Optimal Transport Autoregression to Forecast High‐Frequency Financial Data Distributions

Effects of the geopolitical risks on Bitcoin returns and volatility

Do collective emotions drive bitcoin volatility? A triple regime-switching vector approach

This study contributes to the growing literature on the determinants of Bitcoin volatility by examining its relationship with financial stress. Building on prior research linking Bitcoin volatility to broader economic and financial uncertainty, we employ a combination of regression analysis, a GARCH-MIDAS framework, and a Vector Autoregression (VAR) model to evaluate both the static and dynamic effects of financial uncertainty on Bitcoin. Preliminary regression results indicate that financial stress measures significantly and negatively predict Bitcoin volatility. The GARCH-MIDAS model confirms these results, showing a strong negative impact of financial stress on the long-term component of volatility. VAR analysis further reveals that Bitcoin volatility decreases in response to shocks in financial stress indicators. These findings highlight Bitcoin’s sensitivity to systemic financial conditions and carry important implications for risk management among cryptocurrency traders, institutional investors, and financial regulators.

This paper extends the study of Bourghelle et al. (2022) to check whether collective emotions could help forecast bitcoin volatility over the period 2018-2021. To this end, we first assess whether consideration of investor sentiment and collective emotions can give us clearer insights into bitcoin dynamics over the period in question and whether it can help to explain the different shifts in price. Formally, we ran causality tests and, as in Bourghelle et al. (2022), built a two equation nonlinear vector autoregressive (VAR) model to assess for further lead-lag effects between bitcoin volatility and collective emotions. Second, we proposed in-sample forecasts of bitcoin volatility to test whether it would be possible to improve our forecasts by taking investors’ emotions and sentiment into account. Our findings show that market sentiment and investors’ emotions provide useful information that can explain shifts, structural breaks, and changes in bitcoin volatility. Further, collective emotions improve bitcoin volatility forecasting as our nonlinear model, including emotions-related news, supplants the benchmark linear model.

This paper extends the study of Bourghelle et al. (2022) to check whether collective emotions could help to forecast bitcoin volatility over the period 2018-2021. To this end, we first assess whether consideration of investor sentiment and collective emotions can give us clearer insights into bitcoin dynamics over the period in question and whether they can help to explain the different price fluctuations. Formally, we ran causality tests and, as in Bourghelle et al. (2022), built a two-equation nonlinear vector autoregressive (VAR) model to assess for further lead-lag effects between bitcoin volatility and collective emotions. Second, we proposed in-sample forecasts of bitcoin volatility to test whether our forecasts could be improved by taking investors’emotions and sentiment into account. Our findings show that market sentiment and investors’ emotions provide useful information that can help to explainfluctuations, structural breaks, and changes in bitcoin volatility. Further, collective emotions improve bitcoin volatility forecasting as our nonlinear model, including emotions-related news, supplants the benchmark linear model.

The autoregressive model is a useful tool to analyze longitudinal data. It is particularly suitable for gerontological research as autoregressive models can be used to establish the causal relationship within a single variable over time as well as the causal ordering between two or more variables (e.g., physical health and psychological well-being) over time through bivariate autoregressive cross-lagged or contemporaneous models. Specifically, bivariate autoregressive models can explore the cross-lagged effects between two variables over time to determine the proper causal ordering between these variables. The advantage of analyzing cross-lagged effects is to test for the strength of prediction between two variables controlling for each variable's previous time score as well as the autoregressive component of the model. Bivariate autoregressive contemporaneous models can also be used to determine causal ordering within the same time point when compared to cross-lagged effects. Since the technique uses structural equation modeling, models are also adjusted for measurement error. This paper will present an introduction to setting up models and a step-by-step approach to analyzing univariate simplex autoregressive models, bivariate autoregressive cross-lagged models, and bivariate autoregressive contemporaneous models.

