Quantile Autoregressive Model Research Articles

Revisiting the asymmetric dynamic dependence of stock returns: Evidence from a quantile autoregression model

The paper provides an overview of the asymmetric dynamic dependency of the conditional return distribution using a quantile autoregression model for three indexes, namely the Shenzhen Component (SZC), the Standard & Poor's 500 (S&P 500) and Stoxx Europe 600 (S&E 600) indexes. Our findings can be summarized as follows. For SZC index, lagged extreme positive returns display more impact on current returns than that of lagged other returns at median and high quantiles; at median and high quantiles lagged positive returns display more impact on current returns than that of lagged negative returns; at lower quantiles lagged positive returns display less impact on current returns than that of lagged negative returns. For S&E 600 index, at low quantiles lagged extreme positive returns display less impact on current returns than that of lagged other returns; at high quantiles lagged extreme positive returns display more impact on current returns than that of lagged other returns; at low quantiles lagged positive returns display less impact on current returns than that of lagged negative returns; at high quantiles lagged positive returns display more impact on current returns than that of lagged negative returns. For S&P 500 index, at low quantiles lagged extreme positive returns display less impact on current returns than that of lagged other returns; at high quantiles lagged extreme positive returns display more impact on current returns than that of lagged other returns; at low quantiles lagged positive returns display less impact on current returns than that of lagged negative returns; and at high quantiles lagged positive returns display more impact on current returns than that of lagged negative returns. We find insignificant asymmetric dynamic dependency of middle returns for the three indexes. The sensitivity of our results is evaluated by a robustness check. The findings of this paper should help investors make appropriate decisions to maintain control of stock returns.

Análise da eficiência de mercado do Ibovespa: uma abordagem com o modelo autorregressivo quantílico

Dependency on financial asset returns has received considerable attention in the finance literature in order to assist in the formulation of strategies of expected positive return and portfolio risk management. However, the market efficiency hypothesis assumes that new information is immediately incorporated to the asset and that the dependency among the returns is null or not significant. Based on this idea, this research aims to analyze the behavior of serial dependence of stock returns of the Ibovespa using the quantile autoregression model (QAR). Daily log-returns of the Bovespa Index from January 2, 2008 to June 13, 2012 have been used. The results indicate that the extreme qua ntiles are associated with positive or negative returns and have a strong and distinct dependence on each other. The dependence of central quantiles is close to zero and similar to the model of ordinary least squares (OLS). The study also identified an asymmetric effect of investors, which was associated with the market state and the location in the quantile. Besides, high past positive or negative autoregressive coefficients lead to future coefficients of the same sign. It is clear, therefore, that the Ibovespa behaves differently from the assumptions of the hypothesis of market efficiency in the weak form. Keywords: quantile autoregression model, market efficiency, dependence.

Modeling population dynamics: A quantile approach

The paper investigates the modeling of population dynamics, both conceptually and empirically. It presents a reduced form representation that provides a flexible characterization of population dynamics. It leads to the specification of a threshold quantile autoregression (TQAR) model, which captures nonlinear dynamics by allowing lag effects to vary across quantiles of the distribution as well as with previous population levels. The usefulness of the model is illustrated in an application to the dynamics of lynx population. We find statistical evidence that the quantile autoregression parameters vary across quantiles (thus rejecting the AR model as well as the TAR model) as well as with past populations (thus rejecting the quantile autoregression QAR model). The results document the nature of dynamics and cycle in the lynx population over time. They show how both the period of the cycle and the speed of population adjustment vary with population level and environmental conditions.

Forecasting the Distribution of Economic Variables in a Data-Rich Environment

This article investigates the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semiparametric specification based on the quantile autoregressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy relative to a stochastic volatility model using the quantile score. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at long horizons and in tails of the distribution, while for the inflation variables the improved performance occurs mostly at the 6-month horizon. We also illustrate the practical relevance of predicting the distribution by considering forecasts at three dates during the last recession.

Asymmetric over- and undershooting of major exchange rates: Evidence from quantile regressions

This paper uses quantile regression techniques to investigate the temporal dependence patterns of major exchange rates around the globe. Specifically, we estimate quantile autoregressive models for daily exchange rate returns of the USD/EUR, USD/JPY, USD/GBP, USD/AUD, USD/CHF and USD/CAD exchange rates between 1999 and 2014. Testing for the equality of cross-quantile-effects, we reveal substantial state-dependence in the return dynamics. In particular, we find that large US dollar appreciations tend to exhibit positive dependence on past returns, whereas large US dollar depreciations tend to exhibit negative dependence on past returns. Around central return quantiles, however, there is virtually no evidence for significant temporal dependence. Exceptions from this pattern are only apparent for the USD/JPY and the USD/CHF exchange rate. Theoretically, our results point to the presence of over- and undershooting in terms of asymmetric exchange rate adjustment to previous day information.

