Quantile Autoregressive Model Research Articles

Endogenous Growth and Environmental Kuznets Curve: Lessons from FDI Impact on Economic Growth in Sub-Saharan Africa

Purpose: This study aims to determine the influence of Foreign Direct Investments (FDI) on economic growth in Sub-Saharan Africa (SSA). It examines the endogenous growth theory and the Environmental Kuznets Curve (EKC) theory, and how they relate to the regional data.Method: Using panel quantile autoregression models, this study explores the relationship between FDI inflows into SSA with energy consumption, carbon emissions, and economic growth. The study is based on data from 1975 to 2018.Result: The study findings conclusively demonstrate that foreign direct investment has a significant impact on the economic growth of the SSA region. Furthermore, the study reveals that energy consumption and carbon emissions in the SSA have consistently increased throughout the study period, with foreign direct investment being identified as the primary driver of this trend. These findings are consistent with the Environmental Kuznets Curve (EKC) hypothesis, as well as the endogenous growth theory, which suggests that FDI operations can have negative consequences on the host environment.Practical Implications for Economic Growth and Development: The study suggests that Sub-Saharan Africa should manage FDI carefully to balance economic growth with environmental sustainability by promoting green investments and creating an investment-friendly environment.

Development of Functional Quantile Autoregressive Model for River Flow Curve Forecasting

AbstractAmong several hydrological processes, river flow is an essential parameter that is vital for different water resources engineering activities. Although several methodologies have been adopted over the literature for modeling river flow, the limitation still exists in modeling the river flow time series curve. In this research, a functional quantile autoregressive of order one model was developed to characterize the entire conditional distribution of the river flow time series curve. Based on the functional principal component analysis, the regression parameter function was estimated using a multivariate quantile regression framework. For this purpose, hourly scale river flow collected from three rivers in Australia (Mary River, Lockyer Valley, and Albert River) were used to evaluate the finite‐sample performance of the proposed methodology. A series of Monte‐Carlo experiments and historical data sets were examined at three stations. Further, uncertainty analysis was adopted for the methodology evaluation. Compared with the existing methods, the proposed model provides more robust forecasts for outlying observations, non‐Gaussian and heavy‐tailed error distribution, and heteroskedasticity. Also, the proposed model has the merit of predicting the intervals of future realizations of river flow time series at the central and non‐central locations. The results confirmed the potential for predicting the river flow time series curve with a high level of accuracy in comparison with the benchmark existing functional time series methods.

Forecasting crude oil volatility and stock volatility: New evidence from the quantile autoregressive model

This paper employs the quantile autoregressive (QAR) model to examine the forecasting relationship between stock volatility and crude oil volatility. We first utilize the sup-Wald test to evaluate Granger causality across various quantile levels, providing valuable information for forecasting. Our findings reveal that the causal effects between stock volatility and crude oil volatility differ considerably across different quantiles, with a V-shaped relationship evident at the quantile level. Results from out-of-sample forecasts indicate that the forecasting effect of oil volatility on stock volatility has both positive and negative impacts. In contrast, when using stock volatility to forecast crude oil volatility, predictability improves relative to the benchmark, particularly at more extreme quantiles. Further analysis highlights the necessity of forecast combinations to achieve an overall improvement in forecasting tasks.

Bayesian quantile inference and order shrinkage for hysteretic quantile autoregressive models

Hysteretic quantile autoregressive model combines the hysteretic patterns and quantile autoregression, which can capture the dynamic relationship and nonlinear characteristics at different quantiles in time series data. In this paper, the Bayesian quantile inference and order shrinkage are studied for a class of hysteretic quantile autoregressive time series models. By using Markov Chain Monte Carlo (MCMC) techniques, the proposed Bayesian quantile method can handle the sparse hysteretic quantile autoregressive model well. It can accurately determine order of the model and estimate non-zero coefficients. Both simulation studies and a data example show that the proposed methods are feasible, reliable and appropriate for analysing the US Gross National Product data set.

