to validate the relationship between carbon dioxide emissions and economic growth. It first performs panel data analysis and quantile regression analysis to estimate the long-run elasticity relationships, and then analyzes the short-run error correction model to verify the causal relationship between the two. The empirical results indicate the following. (1) The long-run relationship between global carbon dioxide emissions and GDP is stable, with 32.6% of the sampled countries showing cross-coupling of the two (with an elasticity value of greater than 1), 47.1% reporting relative-decoupling (with an elasticity value between 0 and 1), and 20.3% seeing absolute-decoupling (with an elasticity value of smaller than 0). (2) The quantile regression shows that long-run elasticity declines along with the rise of carbon dioxide emission quantiles. In other words, cross-coupling turns into relative-decoupling. (3) The analysis of short-run panel data and quantile regressions mostly support the feedback relationship between carbon dioxide emissions growth and economic growth. This is consistent with the hypothesis developed by Kuznets. (4) According to the results of the quantile regression, the higher the quantiles, the faster and more stable of the short-run error-correction mechanism of the adjustments from short-run disequilibrium to long-run equilibrium. (5) Under the low-quantile carbon dioxide emissions growth and economic growth, the relationship between these two is not stable of the short-run disequilibrium adjustments in the error-correction adjustment process. However, the relationship between these two is steady and feedback in the case of high quantiles. Therefore, the first priority to combat global warming is to focus on the countries with high economic growth and high carbon dioxide emissions growth.     

Growth in stress

We propose a new global risk index, Growth-in-Stress (GiS), that measures the expected fall in a country’s GDP as the global factors, which drive world growth, are subject to stressful conditions. Using the GDP growth rates of 87 countries, we find that, since the 2008 financial crisis, though mainly from 2011 on, the world overall has fallen in a state of complacency, with the cross-sectional average GiS falling quite dramatically; in 2015, the average worst outcome seems to be no growth at the 95% probability factor stress. However, the cross-sectional dispersion within groups is quite variable: it is the smallest among industrialized countries and the largest among emerging and developing countries. We also measure the factor stress on different quantiles of the GDP growth distribution of each country. We calculate an Armageddon-type event as we seek to find the GiS on the 5% quantile of growth under the extreme 95% probability events of the factors, and find that it can be as large as an annual 20% fall in GDP.     

Set identification via quantile restrictions in short panels

This paper studies the identifying power of conditional quantile restrictions in short panels with fixed effects. In contrast to classical fixed effects models with conditional mean restrictions, conditional quantile restrictions are not preserved by taking differences in the regression equation over time. This paper shows however that a conditional quantile restriction, in conjunction with a weak conditional independence restriction, provides bounds on quantiles of differences in time-varying unobservables across periods. These bounds carry observable implications for model parameters which generally result in set identification. The analysis of these bounds includes conditions for point identification of the parameter vector, as well as weaker conditions that result in point identification of individual parameter components.     

Modelling firm‐size distribution using Box–Cox heteroscedastic regression

Using the Box–Cox regression model with heteroscedasticity (BCHR), we re‐examine the size distribution of the Portuguese manufacturing firms studied by Machado and Mata ( 2000 ) using the Box–Cox quantile regression (BCQR) method. We show that the BCHR model compares favourably against the BCQR method. In particular, the BCHR model can answer the key questions addressed by the BCQR method, with the advantage that the estimated quantile functions are monotonic. Furthermore, estimation of the BCHR model is straightforward and the confidence intervals of the BCHR regression quantiles are easy to compute. Copyright © 2006 John Wiley & Sons, Ltd.