Linear Granger Causality Research Articles

Extreme co-movements between CO2 emission allowances and commodity markets and their response to economic policy uncertainty

This study employs the generalized extreme value - autoregressive conditional Fréchet - tail quotient correlation coefficient (GEV-AcF-TQCC) analytical framework to investigate the extreme co-movements between the EU carbon futures market and the commodity futures market. Subsequently, it also examines the response of the dynamic tail quotient correlation coefficient (TQCC) values to economic policy uncertainty stemming from the US using the linear Granger causality test. The empirical results demonstrate that the tail risk indices for both upside and downside trends of the two futures markets experience changes most of the time and show drastic changes during extreme events. More importantly, before the outbreaks of the COVID-19 pandemic (from September 2019 to February 2020) and the Russia-Ukraine conflict (from May 2021 to February 2022), the dynamic TQCC values for the downside trends of the two futures markets remain at relatively high levels. Of note, when examining the dynamic TQCC values between GSCI_down and EUA_down, as well as between GSCI_down and EUA_up, it can be observed that these TQCC values rise to higher levels during periods of extreme volatility. However, they quickly decline as the GSCI futures market experiences significant fluctuations during its downside trend. This pattern indicates a tail risk spillover effect from the GSCI futures market to the EUA futures market. Further analysis using the linear Granger causality test reveals that economic policy uncertainty is a significant driver of the extreme co-movements between the EU carbon and the commodity futures markets in most cases, in addition to the extreme co-movements between the downside trend of the EU carbon futures market and the upside trend of the commodity futures market. The insights gained from this study can provide valuable guidance and enlightenment for policymakers, financial investors, and academic researchers in understanding the dynamics of the extreme relationship between the two markets under discussion, and the impacts of economic policy uncertainty on their extreme co-movements.

CLIMATE RISKS AND PREDICTABILITY OF COMMODITY RETURNS AND VOLATILITY: EVIDENCE FROM OVER 750 YEARS OF DATA

We analyze whether metrics of climate risks, as captured primarily by changes in temperature anomaly and its stochastic volatility (SV), can predict returns and volatility of 25 commodities, covering the overall historical period of 1258 to 2021. To this end, we apply a higher-order nonparametric causality-in-quantiles test to not only uncover potential in-sample predictability in the entire conditional distribution of commodity returns and volatility but also to account for nonlinearity and structural breaks which exist between commodity returns and the metrics of climate risks. We find that, unlike in the misspecified linear Granger causality tests, climate risks do predict commodity returns and volatility, though the impact on the latter is stronger, in terms of the coverage of the conditional distribution. Insights from our findings can benefit academics, investors, and policymakers in their decision-making.

Foreign Exchange Reserves and Economic Growth of Brazil: A Nonlinear Approach

Foreign Exchange Reserves and Economic Growth of Brazil: A Nonlinear Approach

Effective Connectivity Estimation by a Hybrid Neural Network, Empirical Wavelet Transform, and Bayesian Optimization.

Accurately measuring nonlinear effective connectivity is a crucial step in investigating brain functions. Brain signals like EEG is nonstationary. Many effective connectivity methods have been proposed but they have drawbacks in their models such as a weakness in proposing a way for hyperparameter and time lag selection as well as dealing with non-stationarity of the time series. This paper proposes an effective connectivity model based on a hybrid neural network model which uses Empirical Wavelet Transform (EWT) and a long short-term memory network (LSTM). The best hyperparameters and time lag are selected using Bayesian Optimization (BO). Due to the importance of generalizability in neural networks and calculating GC, an algorithm was proposed to choose the best generalizable weights. The model was evaluated using simulated and real EEG data consisting of attention deficit hyperactivity disorder (ADHD) and healthy subjects. The proposed model's performance on simulated data was evaluated by comparing it with other neural networks, including LSTM, CNN-LSTM, GRU, RNN, and MLP, using a Blocked cross-validation approach. GC of the simulated data was compared with GRU, linear Granger causality (LGC), Kernel Granger Causality (KGC), Partial Directed Coherence (PDC), and Directed Transfer Function (DTF). Our results demonstrated that the proposed model was superior to the mentioned models. Another advantage of our model is robustness against noise. The results showed that the proposed model can identify the connections in noisy conditions. The comparison of the effective connectivity of ADHD and the healthy group showed that the results are in accordance with previous studies.

