Long Short-Term Memory (LSTM) models are a special case of recurrent neural networks and have become a standard tool in the deep learning community for time series prediction. Despite the common belief that deep neural networks can handle highly nonlinear and noisy data, standard LSTM models are not robust to outliers.

In this talk, we introduce a robust version of LSTM. Two quick fixes for improving robustness are considered: (i) scaling the time series using robust statistics such as the median and MAD, and (ii) replacing the least squares loss function with the Huber loss. A further improvement is achieved by adding a cleaning step within an iterated version of LSTM, which forms our proposed robust LSTM model.

Using simulation experiments, we show that robust LSTM can handle different types of outliers, including level shifts and patches of outliers. Finally, we explore how robust LSTM models can be used for outlier detection in time series and evaluate the accuracy of this detection approach.

Since their introduction, ordinal patterns have become a popular tool for data analysis. As the name may already suggest, ordinal patterns capture the ordinal structure of the underlying data. They have many desirable properties like invariance under monotone transformations, robustness with respect to small noise and simplicity in application. In particular, ordinal patterns are able to capture possibly non-linear dependence.

Recently, there has been a growing interest in extending ordinal patterns to multivariate time series in a way that takes potential correlations between the movement of the variables into account.

We describe different concepts for measuring cross-dependence in sequentially observed random vectors, which are based on ordinal patterns or multivariate generalizations of them. In all cases, we derive the limiting distribution of the corresponding test statistics. In a simulation study, we compare the performance of these statistics with three competitors, namely, classical Pearson's and Spearman's correlation as well as the rank-based Chatterjee's correlation coefficient.