To explore the impact of factors from the traditional financial market, such as economic policy uncertainty, oil prices, the NASDAQ index, and gold prices, to identify factors contributing to Bitcoin volatility. This study uses traditional OLS (ordinary least squares) regression analysis to examine how different external factors affect Bitcoin price volatility from January 2014 to March 2023. By employing a comprehensive approach to recognize the distinctive characteristics of the Bitcoin market, namely, 24-hour trading and the short duration of its existence, we’ve included a wide spectrum of data to ensure a cohesive comparison with other financial datasets. The findings of the statistical analysis indicate that EPU and the NASDAQ index promote positive fluctuations in Bitcoin volatility, whereas gold prices act as a dampener. Conversely, we do not find empirical support for the influence of energy prices, such as oil, on Bitcoin volatility. These findings indicate that we should not undervalue Bitcoin in any financial transaction scenario. It means that all stakeholders should treat the issue of Bitcoin volatility more seriously, even including governments, who should actively regulate the Bitcoin market, and investors, who should recognize the dangers of this volatility, make rational decisions based on individual circumstances, and employ flexible trading strategies.

How do economic policy uncertainty and geopolitical risk drive Bitcoin volatility?

In this work, I studied whether news media sentiments have an impact on Bitcoin volatility. In doing so, I applied three different range-based volatility estimates along with two different sentiments, namely psychological sentiments and financial sentiments, incorporating four various sentiment dictionaries. By analyzing 17,490 news coverages by 91 major English-language newspapers listed in the LexisNexis database from around the globe from January 2012 until August 2021, I found news media sentiments to play a significant role in Bitcoin volatility. Following the heterogeneous autoregressive model for realized volatility (HAR-RV)—which uses the heterogeneous market idea to create a simple additive volatility model at different scales to learn which factor is influencing the time series—along with news sentiments as explanatory variables, showed a better fit and higher forecasting accuracy. Furthermore, I also found that psychological sentiments have medium-term and financial sentiments have long-term effects on Bitcoin volatility. Moreover, the National Research Council Emotion Lexicon showed the main emotional drivers of Bitcoin volatility to be anticipation and trust.

PurposeThis paper aims to investigate the effect of the economic policy uncertainty (EPU), geopolitical risk (GPR) and climate policy uncertainty (CPU) of USA on Bitcoin volatility from August 2010 to August 2022.Design/methodology/approachIn this paper, the authors have adopted the empirical strategy of Yen and Cheng (2021), who modified volatility model of Wang and Yen (2019), and the authors use an OLS regression with Newey-West error term.FindingsThe results using OLS regression with Newey–West error term suggest that the cryptocurrency market could have hedge or safe-haven properties against EPU and geopolitical uncertainty. While the authors find that the CPU has a negative impact on the volatility of the bitcoin market. Hence, the authors expect climate and environmental changes, as well as indiscriminate energy consumption, to play a more important role in increasing Bitcoin price volatility, in the future.Originality/valueThis study has two implications. First, to the best of the authors’ knowledge, the study is the first to extend the discussion on the effect of dimensions of uncertainty on the volatility of Bitcoin. Second, in contrast to previous studies, this study can be considered as the first to examine the role of climate change in predicting the volatility of bitcoin. This paper contributes to the literature on volatility forecasting of cryptocurrency in two ways. First, the authors discuss volatility forecasting of Bitcoin using the effects of three dimensions of uncertainty of USA (EPU, GPR and CPU). Second, based on the empirical results, the authors show that cryptocurrency can be a good hedging tool against EPU and GPR risk. But the cryptocurrency cannot be a hedging tool against CPU risk, especially with the high risks and climatic changes that threaten the environment.