Financial market connectedness between the U.S. and China: A new perspective based on non-linear causality networks

This paper analyzes the connectedness between the financial markets in the U.S. and China based on non-linear Granger causality and quantile Granger causality networks. We extend the linear Granger causality network proposed by Billio et al. (2012) and support the importance of multi-class market interactions highlighted by Bollerslev et al. (2018). We find that non-linear Granger causality between stock, bond, and foreign exchange markets in the U.S. and China provides more interconnectedness than linear Granger causality. Both the strength and the direction of the connectedness are related to the quantile of market returns, as evidenced by the fact that the left (right) tail quantiles provide more causal effects than the middle quantiles and the mean. We characterize this phenomenon as the “smiling curve” of causality connectedness, and we show the “smiling curve” for each country and financial submarket. Compared to the financial markets in China, those in the U.S. appear to be more central to the connectedness network, with the main route being the stock market. When market returns are in the right tail quantile interval, the U.S. financial market has more capacity to receive information from various markets than China does. When market returns are in the left tail quantile interval and at the middle quantiles, the Chinese financial markets are more susceptible to shocks than those in the United States, with the Chinese stock and bond markets being more sensitive than the foreign exchange market.

Comparison of the Asymmetric Relationship between Bitcoin and Gold, Crude Oil, and the U.S. Dollar before and after the COVID-19 Outbreak

This paper aims to reveal the asymmetric co-integration relationship and asymmetric causality between Bitcoin and global financial assets, namely gold, crude oil and the US dollar, and make a comparison for their asymmetric relationship before and after the COVID-19 outbreak. Empirical results show that there is no linear co-integration relationship between Bitcoin and global financial assets, but there are nonlinear co-integration relationships. There is an asymmetric co-integration relationship between the rise in Bitcoin prices and the decline in the US Dollar Index (USDX), and there is a nonlinear co-integration relationship between the decline of Bitcoin and the rise and decline in the prices of the three financial assets. To be specific, there is a Granger causality between Bitcoin and crude oil, but not between Bitcoin and gold/US dollar. Before the outbreak of the COVID-19 pandemic, there was an Asymmetric Granger causality between the decline in gold prices and the rise in Bitcoin prices. After the outbreak of the pandemic, there is an asymmetric Granger causality between the decline in crude oil prices and the decline in Bitcoin prices. The COVID-19 epidemic has led to changes in the causality between Bitcoin and global financial assets. However, there is not a linear Granger causality between the US dollar and Bitcoin. Last, the practical implications of the findings are discussed here.

Global geopolitical risk and volatility connectedness among China's sectoral stock markets

Employing the time-varying parameter vector autoregressive (TVP-VAR) connectedness index and nonparametric causality-in-quantiles test, this paper investigates the causal effect of global geopolitical risk on the dynamic volatility connectedness within China's sectoral stock markets. The TVP-VAR connectedness index results reveal significant volatility connectedness among China's stock market sectors, and the industrial, consumer discretionary, and raw material sectors play a critical systemic role throughout the sample period. The Granger causality test results show that the causality-in-quantiles test demonstrates superior performance compared to the linear Granger causality test, and it is evident that global geopolitical risk exhibits significant nonlinear causality effects on both the overall volatility connectedness among sectors and the net volatility connectedness across different sectors.

