BDS Test Research Articles

Bitcoin, Fintech, Energy Consumption, and Environmental Pollution Nexus: Chaotic Dynamics with Threshold Effects in Tail Dependence, Contagion, and Causality

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo’s R/S tests; and Phillips’ and Geweke and Porter-Hudak’s fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO2 emissions as well as causality from energy consumption to CO2 emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech.

Asymmetric Effects of COVID-19 Deaths and Oil Price Shocks on Stock Market Returns in Some Selected African Countries: Evidence From Nonlinear ARDL Approach

This study investigates the asymmetric impact of oil price shocks and COVID-19 total deaths on Kenya, Morocco, Nigeria and South Africa stock market returns. To achieve this objective employing weekly time series data from March 13, 2020 to September 23, 2022, first, we apply the BDS test which confirm the nonlinearity of each series. Second, stationarity tests are used to investigate each series for unit root. The results show that series are stationary in level and in first difference. Third, the bounds test reveals that the series have a cointegration relationship and we apply the nonlinear autoregressive distributed lag (ARDL) ARDL framework to decompose oil price into positive and negative partial sum to investigate a possible asymmetric effect of oil price on stock market returns. The main findings of the asymmetric ARDL model reveal that, in the short-run dynamic, a positive shock in the oil price have a negative and positive effect on stock market returns in Morocco and South Africa respectively. The result is insignificant for Kenya and Nigeria. A negative shock in the oil price have a negative effect on the stock returns in Nigeria, South Africa and in Kenya, Morocco with one period lag. Furthermore, in the long-run, a positive shock in oil price exerts a negative effect on the stock market performance in Morocco and Nigeria while a negative shock in oil price leads to a negative effect also on the stock market returns. The total deaths present a counterintuitive result. Both in the long-run and short-run dynamic, the total number of deaths due to COVID-19 have a significant increasing effect on stock market returns in Kenya, Morocco and South Africa except for Nigeria.

A Hybrid Approach Combining the Lie Method and Long Short-Term Memory (LSTM) Network for Predicting the Bitcoin Return

This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z2 −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White’s test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers.

Forecasting the Stock Market Returns Using nonlinear hybrid GARCH-SETAR model

Forecasting stock market returns is a valuable tool for investors seeking to enhance their gains in stock trading. Predicting stock prices proves to be a formidable endeavor due to its substantial volatility, non-linear characteristics trends, and responsiveness to multifaceted variables, including economic conditions, market trends, seasonality, and sentiment. Despite these complexities, non-linear methodologies like threshold time series and conditional heteroscedasticity models are underutilized. This study aims to assess the predictive capabilities of a hybrid GARCH-SETAR model in the context of stock market returns, encompassing both Islamic and conventional stocks listed on the Pakistan Stock Exchange. The Islamic and conventional stock markets in Pakistan represented by KMI-30, KSE-30 and KSE-100 selected contain daily data from January, 2012 till June, 2023. After the confirmation of stationarity, ARCH effect and non-linearity by ADF, PP unit root, ARCH-LM and BDS test respectively the best estimated linear traditional Box-Jenkins ARIMA, non-linear threshold SETAR and ARIMA-GARCH models are selected based on AIC and BIC information criteria’s. The best proposed hybrid GARCH-SETAR model is also selected based on AIC and BIC information criteria’s. It is revealed that the one-step-ahead recursive forecast performance proposed hybrid GARCH-SETAR model outperforms all other selected linear and non-linear models for both Islamic and conventional stock markets based on RMSE, MAE, MAPE and SMAPE forecast evaluation criteria’s.

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

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

Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets

Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change.

NONLINEAR EFFECTS OF CRUDE OIL DEPENDENCY ON FOOD PRICES IN CHINA: EVIDENCE FROM QUANTILE-ON-QUANTILE APPROACH

The repercussions of disruptions in the global crude oil market have a substantial influence on economies worldwide. Oil shocks are considered important estimators of many economic variables. The current research examines the effects of oil price shocks on food prices in China using monthly data from 2000M1 to 2021M12. The estimation is done using the Quantile on Quantile (QQ) estimation technique. The BDS test is used to test nonlinear dependence in variables. The results of this test confirm the presence of nonlinear dependence in variables. The estimated results of the QQ technique suggest a strong association between oil prices and food prices nexus in China with significant disparities across the quantiles. The lower and medium quantiles show a poor negative effect of crude oil prices on food prices. Nevertheless, it has been shown that there exists a strong positive correlation in the higher quantiles of the distribution, which suggests that an increase in global oil prices directly impacts the costs of food. The outcome of the study offers significant policy recommendations aimed at mitigating the detrimental impact of oil prices on food prices in China.