Preface. 1 EViews workfile and descriptive data analysis. 1.1 What is the EViews workfile? 1.2 Basic options in EViews. 1.3 Creating a workfile. 1.4 Illustrative data analysis. 1.5 Special notes and comments. 1.6 Statistics as a sample space. 2 Continuous growth models. 2.1 Introduction. 2.2 Classical growth models. 2.3 Autoregressive growth models. 2.4. Residual tests. 2.5 Bounded autoregressive growth models. 2.6 Lagged variables or autoregressive growth models. 2.7 Polynomial growth model. 2.8 Growth models with exogenous variables. 2.9 A Taylor series approximation model. 2.10 Alternative univariate growth models. 2.11 Multivariate growth models. 2.12 Multivariate AR(p) GLM with trend. 2.13 Generalized multivariate models with trend. 2.14 Special notes and comments. 2.15 Alternative multivariate models with trend. 2.16 Generalized multivariate models with time-related effects. 3 Discontinuous growth models. 3.1 Introduction. 3.2 Piecewise growth models. 3.3 Piecewise S-shape growth models. 3.4 Two-piece polynomial bounded growth models. 3.5 Discontinuous translog linear AR(1) growth models. 3.6 Alternative discontinuous growth models. 3.7 Stability test. 3.8 Generalized discontinuous models with trend. 3.9 General two-piece models with time-related effects. 3.10 Multivariate models by states and time periods. 4 Seemingly causal models. 4.1 Introduction. 4.2 Statistical analysis based on a single time series. 4.3 Bivariate seemingly causal models. 4.4 Trivariate seemingly causal models. 4.5 System equations based on trivariate time series. 4.6 General system of equations. 4.7 Seemingly causal models with dummy variables. 4.8 General discontinuous seemingly causal models. 4.9 Additional selected seemingly causal models. 4.10 Final notes in developing models. 5 Special cases of regression models. 5.1 Introduction. 5.2 Specific cases of growth curve models. 5.3 Seemingly causal models. 5.4 Lagged variable models. 5.5 Cases based on the US domestic price of copper. 5.6 Return rate models. 5.7 Cases based on the BASICS workfile. 6 VAR and system estimation methods. 6.1 Introduction. 6.2 The VAR models. 6.3 The vector error correction models. 6.4 Special notes and comments. 7 Instrumental variables models. 7.1 Introduction. 7.2 Should we apply instrumental models? 7.3 Residual analysis in developing instrumental models. 7.4 System equation with instrumental variables. 7.5 Selected cases based on the US-DPOC data. 7.6 Instrumental models with time-related effects. 7.7 Instrumental seemingly causal models. 7.8 Multivariate instrumental models based on the US-DPOC. 7.9 Further extension of the instrumental models. 8 ARCH models. 8.1 Introduction. 8.2 Options of ARCH models. 8.3 Simple ARCH models. 8.4 ARCH models with exogenous variables. 8.5 Alternative GARCH variance series. 9 Additional testing hypotheses. 9.1 Introduction. 9.2 The unit root tests. 9.3 The omitted variables tests. 9.4 Redundant variables test (RV-test). 9.5 Nonnested test (NN-test). 9.6 The Ramsey RESET test. 9.7 Illustrative examples based on the Demo.wf1. 10 Nonlinear least squares models. 10.1 Introduction. 10.2 Classical growth models. 10.3 Generalized Cobb-Douglas models. 10.4 Generalized CES models. 10.5 Special notes and comments. 10.6 Other NLS models. 11 Nonparametric estimation methods. 11.1 What is the nonparametric data analysis. 11.2 Basic moving average estimates. 11.3 Measuring the best fit model. 11.4 Advanced moving average models. 11.5 Nonparametric regression based on a time series. 11.6 The local polynomial Kernel fit regression. 11.7 Nonparametric growth models. Appendix A: Models for a single time series. A.1 The simplest model. A.2 First-order autoregressive models. A.3 Second-order autoregressive model. A.4 First-order moving average model. A.5 Second-order moving average model. A.6 The simplest ARMA model. A.7 General ARMA model. Appendix B: Simple linear models. B.1 The simplest linear model. B.2 Linear model with basic assumptions. B.3 Maximum likelihood estimation method. B.4 First-order autoregressive linear model. B.5 AR(p) linear model. B.6 Alternative models. B.7 Lagged-variable model. B.8 Lagged-variable autoregressive models. B.9 Special notes and comments. Appendix C: General linear models. C.1 General linear model with i.i.d. Gaussian disturbances. C.2 AR(1) general linear model. C.3 AR(p) general linear model. C.4 General lagged-variable autoregressive model. C.5 General models with Gaussian errors. Appendix D: Multivariate general linear models. D.1 Multivariate general linear models. D.2 Moments of an endogenous multivariate. D.3 Vector autoregressive model. D.4 Vector moving average model. D.5 Vector autoregressive moving average model. D.6 Simple multivariate models with exogenous variables. D.7 General estimation methods. D.8 Maximum likelihood estimation for an MGLM. D.9 MGLM with autoregressive errors. References. Index.