The Sustainability of External Debt in OECD Countries: Evidence from Quantile Autoregression

This paper will investigate the sustainability of external debt for 21 OECD countries. We modify the solvency condition in an open economy derived by Sawada (1994). The quantile autoregression (QAR) model is applied to test the stationary property of the net external surplus process. The empirical results show that at each quantitle, the net external surplus process is stationary for six countries. It reveals a unit root behavior for the US at each quantile. However, there is a varied behavior across different quantiles for 14 countries. It indicates the asymmetric dynamic behavior of the net external surplus process.

Stress-Testing U.S. Bank Holding Companies: A Dynamic Panel Quantile Regression Approach

Abstract We propose an econometric framework for estimating capital shortfalls of bank holding companies (BHCs) under pre-specified macroeconomic scenarios. To capture the nonlinear dynamics of bank losses and revenues during periods of financial stress, we use a fixed effects quantile autoregressive (FE-QAR) model with exogenous macroeconomic covariates, an approach that delivers a superior out-of-sample forecasting performance relative to the standard linear framework. According to the out-of-sample forecasts, the realized net charge-offs during the 2007–09 crisis fall within the multi-step-ahead density forecasts implied by the FE-QAR model, but are frequently outside the density forecasts generated using the corresponding linear model. This difference reflects the fact that the linear specification substantially underestimates loan losses, especially for real estate loan portfolios. Employing the macroeconomic stress scenario used in CCAR 2012, we use the density forecasts generated by the FE-QAR model to simulate capital shortfalls for a panel of large BHCs. For almost all institutions in the sample, the FE-QAR model generates capital shortfalls that are considerably higher than those implied by its linear counterpart, which suggests that our approach has the potential to detect emerging vulnerabilities in the financial system.

Stress-testing US bank holding companies: A dynamic panel quantile regression approach

We propose an econometric framework for estimating capital shortfalls of bank holding companies (BHCs) under pre-specified macroeconomic scenarios. To capture the nonlinear dynamics of bank losses and revenues during periods of financial stress, we use a fixed effects quantile autoregressive (FE-QAR) model with exogenous macroeconomic covariates, an approach that delivers a superior out-of-sample forecasting performance relative to the standard linear framework. According to the out-of-sample forecasts, the realized net charge-offs during the 2007–09 crisis fall within the multi-step-ahead density forecasts implied by the FE-QAR model, but are frequently outside the density forecasts generated using the corresponding linear model. This difference reflects the fact that the linear specification substantially underestimates loan losses, especially for real estate loan portfolios. Employing the macroeconomic stress scenario used in CCAR 2012, we use the density forecasts generated by the FE-QAR model to simulate capital shortfalls for a panel of large BHCs. For almost all institutions in the sample, the FE-QAR model generates capital shortfalls that are considerably higher than those implied by its linear counterpart, which suggests that our approach has the potential to detect emerging vulnerabilities in the financial system.

Evaluating forecast performances of the quantile autoregression models in the present global crisis in international equity markets

In this research, we compare the one-step-ahead out-of-sample forecast performances of the linear Quantile Autoregression (QAR) model as well as the latest sophisticated nonlinear copula-based QAR models for four daily equity index returns during the current financial tumultuous period. In addition, two Conditional Autoregressive Value-at-Risk (CAViaR) models proposed by Engle and Manganelli (2004) are also considered. In order to obtain the robust evaluation results, we estimate the time-varying parameters via two forecasting schemes (recursive and rolling) and examine the accuracy of the Value-at-Risk (VaR) forecast by three different test procedures. Our main findings are that the CAViaR models provide good forecast performance in most cases and they are superior to both linear and nonlinear copula-based QAR models.

Stress-Testing U.S. Bank Holding Companies: A Dynamic Panel Quantile Regression Approach

We propose an econometric framework for estimating capital shortfalls of bank holding companies (BHCs) under pre-specified macroeconomic scenarios. To capture the nonlinear dynamics of bank losses and revenues during periods of financial stress, we use a fixed effects quantile autoregressive (FE-QAR) model with exogenous macroeconomic covariates, an approach that delivers a superior out-of-sample forecasting performance compared with the standard linear framework. According to the out-of-sample forecasts, the realized net charge-offs during the 2007-09 crisis are within the multi-step-ahead density forecasts implied by the FE-QAR model, but they are frequently outside the density forecasts generated using the corresponding linear model. This difference reflects the fact that the linear specification substantially underestimates loan losses, especially for real estate loan portfolios. Employing the macroeconomic stress scenario used in CCAR 2012, we use the density forecasts generated by the FE-QAR model to simulate capital shortfalls for a panel of large BHCs. For almost all institutions in the sample, the FE-QAR model generates capital shortfalls that are considerably higher than those implied by its linear counterpart, which suggests that our approach has the potential for detecting emerging vulnerabilities in the financial system.