The asymmetric effect of G7 stock market volatility on predicting oil price volatility: Evidence from quantile autoregression model

This paper investigates the asymmetric effect of G7 stock market volatility on predicting oil price volatility under different oil market conditions by using the quantile autoregression model. Both in- and out-of-sample results demonstrate the prediction superiority and effectiveness of the quantile autoregression model. The US and Canada's stock markets exhibit the strongest predictive ability across the entire distribution, while the UK demonstrates strong predictive power specifically during periods of high oil price volatility. Japan, Germany, France, and Italy as oil importers can predict low and median oil volatility. The strong predictability of G7 stock volatility may be attributable to their significant impact on the business cycle and investor sentiment. This asymmetric prediction ability arises not only from the average volatility shocks at various quantiles but also from the bad and good stock volatility at different quantiles. Further research suggests that bad stock volatility appears to be more predictable than good stock volatility, especially in high oil price fluctuations. Furthermore, the superiority and effectiveness of the quantile autoregression model in predicting oil volatility are proven to be applicable to emerging markets. This study may provide useful insights for policymakers, businesses, and investors to improve crude oil risk prediction and risk management under different market conditions.

Option pricing revisited: The role of price volatility and dynamics

The analysis of option pricing in derivative markets has commonly relied on the Black-Scholes model. This paper presents a conceptual and empirical analysis of option pricing with a focus on the validity of key assumptions embedded in the Black-Scholes model. Going beyond questioning the lognormality assumption, we investigate the role played by two assumptions made about the nature of price dynamics: quantile-specific departures from a unit root process, and the role of quantile-specific drift. Our analysis relies on a Quantile Autoregression (QAR) model that provides a flexible representation of the price distribution and its dynamics. Applied to the soybean futures market, we examine the validity of assumptions made in the Black-Scholes model along with their implications for option pricing. We document that price dynamics involve different responses in the tails of the distribution: overreaction and local instability in the upper tail, and underreaction in the lower tail. Investigating the implications of our QAR analysis for option pricing, we find that failing to capture local instability in the upper tail is more serious than failing to capture “fat tails” in the price distribution. We also find that the most serious problem with the Black-Scholes model arises in its representation of price dynamics in the lower tail.

Uncertain quantile autoregressive model

The propose of uncertain time series is to explore the relationship between response variables and explanatory variables over time based on the imprecise observations. In order to more comprehensively describe the overall picture of the relationship between variables under the time series, a new uncertain quantile autoregressive model is proposed. By studying the uncertain quantile autoregressive model, the estimated method under different quantiles of its unknown parameters is proposed. Based on the fitted uncertain quantile autoregressive model, the residual is analyzed. Furthermore, uncertainty hypothesis testing are used to verify the reasonableness and accuracy of the estimates under different quantiles. Moreover, the point estimate and interval estimate of the predicted value are presented. Finally, the rationality and validity of the model are verified by two examples.

Can Digital Rural Construction Improve China’s Agricultural Surface Pollution? Autoregressive Modeling Based on Spatial Quartiles

The problem of agricultural surface pollution is becoming increasingly prominent, directly impeding the realization of the goals of “industrial prosperity and ecological livability” in the strategy of rural revitalization. To thoroughly analyze the impact of Digital Rural Construction on agricultural surface pollution and to effectively strengthen the prevention and control measures, the Moran index was used to assess the influence of agricultural surface pollution in 31 provinces and cities across China. The Moran index was employed to conduct global and local spatial autocorrelation analysis of agricultural surface source pollution, and a panel quantile autoregressive model was constructed to explore the effects of Digital Rural Construction on such pollution. The results show the following: (1) agricultural surface pollution in each province and city exhibits spatial spillover effects that are growing stronger; (2) the spatial impact of agricultural surface pollution on neighboring provinces and cities follows an inverted U-shaped pattern at different levels of pollution; (3) the relationship between the degree of agricultural surface pollution and the impact of Digital Rural Construction on it also follows an inverted U-shaped pattern, wherein improvements are observed as the pollution levels deepen. When the level of agricultural surface pollution is located in the quartile point 0.1, the improvement effect of Digital Rural Construction on agricultural surface pollution is small (0.0484), as the quartile point increases, the improvement effect is gradually increased, and it reaches the maximum value at the quartile point 0.5 (0.523), and the coefficient of agricultural surface pollution decreases to the minimum value at the quartile point 0.9 (0.423).

