Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral analysis, we propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches, including the extraction of nonstationary signals with discontinuities in their behavior. The method introduced is equivalent to a {\em nonstationary Fourier mode decomposition} (NFMD) for nonstationary and nonlinear temporal signals, allowing for the accurate identification of instantaneous frequencies and their amplitudes. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy to quantify the time-dependent evolution of charging dynamics at the nanoscale.
COVID-19 has been a public health emergency of international concern since early 2020. Reliable forecasting is critical to diminish the impact of this disease. To date, a large number of different forecasting models have been proposed, mainly including statistical models, compartmental models, and deep learning models. However, due to various uncertain factors across different regions such as economics and government policy, no forecasting model appears to be the best for all scenarios. In this paper, we perform quantitative analysis of COVID-19 forecasting of confirmed cases and deaths across different regions in the United States with different forecasting horizons, and evaluate the relative impacts of the following three dimensions on the predictive performance (improvement and variation) through different evaluation metrics: model selection, hyperparameter tuning, and the length of time series required for training. We find that if a dimension brings about higher performance gains, if not well-tuned, it may also lead to harsher performance penalties. Furthermore, model selection is the dominant factor in determining the predictive performance. It is responsible for both the largest improvement and the largest variation in performance in all prediction tasks across different regions. While practitioners may perform more complicated time series analysis in practice, they should be able to achieve reasonable results if they have adequate insight into key decisions like model selection.
Time series observations can be seen as realizations of an underlying dynamical system governed by rules that we typically do not know. For time series learning tasks, we need to understand that we fit our model on available data, which is a unique realized history. Training on a single realization often induces severe overfitting lacking generalization. To address this issue, we introduce a general recursive framework for time series augmentation, which we call Recursive Interpolation Method, denoted as RIM. New samples are generated using a recursive interpolation function of all previous values in such a way that the enhanced samples preserve the original inherent time series dynamics. We perform theoretical analysis to characterize the proposed RIM and to guarantee its test performance. We apply RIM to diverse real world time series cases to achieve strong performance over non-augmented data on regression, classification, and reinforcement learning tasks.
In this paper, in following of the first part (which ADF tests using ACI evaluation) has conducted, Time Series (TSs) are analyzed using decomposition analysis. In fact, TSs are composed of four components including trend (long term behavior or progression of series), cyclic component (non-periodic fluctuation behavior which are usually long term), seasonal component (periodic fluctuations due to seasonal variations like temperature, weather condition and etc.) and error term. For our case of cyber-attack detection, in this paper, two common ways of TS decomposition are investigated. The first method is additive decomposition and the second is multiplicative method to decompose a TS into its components. After decomposition, the error term is tested using Durbin-Watson and Breusch-Godfrey test to see whether the error follows any predictable pattern, it can be concluded that there is a chance of cyber-attack to the system.
Hyper-parameters of time series models play an important role in time series analysis. Slight differences in hyper-parameters might lead to very different forecast results for a given model, and therefore, selecting good hyper-parameter values is indispensable. Most of the existing generic hyper-parameter tuning methods, such as Grid Search, Random Search, Bayesian Optimal Search, are based on one key component - search, and thus they are computationally expensive and cannot be applied to fast and scalable time-series hyper-parameter tuning (HPT). We propose a self-supervised learning framework for HPT (SSL-HPT), which uses time series features as inputs and produces optimal hyper-parameters. SSL-HPT algorithm is 6-20x faster at getting hyper-parameters compared to other search based algorithms while producing comparable accurate forecasting results in various applications.
In time series data analysis, detecting change points on a real-time basis (online) is of great interest in many areas, such as finance, environmental monitoring, and medicine. One promising means to achieve this is the Bayesian online change point detection (BOCPD) algorithm, which has been successfully adopted in particular cases in which the time series of interest has a fixed baseline. However, we have found that the algorithm struggles when the baseline irreversibly shifts from its initial state. This is because with the original BOCPD algorithm, the sensitivity with which a change point can be detected is degraded if the data points are fluctuating at locations relatively far from the original baseline. In this paper, we not only extend the original BOCPD algorithm to be applicable to a time series whose baseline is constantly shifting toward unknown values but also visualize why the proposed extension works. To demonstrate the efficacy of the proposed algorithm compared to the original one, we examine these algorithms on two real-world data sets and six synthetic data sets.
Accurately estimating a battery's state of health (SOH) helps prevent battery-powered applications from failing unexpectedly. With the superiority of reducing the data requirement of model training for new batteries, transfer learning (TL) emerges as a promising machine learning approach that applies knowledge learned from a source battery, which has a large amount of data. However, the determination of whether the source battery model is reasonable and which part of information can be transferred for SOH estimation are rarely discussed, despite these being critical components of a successful TL. To address these challenges, this paper proposes an interpretable TL-based SOH estimation method by exploiting the temporal dynamic to assist transfer learning, which consists of three parts. First, with the help of dynamic time warping, the temporal data from the discharge time series are synchronized, yielding the warping path of the cycle-synchronized time series responsible for capacity degradation over cycles. Second, the canonical variates retrieved from the spatial path of the cycle-synchronized time series are used for distribution similarity analysis between the source and target batteries. Third, when the distribution similarity is within the predefined threshold, a comprehensive target SOH estimation model is constructed by transferring the common temporal dynamics from the source SOH estimation model and compensating the errors with a residual model from the target battery. Through a widely-used open-source benchmark dataset, the estimation error of the proposed method evaluated by the root mean squared error is as low as 0.0034 resulting in a 77% accuracy improvement compared with existing methods.
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal physiological data presents many analytic challenges: the data is noisy, contains many missing values, and each series has a different length. Most methods proposed for time series analysis and classification do not handle datasets with these characteristics nor do they offer interpretability and explainability, a critical requirement in the health domain. We propose an unsupervised method for learning representations of time series based on common patterns identified within them. The patterns are, interpretable, variable in length, and extracted using Byte Pair Encoding compression technique. In this way the method can capture both long-term and short-term dependencies present in the data. We show that this method applies to both univariate and multivariate time series and beats state-of-the-art approaches on a real world dataset collected from wearable sensors.
This paper surveys state-of-the-art methods and models dedicated to time series analysis and modeling, with the final aim of prediction. This review aims to offer a structured and comprehensive view of the full process flow, and encompasses time series decomposition, stationary tests, modeling and forecasting. Besides, to meet didactic purposes, a unified presentation has been adopted throughout this survey, to present decomposition frameworks on the one hand and linear and nonlinear time series models on the other hand. First, we decrypt the relationships between stationarity and linearity, and further examine the main classes of methods used to test for weak stationarity. Next, the main frameworks for time series decomposition are presented in a unified way: depending on the time series, a more or less complex decomposition scheme seeks to obtain nonstationary effects (the deterministic components) and a remaining stochastic component. An appropriate modeling of the latter is a critical step to guarantee prediction accuracy. We then present three popular linear models, together with two more flexible variants of the latter. A step further in model complexity, and still in a unified way, we present five major nonlinear models used for time series. Amongst nonlinear models, artificial neural networks hold a place apart as deep learning has recently gained considerable attention. A whole section is therefore dedicated to time series forecasting relying on deep learning approaches. A final section provides a list of R and Python implementations for the methods, models and tests presented throughout this review. In this document, our intention is to bring sufficient in-depth knowledge, while covering a broad range of models and forecasting methods: this compilation spans from well-established conventional approaches to more recent adaptations of deep learning to time series forecasting.