Distance correlation (dCorr) is a test statistic that can identify non-linear dependence patterns between random variables. Variations of dCorr have been applied in sequences of dependent random variables, including time series. The necessity of exploring dependencies between lags of time series or cross-dependence between distinct time series has resulted in closed forms of dCorr distributions for the case of null hypothesis—independence. Nonetheless, their assumptions and complex expressions hinder their application to a variety of forecasting applications. Consequently, non-parametric dependence hypothesis tests procedures—e.g., bootstraps—appear as an adequate alternative. However, consistent bootstrap approaches require stationary time series and, as a result, signal transformations. On the one hand, there is a plethora of such transformations; on the other, each of these silently imply different assumptions regarding the ratio of the deterministic elements over “noisy” elements of the time series, i.e., the signal-to-noise ratio. The aim of this paper is to explore the effect of the implied signal-to-noise ratio on the hypothesis p-values as derived by a bootstrap hypothesis test procedure. The relationship of these p-values with the stationary transformations (and the corresponding signal-to-noise ratio) is demonstrated with currency exchange-related time series.

Linear correlation test statistics, e.g., Pearson's correlation coefficient, dominated the time series analysis for decades offering significant achievements as well as featuring limitations. In that framework, the econometric time series were a subset of sequential random variables that pointed out the necessity of extending the time series analysis in the non-linear serial dependence domain. The introduction of distance correlation (dCorr) in 2007 showed potential in that direction. However, the complexity of the accompanying mathematical expressions and restrictive assumptions, e.g., of independent and identically distributed or strictly stationary time series, resulted in relatively slow progress. To tackle this complexity and restrictions, past research works assuming stationary time series introduced various bootstrap procedures to derive the upper 95% confidence bound of the null hypothesis test. In this paper, we introduce a bootstrap procedure based on Monte Carlo simulations instead, providing both upper and lower bounds of null hypothesis. We also discuss distinct types of white noises and how these are related to the null hypothesis. The derived null hypothesis bounds are estimated regardless of the type of the observed time series, and therefore in the case of non-stationary time series as well. The efficiency of the proposed method is demonstrated with three econometric variables, which can be used in currency exchange rates applications.

Currency exchange markets are among the largest markets worldwide. Due to their decentrilised nature and the variation of the engaged stakeholders (i.e., from big funds and corporates to small enterprises and citizens), the currency exchange rate forecasting is a challenging task, crucial in decision making and democratisation of this domain. The main objective of this paper is to explore dependence patterns among various econometric time series, directly, or indirectly, related to currency exchange rate time series. Thereafter, on top of this dependence analysis, we deliver machine learning algorithms (e.g., support vector classifiers) to predict future values of currency exchange rates. Under this framework, the notions of time series autocorrelation and cross-correlation are utilised. However, both exhibit limitations because they cannot depict non-linear dependances. To tackle this caveat, we analyse the absolute values of the returns (i.e., percentage change) of the examined time series. The efficiency of the proposed procedure is demonstrated with eight currency exchange rate time series and eleven exogenous econometric time series related to the former. Finally, we trained eight support vector classifiers, one for each currency pair, all of which reached an accuracy level of approximately 80%.

The market of foreign exchange is one of the largest markets worldwide. However, predicting the price of exchange currency pairs is a very difficult problem due to the fact that exchange rate time series demonstrate a highly non-linear and non-stationary behavior, being affected by a series of parameters which are difficult to model efficiently. This study attempts to compare five machine learning and neural network classifiers: Logistic Regression model, Support Vector Classifier, Gaussian Naive Bayes, Random Forest and Multi-layer Perceptron. The most highly correlated features are evaluated and compared for predicting the day ahead trend of the Euro-United States Dollar (EUR-USD) currency pair. Results indicate that model selection is not as significant as the combination of the most important features for the accuracy of the prediction.