On the utilization controversy in the demand-led growth literature: A quantile unit root approach

The demand-led growth literature is embroiled in a controversy surrounding the long-run stationarity of capacity utilization. One perspective posits that a non-stationary rate of capacity utilization implies its endogeneity to aggregate demand, aligning with the neo-Kaleckian model. In contrast, an opposing viewpoint suggests the possibility of long-run stability independent of demand fluctuations. Conventional empirical approaches generally support the latter viewpoint. This study proposes a novel way to estimate capacity utilization persistence by using a quantile autoregression (QAR) model, which allows for the possibility that shocks of different signs and magnitudes impact capacity utilization differently. Using official survey measures from developed and developing countries, we find evidence in favor of local unit root tendencies, with recessions exhibiting persistent effects on utilization. Additionally, we identify an asymmetric capacity utilization response, where, in general, recessive shocks are persistent while positive shocks are transitory. These results provide a fresh perspective on how capacity utilization responds to different economic conditions.

Examination of the impacts of the immediate interest rate of the United States and the VIX on the Dow Jones Islamic Market Index

AbstractThis study examines the effects of the market volatility index of the Chicago Board Options Exchange (VIX) and the immediate interest rate of the United States on the Dow Jones Islamic Market Index (DJIMI) using quantile‐based techniques and wavelet coherence (WTC) analysis with monthly data for the period January 2010to May 2021. A quantile cointegration model indicated that the relationship between the VIX and the DJIMI can be valid in the long term since the estimated coefficients are negative and statistically significant across the quantiles 0.05 and 0.50, while a quantile autoregressive model revealed that large negative and positive changes in the VIX and the immediate interest rate of the United States do not have a significant impact on the DJIMI in the short term. Allowing the role of regime changes, it was found by the quantile regression model that an increase in the VIX lowers the performance in the DJIMI, supported by the WTC. It was also underlined that the DJIMI may not benefit from the positive financial conditions. According to the quantile regression models, the immediate interest rate of the US has asymmetrical effects, and the stabilizing effect of the increase/decrease is valid during bearish/bullish market conditions in the DJIMI.

Variable selection for quantile autoregressive model: Bayesian methods versus classical methods

In this article, we introduce three Bayesian variable selection methods for the quantile autoregressive model with explanatory variables. The Gibbs sampling algorithms are developed for each method by setting different priors. The numerical simulations suggest that the Gibbs sampling algorithms converge fast and Bayesian variable selection methods are reliable. A real example is given to analysis the relationship between the count of total rental bikes and five explanatory variables. Both simulations and data example indicate that the proposed methods are feasible, reliable, and appropriate for analyzing the Bike Sharing data set.

Analysis of wildfires and their extremes via spatial quantile autoregressive model

Analysis of wildfires and their extremes via spatial quantile autoregressive model

Agricultural diversification, productivity, and food security across time and space

AbstractThis article presents an investigation of agricultural production risk over time and across space and its implications for food security. The econometric approach involves a Quantile Autoregressive (QAR) model and a copula to provide a flexible representation of the distribution of yield risk and its evolution over time and across space. The analysis relies on a two‐step estimation method to evaluate the multivariate yield distribution and its spatial and temporal evolution. Linkages between agricultural production risk and the economics of food security are explored, with implications for the welfare cost of food insecurity. The approach is illustrated in an econometric application to regional wheat and corn yields in Italy. The analysis provides new and useful information on the evolving linkages between agricultural production risk, productivity, and food security. Our integrated approach documents the role of regional diversification and of productivity growth along with their effects on food security.

Risk of declined company performance during COVID-19–Spatial quantile autoregression based on network analysis

There is a great deal of literature regarding the performance of listed companies during periods of financial distress and/or financial crisis. However, very few of them considered the interaction of companies and its impact on performance. This paper introduces network structure and a spatial quantile autoregressive model to study the heterogeneous effect of exogenous variables on the different quantiles of company performance during COVID-19 pandemic. We find that the interconnectedness between listed companies in China changed significantly after the outbreak of COVID-19. The pandemic outbreak, as well as company size, robustness of the supply chain, and other exogenous variables, significantly affect company performance. In addition, we identify four major drivers of company performance from the perspective of spatial analysis. We also find that the impact of explanatory variables shows distributional heterogeneity.