Research of the non-linear dynamic relationship between global economic policy uncertainty and crude oil prices

This paper examines the relationship between global economic policy uncertainty (GEPU, Global economic policy uncertainty refers to the fact that market actors cannot accurately predict whether the government will change the current economic policy, if so, when the government will make changes, and what the content of the current policy changes will be. These are difficult for economic actors to accurately predict.) and crude oil prices from a global perspective within a non-linear analytical framework. Firstly, the non-linear dynamic trends between GEPU and WTI (West Texas Intermediate) crude oil prices are examined using the VAR-filtered BDS test, followed by the test of the non-linear Granger causality, which shows significant non-linear causal relationship between GEPU and WTI oil prices. Further, this paper use threshold vector autoregressive model (TVAR) and threshold vector error correction model (TVECM) to analysis the long-term and short-term non-linear dynamic adjustment processes between GEPU and WTI oil prices, the result shows that there is an optimal threshold between GEPU and WTI. In the low global economic policy uncertainty regime, the relationship between GEPU and WTI is mutually beneficial, while in the high global economic policy uncertainty regime, the relationship between GEPU and WTI is mutually inhibited. Meanwhile, the TVECM results show that in the first regime, GEPU adjusts towards equilibrium at a faster rate, while in the second regime, WTI adjusts towards equilibrium at a faster rate.

On the connection between clean energy stocks and African stock markets: does uncertainty due to infectious diseases matter?

PurposeAs financial markets for environmentally friendly investment grow in both scope and size, analyzing the relationship between green financial markets and African stocks becomes an important issue. Therefore, this paper examines the role of infectious disease-based uncertainty on the dynamic spillovers between African stock markets and clean energy stocks.Design/methodology/approachThe authors employ the dynamic spillover in time and frequency domains and the nonparametric causality-in-quantiles approach over the period of November 30, 2010, to August 18, 2021.FindingsThese findings are discernible in this study's analysis. First, the authors find evidence of strong connectedness between the African stock markets and the clean energy market, and long-lived but weak in the short and medium investment horizons. Second, the BDS test shows that nonlinearity is crucial when examining the role of infectious disease-based equity market volatility in affecting the interactions between clean energy stocks and African stock markets. Third, the causal analysis provides evidence in support of a nonlinear causal relationship between uncertainties due to infectious diseases and the connection between both markets, mostly at lower and median quantiles.Originality/valueConsidering the global and recent use of clean energy equities and the stock markets for hedging and speculative purposes, one may argue that rising uncertainties may significantly influence risk transmissions across these markets. This study, therefore, is the first to examine the role of pandemic uncertainty on the connection between clean stocks and the African stock markets.

Assessment of Stock Market Liquidity and Efficiency: Evidence from an Emerging Country

The study examines the market efficiency, multi-dimensions of liquidity, and their interconnectedness for the Emerging Indian Stock Market. In contrast to the extant literature, the current study involves testing the market liquidity considering multi-dimensions such as depth, breadth, immediacy, tightness, and resiliency. Second, the study used a battery of tests to determine efficiency, including the Ljung and Box, runs test, Bartel test, Variance ratio, and BDS tests. Furthermore, using five quintiles classified by market depth, the linkage of market efficiency and liquidity is also being investigated. The findings show that during the pandemic, the Indian stock market has been proven to be efficient, suggesting that there are no abnormal returns. Moreover, the research demonstrates that during the COVID-19 pandemic, large volumes of securities are traded quickly and at a lower price effect, but with higher trading costs for completing a market transaction. However, it is worth noting that increased liquidity equates to greater efficiency, while lower liquidity equates to inefficiency.

THE EFFECTS OF COVID-19 ON MULTIFRACTALITY AND LONG-MEMORY IN ETHEREUM’S RETURNS

The global COVID-19 pandemic has shaken the global economy, not sparing the cryptocurrency market. In this paper, we investigate the impact of the COVID-19 pandemic on the dynamics of log returns of the Ethereum. The observed period is divided into three parts: the pre-pandemic period, the pandemic-induced shock, and the period after the pandemic-induced shock on the cryptocurrency market. The research focuses on the impact of the pandemic on the degree of non-linearity and multifractality of log returns. To assess the degree of non-linearity, we used the BDS test and the value of the largest Lyapunov exponent. For multifractality, long-range correlations and information efficiency, we used MF-DFA (Multifractal Detrended Fluctuation Analysis). The research results show that all observed periods have a pronounced non-linearity, but that there is no evidence of the existence of low-dimension chaos. Also, based on the results of the MF-DFA analysis, we conclude that the COVID-19 pandemic has significantly affected the long memory of the log returns of the Ethereum; however, their dynamics and characteristics are returning to the trends present before the pandemic.