How do fossil energy markets and carbon markets affect each other? Based on the grainger causal relationship on quantiles

The fossil energy and the carbon market are closely connected, but few articles have applied the Granger causality method on quantiles to explore the bi-directional causality between carbon prices and fossil fuels. Most articles use conditional mean regression models to test linear Granger causality, but are unable to assess tail causality or nonlinear causality. In order to accomplish the objective of studying the interaction of carbon and fossil energy markets at different quartiles, we use the method of Granger causality at quartiles, which allows us to assess median and tail causality and to gain insights into how carbon and traditional fossil energy markets interact under different market conditions. This paper analyzes the causal relationships between carbon prices and coal, oil, and gas from June 1, 2015 to October 31, 2022 across all quantiles. We find no indication of Granger-causality from carbon to oil and gas at the middle quantile. However, at the lower and upper quantiles, we discover the causal relationship between changes in carbon prices and traditional energy prices. The asymmetric two-way causal relationship between the carbon market and the fossil energy market has prompted the government to carry out differentiated management, as well as to improve energy efficiency.

Schizophrenia MEG Network Analysis Based on Kernel Granger Causality.

Network analysis is an important approach to explore complex brain structures under different pathological and physiological conditions. In this paper, we employ the multivariate inhomogeneous polynomial kernel Granger causality (MKGC) to construct directed weighted networks to characterize schizophrenia magnetoencephalography (MEG). We first generate data based on coupled autoregressive processes to test the effectiveness of MKGC in comparison with the bivariate linear Granger causality and bivariate inhomogeneous polynomial kernel Granger causality. The test results suggest that MKGC outperforms the other two methods. Based on these results, we apply MKGC to construct effective connectivity networks of MEG for patients with schizophrenia (SCZs). We measure three network features, i.e., strength, nonequilibrium, and complexity, to characterize schizophrenia MEG. Our results suggest that MEG of the healthy controls (HCs) has a denser effective connectivity network than that of SCZs. The most significant difference in the in-connectivity strength is observed in the right frontal network (p=0.001). The strongest out-connectivity strength for all subjects occurs in the temporal area, with the most significant between-group difference in the left occipital area (p=0.0018). The total connectivity strength of the frontal, temporal, and occipital areas of HCs exhibits higher values compared with SCZs. The nonequilibrium feature over the whole brain of SCZs is significantly higher than that of the HCs (p=0.012); however, the results of Shannon entropy suggest that healthy MEG networks have higher complexity than schizophrenia networks. Overall, MKGC provides a reliable approach to construct MEG brain networks and characterize the network characteristics.

Linear and Nonlinear Relationship Between Real Exchange Rate, Real Interest Rate and Consumer Price Index: An Empirical Application for Countries with Different Levels of Development

The research population of this study consists of Australia, Azerbaijan, Egypt, Brazil, Chile, Canada, Hungary, Pakistan, India, Ukraine and the United Kingdom. For these countries; T, the relationship between Exchange Rate Index (exc), Real Interest Rate (int) and Consumer Price Index (cpi) variables were examined. Data from 2000Q1 to 2021Q3 were used in the study. The data are taken from the IMF's data bank. Analysis was done in R-Studio. Wo Seasonality Test, Augmented Dickey-Fuller Test, Linear Granger Causality Analysis and Nonlinear Granger Causality Analysis were used to investigate the relationship between variables. The theory claims that there is causality in both directions between exchange rate, interest rate and inflation. In the study, the relationship between these variables was investigated with linear and nonlinear causality tests. It is thought that the empirical results that contradict the theory are caused by the development levels of the countries, their macroeconomic structures, the applied fiscal and monetary policy instruments, the conjuncture and the analysis methods. The study aims to investigate these claims. For this reason, the development levels, sociocultural and socioeconomic structures of the selected countries were requested to be different. In addition, two different test methods, linear and non-linear, were preferred for the causality relationship. It was observed that the selected analysis methods significantly affected the results. Linear causality analysis results are closer to theoretical implications. However, the level of development of the countries does not have a significant effect on the relationship between the variables.

Do Extreme CIT Position Changes Move Prices in Grain Futures Markets?

