This paper aims at comparing different forecasting strategies combined with the STL decomposition method. STL is a versatile and robust time series decomposition method. The forecasting strategies we consider are as follows: three statistical methods (ARIMA, ETS, and Theta), five machine learning methods (KNN, SVR, CART, RF, and GP), and two versions of RNNs (CNN-LSTM and ConvLSTM). We conduct the forecasting test on six horizons (1, 6, 12, 18, and 24 months). Our results show that, when applied to monthly industrial M3 Competition data as a preprocessing step, STL decomposition can benefit forecasting using statistical methods but harms the machine learning ones. Moreover, the STL-Theta combination method displays the best forecasting results on four over the five forecasting horizons.

We propose a novel decomposition method for electromyographic signals based on blind source separation. Using the cyclostationary properties of motor unit action potential trains (MUAPt), it is shown that the MUAPt can be decomposed by joint diagonalization of the cyclic spatial correlation matrix of the observations. After modeling the source signals, we provide the proof of orthogonality of the sources and of their delayed versions in a cyclostationary context. We tested the proposed method on simulated signals and showed that it can decompose up to six sources with a probability of correct detection and classification >95%, using only eight recording sites. Moreover, we tested the method on experimental multi-channel signals recorded with thin-film intramuscular electrodes, with a total of 32 recording sites. The rate of agreement of the decomposed MUAPt with those obtained by an expert using a validated tool for decomposition was >93%.

Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.