Uncertainty due to infectious diseases and bitcoin-gold nexus: Evidence from a non-parametric causality-in-quantiles approach

The interconnection between bitcoin and gold markets has attracted a lot of interest among investors, policy makers, practitioners and market participants. The objective of this paper is to examine the role of infectious diseases-based uncertainty on the connection between bitcoin and gold markets using a battery of spillovers and causality tests. The following findings are discernible from our analyses. First, the spillover tests, there exists a low level of connection between the two markets, and implying that there were diversification options. Second, the spillover results also reveal that the gold market is a net transmitter of volatility, while bitcoin market is a net receiver of the shocks. Third, BDS test shows strong evidence of nonlinearity is a very crucial factor to be put into consideration when examining the role of health-based uncertainty affecting the interactions between bitcoin and gold markets. Fourth, there is evidence of a linear relationship between bitcoin-gold connectedness and infectious diseases uncertainty mostly for the full sample period. Fifth, the non-parametric causality-in-quantile test confirms that the connectedness between uncertainty due to infectious diseases and the markets is stronger mostly around the lower quantiles. These results have important policy implications for policymakers and market participants.

Do geopolitical oil price risk influence stock market returns and volatility of Pakistan: Evidence from novel non-parametric quantile causality approach

The influence of oil price disturbances and geopolitical risk on stock returns and volatility has been investigated by many scholars in different settings, though few of these have scrutinized this effect under distinct market trends. In this regard, this study investigates the causal upshot of geopolitical oil price threats on stock returns and volatility under distinct market trends in the Pakistan stock market. For this objective, the study utilizes a recently developed non-parametric quantile causality approach by exercising monthly data ranging between January 2004 and September 2022. The findings of the BDS and parameter stability tests expose that the series has nonlinear and unstable features, which leads to the novel model of non-parametric causality quantile. Likewise, the outcomes of the empirical analysis reveal that geopolitical oil price displacements have a causal influence on security returns only in normal market conditions, whereas it has a causal effect on volatility in all market conditions. This research makes policy suggestions for academics, businesses, and the Pakistani government based on its conclusions.

On the connection between international REITs and oil markets: The role of economic policy uncertainty

The interconnection between the international Real Estate Investment Trust (REITs) and oil markets has attracted much interest among investors, policymakers, practitioners, and academics. The focus of this paper is to examine the role of US economic policy uncertainty on the connection between international REITs and oil markets. The following findings are perceptible from our analyses. First, the spillover tests show a significantly high level of connection between the two markets. Second, the spillover results also reveal that the oil market is a net receiver of the shocks, while most REIT markets are net transmitters of the volatility. Third, the BDS test shows strong evidence that nonlinearity is crucial when examining policy uncertainty's role in affecting the interactions between REITs and oil markets. Fourth, the non-parametric causality-in-quantile test confirms that the connectedness between economic policy uncertainty and the link between REITs and oil markets is stronger, mostly around the lower and median quantiles. These results have important policy implications for policymakers and market participants.

An application of extenics, spatial factors, and natural resource market in China: The role of artificial intelligence and geopolitical risk

Scientific breakthroughs in recent years have earned widespread recognition. The significance of extenics has become so vital that the discipline is continuously evolving. Additionally, with the deployment of extenics and other innovations, the countries are now more connected and spatially reliant, influencing the global economy. The current study aims to investigate the role of extenics (measured by artificial intelligence (AI)) and spatial factors (measured by geopolitical risk (GPR)) in affecting the natural resources market (NRM). The analysis is performed on the Chinese economy data range from 1985 to 2022. The empirical assessment is carried out by using the unit root tests (Augmented Dickey fuller (ADF) and Phillips-Perron (PP) test), the non-linearity test (BDS test), and the non-linear autoregressive distributed lag (NARDL) model. The NARDL results show an asymmetric relationship between AI, GPR, and NRM in both the short run (SR) and long run (LR). A positive (negative) shock to AI, according to the findings, lowers (raises) natural resource rent and hence improves the natural resource market. Similarly, a positive (negative) shock to the GPR increases (decreases) natural resource rent and allows for the exploitation of the natural resource market. The study suggests that in addition to concentrating on extenics applications, the Chinese government needs to strengthen and reform its strategies to regulate spatial impacts to optimize its natural resource market.

Nonlinearity in emerging market indices: A comprehensive study of stock exchange market dynamics

This research examines the presence of nonlinearities in N‑11 developing economies using various nonlinearity tests. The initial tests include BDS and Runs tests as indicators of nonlinearity. Subsequently, direct nonlinearity tests by White (1989) and Teräsvirta et al. (1993), Keenan (1985) and Tsay (1986) are employed. Finally, the Threshold Autoregressive test is conducted to complement other test. The results reveal the prevalence of nonlinearities and cyclical patterns in the stock indexes of these economies, challenging the assumptions of the Efficient Market Hypothesis (EMH).