Extremal quantile autoregression for heavy-tailed time series

The conventional quantile estimator of the extreme conditional quantiles under quantile autoregression models is relatively unstable due to data sparsity in the tails. Extreme value theory provides a mathematical foundation of extrapolation to estimate extreme quantiles. However, the asymptotic distributions of existing estimators are often complicated making it inconvenient to apply for statistical inference. We develop a new adaptive estimation procedure based on a generalized Hill estimator of the extreme value index to estimate extreme conditional quantiles in autoregression models. We establish the asymptotic normality of the proposed estimators under some regularity conditions by applying the martingale central limit theorem. The asymptotic variances have closed expressions and can be directly estimated. Based on these results, we propose a procedure to construct confidence intervals for the extreme conditional quantiles. We also provide a diagnostic tool to check the heavy-tailedness of the distribution. Simulation studies and a real data analysis are carried out to demonstrate the advantages of the proposed methods over existing approaches.

Dynamic Network Quantile Regression Model

We propose a dynamic network quantile regression model to investigate the quantile connectedness using a predetermined network information. We extend the existing network quantile autoregression model of Zhu et al. by explicitly allowing the contemporaneous network effects and controlling for the common factors across quantiles. To cope with the endogeneity issue due to simultaneous network spillovers, we adopt the instrumental variable quantile regression (IVQR) estimation and derive the consistency and asymptotic normality of the IVQR estimator using the near epoch dependence property of the network process. Via Monte Carlo simulations, we confirm the satisfactory performance of the IVQR estimator across different quantiles under the different network structures. Finally, we demonstrate the usefulness of our proposed approach with an application to the dataset on the stocks traded in NYSE and NASDAQ in 2016.

Maximum likelihood estimation for quantile autoregression models with Markovian switching

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting.

Investor sentiment and Bitcoin relationship: A quantile-based analysis

This paper applies a quantile-based analysis to investigate the causal relationships between Bitcoin and investor sentiment by considering the possible effects of the ongoing COVID-19 pandemic. Such an analysis allows investigating the predictive power of investor sentiment (Bitcoin) on Bitcoin (investor sentiment) at different levels of the distributions. Results emphasize that only Bitcoin returns/volatility have significant predictive power on the investor sentiment whether investors are fear or greed before and over the COVID-19 period. Moreover, the COVID-19 crisis has no effect on the causal relationship between the two variables. Further analysis shows an asymmetric causality observed only during the pandemic period. Furthermore, the quantile autoregressive regression model shows a significant positive relationship between investor sentiment and Bitcoin returns.

The effects of economic policy uncertainty on the US REITs ETFs: A quantile analysis

ABSTRACT This paper investigates the impact of economic policy uncertainty (EPU) on real estate investment trusts (REITs) ETFs in a quantile-based framework by employing the nonparametric causality test and the quantile autoregressive (QAR) model. Using data covering the returns of eight major United States (US) Real Estate Investment Trusts (REIT) exchange-traded funds (ETFs) over the period spanning 2 January 2012 to 28 February 2019, we find that there is a weak predictive power of EPU in REITs’ returns and volatility. Our findings indicate that EPU has a leading effect on the real estate market returns at the mean level. However, we find no causality running from EPU to real estate markets volatility at all quantiles, indicating a weak influence of uncertainty on the real estate markets. Besides, our results report a significant impact of the EPU on the returns at the lower and upper quantiles. Yet, the impact is not symmetrical since the EPU shows a positive (negative) impact on the returns during the bearish (bullish) market condition. Moreover, the lagged EPU impacts the REITs negatively only during the normal and bullish market conditions, given all the estimated coefficients being negative and significant. Our results entail policy implications for investors, regulators, and asset managers.

The dynamic effects of price support policy on price volatility: The case of the rice market in China

AbstractThis study examines the economic and welfare effects of a commodity price support policy. It conceptually and empirically evaluates the effects of the domestic pricing policy on the distribution of commodity prices, with an application to the price support program in the Chinese rice market. The empirical analysis relies on a Censored Quantile Autoregression (CQAR) model, which provides a refined and flexible representation of the evolving distribution of prices under a price support program. Based on monthly data over the period 2000–2018, we develop and estimate an econometric model documenting the price effects of policy interventions. We study how a price support program affects price distribution both in the short term and long term. We find that such a program has reduced the domestic rice price volatility, evidenced by lowered variation and increased right‐skewness of the price distribution. We also show how China's rice programs' high price support level during the period 2008–2015 caused significant censoring effects and price enhancement with adverse impacts on consumer welfare across all income levels. We further examine alternative situations where a moderate price support level can reduce the long‐term mean price without generating consumer welfare losses. Our analysis and findings have implications for the implementation of agricultural price support policies in many developing countries.