In this paper, we analyse two interesting applications related to the dynamics of economic phenomena linked to the Efficient Market Hypothesis (EMH), informative surprises, and the Model-Data Paradox of Chaos in certain top currency pairs from the foreign exchange market (FOREX). On the one hand, we empirically show that the FOREX market reacts under the Efficient Market Hypothesis in some cases, creating a significant variation in a short period of time (15, 30, and 60 min) in the quotes of the main currencies from the most important economic regions in the West (the United States, Europe, and the United Kingdom). This variation would depend on the actual deviation of high-impact macroeconomic news reported by these markets in relation to trade balance, unemployment rate, Gross Domestic Product (GDP), retail sales, the Industrial Production Index (IPI), and the Consumer Price Index (CPI). On the other hand, by testing the Model-Data Paradox of Chaos, we empirically verify that if we consider all the information available in the financial markets of currencies (or at least, more desegregated data) instead of daily data, and we apply a robust chaotic behaviour detection method, we can find differences in relation to the detection of chaos on the same series but with different temporal frequencies. This allows us to confirm that behind these financial time series which show an apparently random irregular evolution, there would be a generating system which, although unknown in principle, would be deterministic (and nonlinear), and we could take advantage of that deterministic character to make predictions, even if only in the short term, understanding “short term” as the time it takes for the market to incorporate these informative surprises in the FOREX market analysed.

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate the local variances in generic regression problems by using kernel smoothers. The proposed schemes can be applied in multidimensional scenarios (not just for time series analysis) and easily in a multi-output framework as well. Moreover, they enable the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even compared with the benchmark techniques. One of these experiments involves a real dataset analysis.

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate local variances in generic regression problems by using of kernel smoothers. The proposed schemes can be applied in multidimesional scenarios (not just for time series analysis) and easily in a multi-output framework, as well. Moreover, they allow the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even comparing with benchmark techniques. One of these experiment involves a real dataset analysis.