This paper proposes an interesting idea in order to efficiently forecast non-stationary time series at multiple times ahead. In order to achieve this, the authors introduce an objective function called Shape and Time Distorsion Loss (STDL) to train deep neural network. The paper is well written, clear, and of certain significance. In Figure 1 the authors illustrate the limitation of certain existing approaches as a way to motivate their contributions. I am not convinced with the arguments presented there.

We consider a general and realistic scenario involving non-stationary time series, consisting of several offline intervals with different distributions within a fixed offline time horizon, and an online interval that continuously receives new samples. For non-stationary time series, the data distribution in the current online interval may have appeared in previous offline intervals. We theoretically explore the feasibility of applying knowledge from offline intervals to the current online interval. To this end, we propose the Mixture of Online and Offline Experts (MOOE). MOOE learns static offline experts from offline intervals and maintains a dynamic online expert for the current online interval. It then adaptively combines the offline and online experts using a meta expert to make predictions for the samples received in the online interval. Specifically, we focus on theoretical analysis, deriving parameter convergence, regret bounds, and generalization error bounds to prove the effectiveness of the algorithm.

One of the latest self-supervised learning (SSL) methods, VICReg, showed a great performance both in the linear evaluation and the fine-tuning evaluation. However, VICReg is proposed in computer vision and it learns by pulling representations of random crops of an image while maintaining the representation space by the variance and covariance loss. However, VICReg would be ineffective on non-stationary time series where different parts/crops of input should be differently encoded to consider the non-stationarity. Another recent SSL proposal, Temporal Neighborhood Coding (TNC) is effective for encoding non-stationary time series. This study shows that a combination of a VICReg-style method and TNC is very effective for SSL on non-stationary time series, where a non-stationary seismic signal time series is used as an evaluation dataset.

In Internet of things (IoT), data is continuously recorded from different data sources and devices can suffer faults in their embedded electronics, thus leading to a high-dimensional data sets and concept drift events. Therefore, methods that are capable of high-dimensional non-stationary time series are of great value in IoT applications. Fuzzy Time Series (FTS) models stand out as data-driven non-parametric models of easy implementation and high accuracy. Unfortunately, FTS encounters difficulties when dealing with data sets of many variables and scenarios with concept drift. We present a new approach to handle high-dimensional non-stationary time series, by projecting the original high-dimensional data into a low dimensional embedding space and using FTS approach. Combining these techniques enables a better representation of the complex content of non-stationary multivariate time series and accurate forecasts. Our model is able to explain 98% of the variance and reach 11.52% of RMSE, 2.68% of MAE and 2.91% of MAPE.

Evaluating predictive models is a crucial task in predictive analytics. This process is especially challenging with time series data where the observations show temporal dependencies. Several studies have analysed how different performance estimation methods compare with each other for approximating the true loss incurred by a given forecasting model. However, these studies do not address how the estimators behave for model selection: the ability to select the best solution among a set of alternatives. We address this issue and compare a set of estimation methods for model selection in time series forecasting tasks. We attempt to answer two main questions: (i) how often is the best possible model selected by the estimators; and (ii) what is the performance loss when it does not. We empirically found that the accuracy of the estimators for selecting the best solution is low, and the overall forecasting performance loss associated with the model selection process ranges from 1.2% to 2.3%. We also discovered that some factors, such as the sample size, are important in the relative performance of the estimators.

For a long time, I heard that the problem of time series could only be approached by statistical methods (AR[1], AM[2], ARMA[3], ARIMA[4]). These techniques are generally used by mathematicians who try to improve them continuously to constrain stationary and non-stationary time series. A friend of mine (mathematician, professor of statistics, and specialist in non-stationary time series) offered me several months ago to work on the validation and improvement of techniques to reconstruct the lightcurve of stars. Indeed, the Kepler satellite[11], like many other satellites, could not continuously measure the intensity of the luminous flux of nearby stars. The Kepler satellite was dedicated between 2009 and 2016 to search for planets outside our Solar System called extrasolar planets or exoplanets. As you have understood, we are going to travel a little further than our planet Earth and deep dive into a galactic journey whose machine learning will be our vessel.

AR models express the current value of the time series linearly in terms of its previous values and the current residual, whereas MA models express the current value of the time series linearly in terms of its current and previous residual series. ARMA models are a combination of AR and MA models, in which the current value of the time series is expressed linearly in terms of its previous values and in terms of current and previous residual series. The time series defined in AR, MA, and ARMA models are stationary processes, which means that the mean of the series of any of these models and the covariance among its observations do not change with time. For non-stationary time series, transformation of the series to a stationary series has to be performed first. ARIMA model generally fits the non-stationary time series based on the ARMA model, with a differencing process which effectively transforms the non-stationary data into a stationary one.

AR models express the current value of the time series linearly in terms of its previous values and the current residual, whereas MA models express the current value of the time series linearly in terms of its current and previous residual series. ARMA models are a combination of AR and MA models, in which the current value of the time series is expressed linearly in terms of its previous values and in terms of current and previous residual series. The time series defined in AR, MA, and ARMA models are stationary processes, which means that the mean of the series of any of these models and the covariance among its observations do not change with time. For non-stationary time series, transformation of the series to a stationary series has to be performed first. ARIMA model generally fits the non-stationary time series based on the ARMA model, with a differencing process which effectively transforms the non-stationary data into a stationary one.