Nonlinear causality testing with stepwise multivariate filtering

This study explores the direction and nature of causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). These are the most liquid and widely traded currency pairs in the world and make up about 90% of total Forex trading worldwide. The data covers the period 3/20/1987-11/14/2007, including the Asian crisis, the dot-com bubble and the period just before the outbreak of the US subprime crisis. The objective of the paper is to test for the existence of both linear and nonlinear causal relationships among these currency markets. The modified Baek-Brock test for nonlinear non-causality is applied on the currency return time series as well as the linear Granger test. Further to the classical pairwise analysis causality testing is conducted in a multivariate formulation, to correct for the effects of the other variables. A new stepwise multivariate filtering approach is implemented. To check if any of the observed causality is strictly nonlinear, the nonlinear causal relationships of VAR/VECM filtered residuals are also examined. Finally, the hypothesis of nonlinear non-causality is investigated after controlling for conditional heteroskedasticity in the data using GARCH-BEKK, CCC-GARCH and DCC-GARCH models. Significant nonlinear causal linkages persisted even after multivariate GARCH filtering. This indicates that if nonlinear effects are accounted for, neither FX market leads or lags the other consistently and currency returns may exhibit statistically significant higher-order moments and asymmetries.nonparametric Granger causality; filtering; multivariate GARCH models; spillovers

The Nonlinear Dynamic Relationship of Exchange Rates: Parametric and Nonparametric Causality testing

The present study investigates the long-term linear and nonlinear causal linkages among six currencies, namely EUR/USD, GBP/USD, USD/JPY, USD/CHF, AUD/USD and USD/CAD. The prime motivation for choosing these exchange rates comes from the fact that they are the most liquid and widely traded, covering about 90% of total FX trading worldwide. The data spans two periods (PI: 3/20/1991 \u2013 3/20/1997, PII: 3/20/2003 \u2013 3/20/2007) before and after the structural break of the Asian financial crisis, which set a platform for departure for causality testing. We apply a new nonparametric test for Granger non-causality by Diks and Panchenko (2005, 2006) as well as the conventional linear Granger test on the return time series. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of pairwise VAR filtered residuals as well as in a six-variate formulation. We find remaining significant bi- and uni-directional causal nonlinear relationships in the return series. Finally, we investigate the hypothesis of nonlinear non-causality after controlling for conditional heteroskedasticity in the data using a GARCH-BEKK model. Our approach allows the entire variance-covariance structure of the currency interrelationship to be incorporated in order to explicitly capture the volatility spillover mechanism. Whilst the nonparametric test statistics are smaller in some cases, significant nonlinear causal linkages persisted even after GARCH filtering during both the pre- and post-Asian crisis period. This indicates that currency returns may exhibit asymmetries and statistically significant higher-order moments.

The Relationship between Crude Oil Spot and Futures Prices: Cointegration, Linear and Nonlinear Causality

The present study investigates the linear and nonlinear causal linkages between daily spot and futures prices for maturities of one, two, three and four months of West Texas Intermediate (WTI) crude oil. The data cover two periods October 1991-October 1999 and November 1999-October 2007, with the latter being significantly more turbulent. Apart from the conventional linear Granger test we apply a new nonparametric test for nonlinear causality by Diks and Panchenko after controlling for cointegration. In addition to the traditional pairwise analysis, we test for causality while correcting for the effects of the other variables. To check if any of the observed causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VECM filtered residuals. Finally, we investigate the hypothesis of nonlinear non-causality after controlling for conditional heteroskedasticity in the data using a GARCH-BEKK model. Whilst the linear causal relationships disappear after VECM cointegration filtering, nonlinear causal linkages in some cases persist even after GARCH filtering in both periods. This indicates that spot and futures returns may exhibit asymmetries and statistically significant higher-order moments. Moreover, the results imply that if nonlinear effects are accounted for, neither market leads or lags the other consistently, videlicet the pattern of leads and lags changes over time.

Direction-of-Change Forecasting using a Volatility- Based Recurrent Neural Network

This paper investigates the profitability of a trading strategy, based on recurrent neural networks, that attempts to predict the direction-of-change of the market in the case of the NASDAQ composite index. The sample extends over the period 2/8/1971 \u2013 4/7/1998, while the sub-period 4/8/1998 - 2/5/2002 has been reserved for out-of-sample testing purposes. We demonstrate that the incorporation in the trading rule of estimates of the conditional volatility changes strongly enhances its profitability during `bear' market periods. This improvement is being measured with respect to a nested model that does not include the volatility variable as well as to a buy & hold strategy. We suggest that our findings can be justified by invoking either the `volatility feedback' theory or the existence of portfolio insurance schemes in the equity markets. Our results are also consistent with the view that volatility dependence produces sign dependence.

Exchange Rates and Fundamentals: Co-Movement, Long-Run Relationships and Short-run Dynamics

The present study builds upon the seminal work of Engel and West [2005, Journal of Political Economy 113, 485-517] and in particular on the relationship between exchange rates and fundamentals. The paper discusses the well-known puzzle that fundamental variables such as money supplies, interest rates, outputs etc. provide help in predicting changes in floating exchange rates. It also tests the theoretical result of Engel and West (2005) that in a rational expectations present-value model, the asset price manifests near-random walk behaviour if the fundamentals are I(1) and the factor for discounting future fundamentals is near one. The study explores the direction and nature of causal interdependencies and cross-correlations among the most widely traded currencies in the world, their country-specific fundamentals and their US-differentials. A new VAR/VECM-GARCH multivariate filtering approach is implemented, whilst linear and nonlinear non-causality is tested on the time series. In addition to pairwise causality testing, several different groupings of variables are explored. The methodology is extensively tested and validated on simulated and empirical data. The implication is that although exchange rates and fundamentals appear to be linked in a way that is broadly consistent with asset-pricing models, there is no indication of a prevailing causal behaviour from fundamentals to exchange rates or vice-versa. When nonlinear effects are accounted for, the evidence implies that the pattern of leads and lags changes over time. These results may influence the greater predictability of currency markets. Overall, fundamentals may be important determinants of FX rates, however there may be some other unobservable variables driving the currency rates that current asset-pricing models have not yet captured.simulation-based inference; causality; random walk; filtering; nonlinearity; asset-pricing