AbstractMost previous studies reject the basic tenet of the Masters Hypothesis that the influx of financial index investments has pressured agricultural futures prices upwards substantially. However, the impact of index investment activities may be more complicated and nuanced than can be detected by the relatively simple linear Granger causality tests used in many previous studies. Our study applies a new cross-quantilogram (CQ) test to weekly index trader positions and returns in four agricultural futures markets. Overall, we find limited support for a significant relationship between extreme index trader position changes and returns, and even less support that increased index trading activities have pushed commodity prices higher.

Uncertainty and realized jumps in the pound-dollar exchange rate: evidence from over one century of data

Abstract We study the importance of economic uncertainty so as to predict realized jumps (hereafter jumps) in the pound-dollar exchange rate. The empirical analysis covers the time period from February 1900 to May 2018 on a monthly basis, incorporating several market states, including various booms and crashes. First, we apply a standard linear Granger causality test in order to identify causal effects from economic uncertainty to jumps. We show that the standard linear Granger causality test fails to capture such casual effects. Providing the misspecification of the linear model, we next make use of a nonparametric causality-in-quantiles test. This test allows us to take into account the substantial evidence of nonlinearity along with the structural breaks between economic uncertainty and jumps. In applying this data-driven robust procedure, we find strong evidence of uncertainty causing jumps of the dollar-pound exchange rate. These results are robust over the entire conditional distribution of jumps, exhibiting the strongest impact at the lowest conditional quantiles considered. In addition, our results are generally found to be robust to alternative measures of uncertainty, jumps generated at a daily frequency based on shorter samples of intraday data, and across three other dollar-based exchange rates.

How COVID-19 influences prices of oil and precious metals: Comparison between data extracted from online searching trends and actual events

The investigation explores whether COVID-19 influences oil and precious metals prices by comparing data extracted from online searching trends and actual events. The study utilizes the Linear Granger causality test & non-parametric causality-in-quantiles method and uses data from January (2020) to March (2021). We have incorporated four mostly trading metals (i.e., Gold, Palladium, Silver, & Platinum) & Crude oil. Although outcomes of Linear Granger causality test show no causal relation between COVID-19 & oil and precious metal prices for both cases (i.e., online searching trends and actual events), the outcomes of the non-parametric test revealed the existence of non-linear association among constructs. Non-parametric test results revealed that COVID-19 significantly influences the prices of oil and precious metals. Therefore, we conclude that policymakers need to contemplate pandemic risk as most critical risk factor for stability of market when developing policies for the market and economy. Furthermore, through this study, investors and policymakers will get noteworthy awareness for thinking out of the box during the crisis.

Nonlinear and nonparametric causal relationship between financial inclusion and sustainable environment in South Asia.

This study analyzes the causal connection between financial inclusion and carbon emission in selected South Asian countries through a quantile technique-based linear Granger and non-parametric causality test. The analysis of the studycovers quarterly data from 1980Q1 to 2019Q4. However, the linear Granger causality assessment outcome does not indicate any causal relationship between financial inclusion and carbon emission. In contrast, results from non-parametric assessment reveal a non-linear connection between the variables. The non-parametric test results of the South Asian countries exhibit that financial inclusion leads to carbon emission, which instigates the deterioration of the environment, except for Bhutan. Subsequently, creating awareness by promoting renewable energy resources is essential while investing in fuel-efficient technology to reduce the dependence on fossil fuels. The results of this study provide significant information to the governments and policymakers in emerging countries to improve financial literacy among people to reduce the risk of global warming by encouraging investment in energy-efficient resources.

