Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, exponential smoothing fails dramatically in the presence of outliers, large amounts of noise, or when the underlying time series changes. We propose a flexible model for time series analysis, using exponential smoothing cells for overlapping time windows. The approach can detect and remove outliers, denoise data, fill in missing observations, and provide meaningful forecasts in challenging situations. In contrast to classic exponential smoothing, which solves a nonconvex optimization problem over the smoothing parameters and initial state, the proposed approach requires solving a single structured convex optimization problem. Recent developments in efficient convex optimization of large-scale dynamic models make the approach tractable. We illustrate new capabilities using synthetic examples, and then use the approach to analyze and forecast noisy real-world time series. Code for the approach and experiments is publicly available.
This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower-dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous-density hidden Markov model with a Gaussian mixture model expressed in the reduced-dimensional space. The analysis can be incorporated into a neural network, which is named a time-series discriminant component network (TSDCN), so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time-based learning algorithm with the Lagrange multiplier method. The TSDCN is considered to enable high-accuracy classification of high-dimensional time-series patterns and to reduce the computation time taken for network training. The validity of the TSDCN is demonstrated for high-dimensional artificial data and EEG signals in the experiments conducted during the study.
This paper analyses how Time Series Analysis techniques can be applied to capture movement of an exchange traded index in a stock market. Specifically, Seasonal Auto Regressive Integrated Moving Average (SARIMA) class of models is applied to capture the movement of Nifty 50 index which is one of the most actively exchange traded contracts globally [1]. A total of 729 model parameter combinations were evaluated and the most appropriate selected for making the final forecast based on AIC criteria [8]. NIFTY 50 can be used for a variety of purposes such as benchmarking fund portfolios, launching of index funds, exchange traded funds (ETFs) and structured products. The index tracks the behaviour of a portfolio of blue chip companies, the largest and most liquid Indian securities and can be regarded as a true reflection of the Indian stock market [2].
Optical satellite sensors cannot see the Earth's surface through clouds. Despite the periodic revisit cycle, image sequences acquired by Earth observation satellites are therefore irregularly sampled in time. State-of-the-art methods for crop classification (and other time series analysis tasks) rely on techniques that implicitly assume regular temporal spacing between observations, such as recurrent neural networks (RNNs). We propose to use neural ordinary differential equations (NODEs) in combination with RNNs to classify crop types in irregularly spaced image sequences. The resulting ODE-RNN models consist of two steps: an update step, where a recurrent unit assimilates new input data into the model's hidden state; and a prediction step, in which NODE propagates the hidden state until the next observation arrives. The prediction step is based on a continuous representation of the latent dynamics, which has several advantages. At the conceptual level, it is a more natural way to describe the mechanisms that govern the phenological cycle. From a practical point of view, it makes it possible to sample the system state at arbitrary points in time, such that one can integrate observations whenever they are available, and extrapolate beyond the last observation. Our experiments show that ODE-RNN indeed improves classification accuracy over common baselines such as LSTM, GRU, and temporal convolution. The gains are most prominent in the challenging scenario where only few observations are available (i.e., frequent cloud cover). Moreover, we show that the ability to extrapolate translates to better classification performance early in the season, which is important for forecasting.
We introduce a new machine learning based technique to detect exoplanets using the transit method. Machine learning and deep learning techniques have proven to be broadly applicable in various scientific research areas. We aim to exploit some of these methods to improve the conventional algorithm based approach used in astrophysics today to detect exoplanets. We used the popular time-series analysis library 'TSFresh' to extract features from lightcurves. For each lightcurve, we extracted 789 features. These features capture information about the characteristics of a lightcurve. We used these features later to train a tree-based classifier using a popular machine learning tool 'lightgbm'. This was tested on simulated data which proved it to be more effective than conventional box least squares fitting (BLS). It produced comparable results to the existing state-of-art models while being much more computationally efficient and without needing folded and secondary views of the lightcurves. On Kepler data, the method is able to predict a planet with an AUC of 0.948 which means that, 94.8% of the time a planet signal is ranked higher than a non-planet signal and Recall of 0.96 meaning, 96% of real planets are classified as planets. With the Nasa's Transiting Exoplanet Survey Satellite (TESS), a reliable classification system is much needed as we are receiving over a million lightcurves per month. However, classification is harder as lightcurves are shorter. Our method is able to classify lightcurves with an accuracy of 98% and is able to identify planets with a Recall of 0.82.