Asymmetric Quantile Persistence and Predictability: The Case of U.S. Inflation

The aim of this paper is to investigate the evidence and implications of time-variation and asymmetry in the persistence of U.S. inflation. We evaluate these features by comparing the out-of-sample forecast performance of two specifications, a Quantile Auto-Regressive (QAR) model and a parametric Auto-Regressive (AR) model in which the volatility of the errors depends on the level of inflation. The results of the comparison show that the parametric quantile forecasts are at least as accurate as the semi-parametric QAR model, in particular for the core inflation measures. This leads us to conclude that the persistence of core inflation can be considered constant and high, but declined for the headline inflation measures. In addition, we find that the recent findings of asymmetric persistence of inflation shocks can be mostly attributed to the positive relation between inflation level and its volatility.

State-Dependent Momentum in International Stock Markets

We estimate quantile autoregression (QAR) models to analyze variations in the autoregressive coefficients of 55 international stock index returns and demonstrate that it is important to allow the autoregressive parameters to vary with quantiles. The empirical results identify distinctively different patterns of autoregressive coefficients in the lower, central and upper quantiles of the distribution across all countries. More specifically, the study suggests that investors follow momentum strategies in lower quantiles or bad states''. We also demonstrate that the quantile autoregression estimates can be used to test for asymmetric responses of the volatility.

Forecasting the Distribution of Economic Variables in a Data-Rich Environment

In this paper we investigate the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semi-parametric specification based on the Quantile Auto-Regressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy with score functions tailored to evaluate quantile, areas of the distribution, and intervals. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at short horizons and low quantiles, while for the inflation variables the improved performance occurs mostly at the one-year horizon. We also consider an application of the distribution forecasts to predict the probability of a future decline in output and employment and illustrate their practical use at three dates during the last recession.

A new Bayesian approach to quantile autoregressive time series model estimation and forecasting

This paper proposes a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated Markov chain Monte Carlo algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out‐of‐sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.

Quantile Correlations and Quantile Autoregressive Modeling

In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Speci cally, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the tted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in nite samples, and an empirical example is presented to illustrate usefulness.

Quantile Elasticity of International Tourism Demand for South Korea Using the Quantile Autoregressive Distributed Lag Model

Using the quantile autoregressive model, this paper investigates international inbound tourism demand for South Korea and its determinants. In contrast to previous studies which have dealt with the conditional mean only, the authors examine the effects of covariates at various conditional quantile levels. US and Japanese tourism demand are considered for inbound tourism demand. For US tourism demand, the costs of living in Korea and competing destinations have moderately significant negative effects at very high and low quantiles only, while income does not have any significant effect on tourism demand. On the other hand, for Japanese tourism demand, income has significant positive effects at lower quantiles, and living costs in Korea and competing destinations have significant negative effects at higher quantiles. These results address the heterogeneity in tourism demand analysis.

Quantile Threshold Effects in the Dynamics of the Dollar/Pound Exchange Rate

This article employs threshold quantile autoregressive models to study the dynamics in the American dollar / British pound exchange rate. We investigate whether the documented carry trade strategies developed by international investors can be fundamented in an apparent existence of predictability in the exchange rate. We extend the literature by estimating a threshold quantile autoregressive model which enables us to analyze the entire conditional quantile process instead of only the conditional mean. Our results show evidence of important heterogeneity associated with the returns on the dollar/pound exchange rate. These features of the data supporting predictability for some regimes are found, particularly, at moderate quantiles. The investment opportunities, however, vanish for extreme regimes within these quantiles, and also for extreme quantiles where the returns on exchange rates seem to be uncorrelated.

Copula-based nonlinear quantile autoregression

Summary Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.

A note on self-weighted quantile estimation for infinite variance quantile autoregression models

This article focuses attention on quantile autoregressive (QAR) models in which the autoregressive coefficients can be dependent on the quantile function. We use the self-weighted quantile regressive estimation for infinite variance QAR models. The asymptotic normality of the estimated parameters are established conditionally on lagged values of the response. In addition, the Wald test statistics are developed for the linear restriction on the parameters. Finally, we discuss the regression rank score test and empirical likelihood method as alternative inference approaches, which do not require the estimations of nuisance parameters.

Copula-Based Nonlinear Quantile Autoregression

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.