Vector Error Correction Model: Prediction of Bi-Directional Causality between Gross Domestic Product and Wage Growth in Kenya

Economic growth and wage growth are very prominent macroeconomic variables in all countries in the World. These two variables are the main signposts signaling the current trends in an economy. To determine the recent behavior of the economy, the government must study and analyze these major variables. The increase in aggregate production in the Kenyan economy has been deteriorating due to the steady rise in the wage bill, especially since the year 2012, in conjunction with the devolved government. An increase in wage rate motivates workers and, in turn, increases the production capacity of a country hence economic growth. An increase in recurrent expenditure implies that the development expenditure will be condensed, which will alter the growth of the economy. The primary goal of this research was to fit vector error correction model on gross domestic product and wage growth data so as to identify the bidirectional causality effects between the two variables. VEC model is superior since it distinguishes between long run and short run relationship among underlying variables in a large sample size. The linear Granger causality test was used to evaluate the causal relationship between the system's variables; hence a causal research design was adopted in this study. This research employed secondary data, which was analyzed using Eviews and STATA statistical software. Data on these target variables was acquired from the World Bank and Central Bank of Kenya. Lastly, this study used yearly time series data for the period 1979 to 2019. It was found that wage growth and GDP granger causes each other and also have a long run relationship since their respective p values were less than 5% significance level. VECM1 (effects of wage growth on GDP) had AIC of -0.2953, RMSE of 1.0039 while the R-squared was 0.7241. Subsequently, effects of GDP on wage growth (VECM2) was found to have an R-squared of 0.7452, AIC of -8.2270 and RMSE of 0.08363. Based on the foregoing findings, it was determined that GDP has more influence on wage growth both in the short and long run. This study thus recommends that the government should keep inflation under control, increase development expenditure to finance projects and fostering a favorable business environment for Small and Medium-sized Enterprises (SMEs) to upsurge total output (productivity) which will in turn, lead to a rise in wage growth, thus a high standard of living for the millions of unemployed Kenyans. Finally, the findings of the current study are expected to be of significance to academicians and also provide appropriate policy options that will help in harmonizing the wage rates, thus managing recurrent expenditure in Kenya.

The outbreak of COVID-19 and stock market liquidity: Evidence from emerging and developed equity markets

The outbreak of the novel corona virus has heightened concerns surrounding the adverse financial effects of the outbreak on stock market liquidity and economic policies. This paper contributes to the emerging strand of studies examining the adverse effects of the virus on varied aspect of global markets. The paper examines the causality and co-movements between COVID-19 and the aggregate stock market liquidity of China, Australia and the G7 countries (Canada, France, Italy, Japan, Germany, the UK and the US), using daily three liquidity proxies (Amihud, Spread and Traded Value) over the period December 2019 to July 2020. Our empirical analysis encompasses wavelet coherence and phase-differences as well as a linear Granger causality test. Linear causality test results suggest that a causal relationship exists between the number of cases of COVID 19 infections and stock market liquidity. To quantitatively examine the degree of causality between COVID-19 outbreak and stock market liquidity, we employ the continuous wavelet coherence approach with results revealing the unprecedented impact of COVID-19 on stock market liquidity during the low frequency bands for countries that were hard hit with the COVID-19 outbreak, i.e., Italy, Germany, France, the UK and the US. Further, evidence shows that there is a heterogeneous lead-lag nexus across scales for the entire period of the study.

Examining the interconnectedness and early warning signals of systemic risks of shadow banks: an application to the Indian shadow bank crisis