Deep learning performs remarkably well on many time series analysis tasks recently. The superior performance of deep neural networks relies heavily on a large number of training data to avoid overfitting. However, the labeled data of many real-world time series applications may be limited such as classification in medical time series and anomaly detection in AIOps. As an effective way to enhance the size and quality of the training data, data augmentation is crucial to the successful application of deep learning models on time series data. In this paper, we systematically review different data augmentation methods for time series. We propose a taxonomy for the reviewed methods, and then provide a structured review for these methods by highlighting their strengths and limitations. We also empirically compare different data augmentation methods for different tasks including time series anomaly detection, classification and forecasting. Finally, we discuss and highlight future research directions, including data augmentation in time-frequency domain, augmentation combination, and data augmentation and weighting for imbalanced class.
Analyzing better time series with limited human effort is of interest to academia and industry. Driven by business scenarios, we organized the first Automated Time Series Regression challenge (AutoSeries) for the WSDM Cup 2020. We present its design, analysis, and post-hoc experiments. The code submission requirement precluded participants from any manual intervention, testing automated machine learning capabilities of solutions, across many datasets, under hardware and time limitations. We prepared 10 datasets from diverse application domains (sales, power consumption, air quality, traffic, and parking), featuring missing data, mixed continuous and categorical variables, and various sampling rates. Each dataset was split into a training and a test sequence (which was streamed, allowing models to continuously adapt). The setting of time series regression, differs from classical forecasting in that covariates at the present time are known. Great strides were made by participants to tackle this AutoSeries problem, as demonstrated by the jump in performance from the sample submission, and post-hoc comparisons with AutoGluon. Simple yet effective methods were used, based on feature engineering, LightGBM, and random search hyper-parameter tuning, addressing all aspects of the challenge. Our post-hoc analyses revealed that providing additional time did not yield significant improvements. The winners' code was open-sourced https://www.4paradigm.com/competition/autoseries2020.
Two common problems in time series analysis are the decomposition of the data stream into disjoint segments, each of which is in some sense 'homogeneous' - a problem that is also referred to as Change Point Detection (CPD) - and the grouping of similar nonadjacent segments, or Time Series Segment Clustering (TSSC). Building upon recent theoretical advances characterizing the limiting distribution free behavior of the Wasserstein two-sample test, we propose a novel algorithm for unsupervised, distribution-free CPD, which is amenable to both offline and online settings. We also introduce a method to mitigate false positives in CPD, and address TSSC by using the Wasserstein distance between the detected segments to build an affinity matrix to which we apply spectral clustering. Results on both synthetic and real data sets show the benefits of the approach.
We develop a new method to detect anomalies within time series, which is essential in many application domains, reaching from self-driving cars, finance, and marketing to medical diagnosis and epidemiology. The method is based on self-supervised deep learning that has played a key role in facilitating deep anomaly detection on images, where powerful image transformations are available. However, such transformations are widely unavailable for time series. Addressing this, we develop Local Neural Transformations(LNT), a method learning local transformations of time series from data. The method produces an anomaly score for each time step and thus can be used to detect anomalies within time series. We prove in a theoretical analysis that our novel training objective is more suitable for transformation learning than previous deep Anomaly detection(AD) methods. Our experiments demonstrate that LNT can find anomalies in speech segments from the LibriSpeech data set and better detect interruptions to cyber-physical systems than previous work. Visualization of the learned transformations gives insight into the type of transformations that LNT learns.
This paper proposes piece-wise matching layer as a novel layer in representation learning methods for electrocardiogram (ECG) classification. Despite the remarkable performance of representation learning methods in the analysis of time series, there are still several challenges associated with these methods ranging from the complex structures of methods, the lack of generality of solutions, the need for expert knowledge, and large-scale training datasets. We introduce the piece-wise matching layer that works based on two levels to address some of the aforementioned challenges. At the first level, a set of morphological, statistical, and frequency features and comparative forms of them are computed based on each periodic part and its neighbors. At the second level, these features are modified by predefined transformation functions based on a receptive field scenario. Several scenarios of offline processing, incremental processing, fixed sliding receptive field, and event-based triggering receptive field can be implemented based on the choice of length and mechanism of indicating the receptive field. We propose dynamic time wrapping as a mechanism that indicates a receptive field based on event triggering tactics. To evaluate the performance of this method in time series analysis, we applied the proposed layer in two publicly available datasets of PhysioNet competitions in 2015 and 2017 where the input data is ECG signal. We compared the performance of our method against a variety of known tuned methods from expert knowledge, machine learning, deep learning methods, and the combination of them. The proposed approach improves the state of the art in two known completions 2015 and 2017 around 4% and 7% correspondingly while it does not rely on in advance knowledge of the classes or the possible places of arrhythmia.