Asymmetric Price Transmission Analysis of the International Soybean Market

This study analyzed the asymmetric price transmission in the international soybean market, using data from the US (Chicago Futures), European (Rotterdam), Brazilian (Paranaguá), Argentinian (Rosario Futures and Rosario Spot), and Chinese (Spot and Futures) markets. The study looked at the price transmission between these markets over a period of almost 10 years, from September 2009 to May 2019. The Phillips-Perron unit root test was used to determine the order of integration of the time series. The Engle-Granger cointegration test failed to find any evidence of cointegration between the Chinese and Argentinian markets with any others of the international markets. The lack of cointegration was associated with highly government intervened markets. The cointegration and threshold test proposed by Enders and Siklos, succeeded in rejecting the Null hypothesis and finding cointegration among the series after structural breaks had been taken into account. The BDS test for nonlinearity showed that most of the time series were nonlinear, which prompted the investigation to look into nonlinear modelling. To evaluate asymmetric price transmission, the study used the Threshold autoregressive (TAR) model and the momentum threshold model (MTAR). The Argentine and Chinese markets were primarily suspected of exhibiting asymmetric price transmission due to structural government intervention. However, the test results failed to reject the null hypothesis and revealed asymmetric price transmission between these markets and the international market. As expected, the results found no evidence of asymmetric price transmission in the Paranaguá, Rotterdam, and Chicago markets. Hence, it can be concluded that symmetric price transmission is more prevalent in the global soybean market than asymmetric price transmission.

Non-linear Speculative Bubbles in the Pakistani Stock Market

Since 1987 many stock markeIs of the world have experienced volatility. This bas been true of many emerging stock markeIs. Our study of daily stock lIllI1'ket data from Pakistan between June 1987 and May 1993 finds the results to be consistent with the impression of great volatility and unpredictability thought to be common in such emerging markets. We used the VAR technique to estimaIe a "presumed" fundamental on stock indices using lagged first differences of natural logs of daily exchange rates and stock indices. We used the Hamilton switching model and associated Walk test to see if such speculative trends were present. We were significantly unable to rule them out. We then tested for ARCH effects, whose presence we failed to Ieject. We then used ARCHgenerated residuals to apply the BDS test of general non-linear structure. We failed to reject the lack of such non-linear structure quite significantly. Thus, the Pakistani stock market during the period of study seems to have exhibited quite complex dynamics, along with apparendy strong trends that may indicate the presence of speculative bubbles. This bas many important implications for Pakistani as well as other emerging markets.

Do changes in land use, water bodies, and grazing pastures have a detrimental influence on environmental quality? Opportunities and threats to long-term growth

Land use activities mainly for economic and agricultural purposes have converted one third to one half of our planet's land surface into urban expansion and agricultural practice, which has had significant impacts on natural ecosystems, food production, and environmental quality, attracting the attention of researchers and policymakers. Consequently, land use is emerging as a fundamental issue in global environmental change and sustainable development. This study represents an addition to the prevailing literature by investigating the asymmetric impacts of land-use and land-cover changes on environmental quality in Pakistan using time series data from 1961 to 2016. Carbon dioxide (CO2) emissions were deemed a dependent variable (a proxy for environmental quality), whereas built-up land, cropland, water bodies, and grazing land were considered independent. A nonlinear ARDL bound testing technique (NARDL) was used to investigate dynamic cointegration among the study variables. Moreover, this study used the BDS test and structural break unit root test to confirm nonlinearity and stationarity of the data set. The results confirm that the variables exhibit asymmetrical co-integration. There is a symmetric unidirectional causation, running from built-up land and grazing land towards CO2 emissions with coefficients of 10.570 and 17.045, respectively. Furthermore, asymmetric causality shows that any positive shocks to built-up land (6.134) and water bodies (20.335) significantly cause CO2 emissions. Similarly, a negative shock to grazing land (16.470) also causes CO2 emissions. By contrast, a neutral effect was found between cropland and CO2 emissions.

Assessing the environmental sustainability corridor: linking oil consumption, hydro energy consumption, and ecological footprint in Turkey.

Climate change has been a topic of significant discourse and debate among scholars and policy makers for several decades. In recent decades, it has become a major problem for the entire human race. Therefore, the present research evaluates the impact of oil consumption, hydro energy use, population density, and economic growth on ecological footprint in Turkey for the period from 1965QI to 2018Q4. This paper uses the BDS test to assess the nonlinearity of the variables in the pre-estimation analysis. The results of the test reveal that non-linearity occurs in all of the variables used in this study. As a consequence, using traditional linear methodologies would produce erroneous results. Our research uses the quantile techniques (quantile cointegration, quantile causality, quantile-on-quantile regression), which are recently developed nonlinear estimate methodologies to assess these associations. The results from the study reveal that oil consumption, hydro energy use, population density, and economic growth contribute to environmental degradation in Turkey in majority of the quantiles. The Granger Causality in Quantiles result also gives credence to the results. The study proposes policy recommendation based on these results.