PurposeThe paper models the financial interconnectedness and systemic risk of shadow banks using Granger-causal network-based measures and takes the Indian shadow bank crisis of 2018–2019 as a systemic event.Design/methodology/approachThe paper employs pairwise linear Granger-causality tests adjusted for heteroskedasticity and return autocorrelation on a rolling window of weekly returns data of 52 financial institutions from 2016 to 2019 to construct network-based measures and calculate network centrality. The Granger-causal network-based measure ranking of financial institutions in the pre-crisis period (explanatory variable) is rank-regressed with the ranking of financial institutions based on maximum percentage loss suffered by them during the crises period (dependent variable).FindingsThe empirical result demonstrated that the shadow bank complex network during the crisis is denser, more interconnected and more correlated than the tranquil period. The closeness, eigenvector, and PageRank centrality established the systemic risk transmitter and receiver roles of institutions. The financial institutions that are more central and hold prestigious positions due to their incoming links suffered maximum loss. The shadow bank network also showed small-world phenomena similar to social networks. Granger-causal network-based measures have out-of-sample predictive properties and can predict the systemic risk of financial institutions.Research limitations/implicationsThe study considers only the publicly listed financial institutions. Also, the proposed measures are susceptible to the size of the rolling window, frequency of return and significance level of Granger-causality tests.Practical implicationsSupervisors and financial regulators can use the proposed measures to monitor the development of systemic risk and swiftly identify and isolate contagious financial institutions in the event of a crisis. Also, it is helpful to policymakers and researchers of an emerging economy where bilateral exposures' data between financial institutions are often not present in the public domain, plus there is a gap or delay in financial reporting.Originality/valueThe paper is one of the first to study systemic risk of shadow banks using a financial network comprising of commercial banks and mutual funds. It is also the first one to study systemic risk of Indian shadow banks.

Conducting Causal Analysis by Means of Approximating Probabilistic Truths.

Simple SummaryThe current paper develops a probabilistic theory of causation and suggests practical routines for conducting causal inference applicable to new machine learning methods that have, so far, remained relatively underutilized in this context.The current paper develops a probabilistic theory of causation using measure-theoretical concepts and suggests practical routines for conducting causal inference. The theory is applicable to both linear and high-dimensional nonlinear models. An example is provided using random forest regressions and daily data on yield spreads. The application tests how uncertainty in short- and long-term inflation expectations interacts with spreads in the daily Bitcoin price. The results are contrasted with those obtained by standard linear Granger causality tests. It is shown that the suggested measure-theoretic approaches do not only lead to better predictive models, but also to more plausible parsimonious descriptions of possible causal flows. The paper concludes that researchers interested in causal analysis should be more aspirational in terms of developing predictive capabilities, even if the interest is in inference and not in prediction per se. The theory developed in the paper provides practitioners guidance for developing causal models using new machine learning methods that have, so far, remained relatively underutilized in this context.

Recognition of Electroencephalography-Related Features of Neuronal Network Organization in Patients With Schizophrenia Using the Generalized Choquet Integrals.

In this study, we focused on the verification of suitable aggregation operators enabling accurate differentiation of selected neurophysiological features extracted from resting-state electroencephalographic recordings of patients who were diagnosed with schizophrenia (SZ) or healthy controls (HC). We built the Choquet integral-based operators using traditional classification results as an input to the procedure of establishing the fuzzy measure densities. The dataset applied in the study was a collection of variables characterizing the organization of the neural networks computed using the minimum spanning tree (MST) algorithms obtained from signal-spaced functional connectivity indicators and calculated separately for predefined frequency bands using classical linear Granger causality (GC) measure. In the series of numerical experiments, we reported the results of classification obtained using numerous generalizations of the Choquet integral and other aggregation functions, which were tested to find the most appropriate ones. The obtained results demonstrate that the classification accuracy can be increased by 1.81% using the extended versions of the Choquet integral called in the literature, namely, generalized Choquet integral or pre-aggregation operators.

Using internet search keyword data for predictability of precious metals prices: Evidence from non-parametric causality-in-quantiles approach

This investigation examines how Google trends-based information can influence predictability of precious metals prices by utilizing Linear Granger causality & non-parametric causality in quantiles approach. Data ranges from January (2004) to March (2021). We have incorporated the four most popular metals (i.e., Gold, Platinum, Palladium, & Silver) & Crude oil. Although findings obtained from linear Granger causality showed no causal link between Google trends series & oil and precious metals prices, rather findings obtained from the non-parametric test show the existence of a non-linear association among constructs. Non-parametric test results show Google trends series can predict the prices of precious metals. Therefore, we conclude that investors, before making investment decisions, first seek information available online, i.e., on Google Trends, to gain some insights about future price movement that would be ideal for any investor. Moreover, investors, policymakers can get noteworthy awareness from this research for thinking out of the box while making investments.