The study investigates the role of commodity prices and tax purpose recognition on bitcoin prices. Since the introduction of bitcoin in 2008, emphasis has focused on economists, policy-makers and analysts drastically increasing bitcoin's accessibility and commodity values (Dumitrescu & Firică, 2014). This study employs GARCH and EGARCH from ARCH/GARCH family on daily nature data. We measure the volatile behavior of bitcoin by employing auto-regressive conditional heteroscedasticity model with the aim to explore the relationship between major commodities and bitcoin volatility. We focus on major commodities like gold, silver, platinum, and crude oil to be regressed with bitcoin. The daily prices of commodities were retrieved from www.investing.com and bitcoin prices from www.coindesk.com for the period from 29April 2013 to 16 October 2018. Results confirmed the currency's long-term volatile behavior, which is due to its composition and market dynamics, whereas the existence of asymmetric information effect is not confirmed. Tax recognition by other countries may in future help in controlling the volatility as bitcoin is not a country-specific security. But, only silver impacts on volatility in comparison to oil prices and platinum, which is due to its similar features with gold. Eventually, bitcoin can be used for risk diversification and money making.

Abstract. This study focuses on the dollar, euro, gold, bitcoin and the impact of bubbles in financial investment instruments on bitcoin returns in the context of Turkey. The causal relationships (using the Toda-Yamamato causality test) between the returns of these financial instruments were also determined. In performing this assessment, the sup augmented Dickey-Fuller (SADF) and generalised SADF (GSADF) tests were employed to determine the existence of bubbles based on the period from 1 August 2018 to 23 March 2018. The volatility of bitcoin was tested by autoregressive conditional variant models. As aresult, it was shown that the observed bubbles in gold’s, the euro’s and the dollar’s returns reduced the volatility of bitcoin’s returns. Then, it was shown that the dollar’s, the euro’s and gold’s returns affected bitcoin’s returns. Keywords. Speculative bubbles, Bitcoin, Investment instruments, Autoregressive conditional heteroskedasticity models, Toda-Yamamato causality. JEL. G10, C58, E44.

Prior research on financial analyst’ quarterly earnings forecasts has documented serial correlation in forecast errors. This paper examines the way serial correlation in quarterly earnings forecast errors varies with firm and analyst attributes such as the firm’s industry and the analyst’s experience and brokerage house affiliation. Finding that serial correlation in forecast errors is significant and seemingly independent of firm and analyst attributes, I model consensus forecast errors as an autoregressive process. I demonstrate that the model of forecast errors that best fits the data is AR(1), and use the obtained autoregressive coefficients to predict consensus forecast errors. Modeling the consensus forecast errors as an autoregressive process, the present study predicts future consensus forecast errors, and proposes a series of refinements to the consensus. These refinements were not presented in prior literature, and can be useful to financial analysts and investors.

Detecting financial reporting fraud is vital for preserving market integrity and protecting investors from substantial losses. Yet, the challenges of high dimensionality and noisy financial data often undermine the effectiveness of existing financial fraud detection systems. To address these issues, this study proposes SISAE‐METADES, a novel framework that integrates a supervised input‐enhanced stacked autoencoder (SISAE) with a meta‐learning–based dynamic ensemble selection (METADES) strategy. Unlike conventional stacked autoencoders, SISAE concatenates the original input at each encoding stage and incorporates label supervision, thereby learning task‐relevant and class‐discriminative representations. These enriched deep features improve both the diversity and competence of base classifiers and enable METADES to achieve more reliable local competence estimation. We validate the proposed framework using financial statement data from Chinese A‐share listed companies (2005–2023), covering 71 indicators. Experimental results show that SISAE‐METADES significantly outperforms standalone SISAE, traditional METADES, and several state‐of‐the‐art baselines. In particular, it achieves substantial improvements in accuracy, recall, and F1‐score, underscoring the robustness and effectiveness of combining supervised deep representation learning with dynamic ensemble selection for financial fraud detection. These findings highlight the framework’s practical significance in reducing investor losses, strengthening market confidence, and promoting the stability of the financial system.