Extreme Correlation in Cryptocurrency Markets

In this paper, we study the contemporaneous tail dependence structure in a pairwise comparison of the ten largest cryptocurrencies, namely Bitcoin, Dash, Dogecoin, Ethereum, Litecoin, Monero, Namecoin, Novacoin, Peercoin, and Ripple. We apply multivariate extreme value theory and we estimate a bias-corrected extreme correlation coefficient. Our findings reveal clear patterns of significantly high bivariate dependency in the distribution tails of some of the most basic and widespread cryptocurrencies, primarily over various downside constraints. This means that extreme correlation is not related to cryptocurrency market volatility per se, but to the trend of the cryptocurrency market. Therefore, extreme correlation increases in bear markets, but not in bull markets for these pairs. Interestingly, there is also a significant number of pairs which exhibit a weak level of dependency in distribution tails

A new buffering theory of social support and psychological stress

A dynamical model linking stress, social support, and health has been recently proposed and numerically analyzed from a classical point of view of integer-order calculus. Although interesting observations have been obtained in this way, the present work conducts a fractional-order analysis of that model. Under a periodic forcing of an environmental stress variable, the perceived stress has been analyzed through bifurcation diagrams and two well-known metrics of entropy and complexity, such as spectral entropy and C0 complexity. The results obtained by numerical simulations have shown novel insights into how stress evolves with frequency and amplitude of the perturbation, as well as with initial conditions for the system variables. More precisely, it has been observed that stress can alternate between chaos, periodic oscillations, and stable behaviors as the fractional order varies. Moreover, the perturbation frequency has revealed a narrow interval for the chaotic oscillations, while its amplitude may present different values indicating a low sensitivity regarding chaos generation. Also, the perceived stress has been noted to be highly sensitive to initial conditions for the symptoms of stress-related ill-health and for the social support received from family and friends. This work opens new directions of research whereby fractional calculus might offer more insight into psychology, life sciences, mental disorders, and stress-free well-being

Antiretroviral therapy of HIV infection using a novel optimal type-2 fuzzy control strategy

Abstract The human immunodeficiency virus (HIV), as one of the most hazardous viruses, causes destructive effects on the human bodies' immune system. Hence, an immense body of research has focused on developing antiretroviral therapies for HIV infection. In the current study, we propose a new control technique for a fractional-order HIV infection model. Firstly, a fractional model of the HIV model is investigated, and the importance of the fractional-order derivative in the modeling of the system is shown. Afterward, a type-2 fuzzy logic controller is proposed for antiretroviral therapy of HIV infection. The developed control scheme consists of two individual controllers and an aggregator. The optimal aggregator modifies the output of each individual controller. Simulations for two different strategies are conducted. In the first strategy, only reverse transcriptase inhibitor (RTI) is used, and the superiority of the proposed controller over a conventional fuzzy controller is demonstrated. Lastly, in the second strategy, both RTI and protease inhibitors (PI) are used simultaneously. In this case, an optimal type-2 fuzzy aggregator is also proposed to modify the output of the individual controllers based on optimal rules. Simulations results demonstrate the appropriate performance of the designed control scheme for the uncertain system

Indirect neural-enhanced integral sliding mode control for finite-time fault-tolerant attitude tracking of spacecraft

In this article, a neural integral sliding mode control strategy is presented for the finite-time fault-tolerant attitude tracking of rigid spacecraft subject to unknown inertia and disturbances. First, an integral sliding mode controller was developed by originally constructing a novel integral sliding mode surface to avoid the singularity problem. Then, the neural network (NN) was embedded into the integral sliding mode controller to compensate the lumped uncertainty and replace the robust switching term. In this way, the chattering phenomenon was significantly suppressed. Particularly, the mechanism of indirect neural approximation was introduced through inequality relaxation. Benefiting from this design, only a single learning parameter was required to be adjusted online, and the computation burden of the proposed controller was extremely reduced. The stability argument showed that the proposed controller could guarantee that the attitude and angular velocity tracking errors were regulated to the minor residual sets around zero in a finite time. It was noteworthy that the proposed controller was not only strongly robust against unknown inertia and disturbances, but also highly insensitive to actuator faults. Finally, the effectiveness and advantages of the proposed control strategy were validated using simulations and comparisons

A new fuzzy reinforcement learning method for effective chemotherapy

A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–Fabrizio fractional-order model of cancer chemotherapy treatment was elaborated and analyzed. A fix-point theorem and an iterative method were implemented to prove the existence and uniqueness of the solutions of the proposed model. Afterward, in order to control cancer through chemotherapy treatment, a fuzzy-reinforcement learning-based control method that uses the State-Action-Reward-State-Action (SARSA) algorithm was proposed. Finally, so as to assess the performance of the proposed control method, the simulations were conducted for young and elderly patients and for ten simulated patients with different parameters. Then, the results of the proposed control method were compared with Watkins’s Q-learning control method for cancer chemotherapy drug dosing. The results of the simulations demonstrate the superiority of the proposed control method in terms of mean squared error, mean variance of the error, and the mean squared of the control action—in other words, in terms of the eradication of tumor cells, keeping normal cells, and the amount of usage of the drug during chemotherapy treatment