What is a Time Series?
A time series is a chronologically ordered sequence of values sampled at constant intervals. It encounters challenges such as missing data and outliers. Common strategies involve imputing missing information or omitting entire records. Irregularly collected data, termed unevenly spaced time series or data streams, may necessitate specific modeling considerations.
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Time series data exhibit three components: trend, seasonality, and residuals (irregularities). Trends represent the overall movement, while seasonality captures regular interval variations. Residuals, the remaining values after removing trend and cyclic oscillations, may include outliers. Real-world time series, characterized by a meaningful irregular component and non-stationarity, pose modeling challenges.
Accurate predictions are intricate, prompting classical methods to decompose time series into these components for separate predictions. Data mining-based technologies are particularly useful for understanding the irregular component, which helps with accurate predictions. Time series, graphically represented with time on the x-axis and recorded values on the y-axis, facilitate visual feature detection such as oscillation amplitude, seasons, cycles, and anomalies.
Time series, or sequences of time-ordered data, offer insights into diverse domains such as energy, meteorology, finance, health, traffic, and industry. Time series forecasting, vital for decision-making, predicts future values, impacting strategies such as reducing fossil fuels. It helps assess renewable energy and demand for electricity in the energy sector.
Meteorology benefits from predicting weather parameters. Finance utilizes it for stock market predictions, while health involves disease spread forecasts. Traffic relies on speed and flow predictions, which the industry uses for production and durability forecasts. Deep learning is becoming more and more popular in machine learning, and it is being used for nonlinear relationship-based time series forecasting.
The collection of time-series data involves the systematic arrangement of samples, observations, or features in a sequential order over a specific duration. In numerous real-world scenarios, time-series datasets naturally manifest, with data being recorded at regular intervals. Instances of such datasets encompass stock prices, digitized speech signals, traffic measurements, sensor data reflecting weather patterns, biomedical measurements, and diverse population data recorded over time.
The study of time-series data includes manipulating numerical data for classification, forecasting, and prediction. Statistical approaches employ a variety of models, such as spectral analysis techniques, auto-regressive moving average (ARMA), moving average (MA), autoregressive (AR), and AR Integrated MA (ARIMA).
Deep Learning Techniques for Time Series Forecasting
The evolution of time series forecasting has seen a shift from traditional statistical methods to machine learning techniques and, more recently, deep learning-based solutions. Here, some standard time series forecasting methods are discussed.
Deep Feed Forward Neural Network (DFFNN): The DFFNN, commonly known as a multi-layer perceptron, evolved to address the limitations of single-layer neural networks in learning specific functions. Its architecture encompasses an input layer, an output layer, and diverse hidden layers. Each hidden layer houses a variable number of neurons, determined during configuration.
The connections between neurons in consecutive layers are modeled through weights calculated during network training. These weights minimize a cost function using gradient descent optimization, and the back-propagation algorithm computes the gradient of the cost function. Activation values in each layer are determined by a feed-forward process, employing rectified linear unit functions for most layers and hyperbolic tangent functions for the output layer in time series forecasting.
Recurrent Neural Network (RNN): Time series forecasting, speech recognition, and language translation are among the sequential data processing tasks that RNNs are most suited for. They handle the temporal dependencies that these types of data contain. Typically, RNN kinds like Elman RNN, Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRU) are used since they are specifically made to address certain problems like vanishing gradients in deep networks.
Bidirectional RNN (BRNN): BRNNs tackle problems requiring information from both past and future data sequences for accurate predictions. Unlike unidirectional networks, BRNNs leverage both forward and backward processing to generate predictions, necessitating the entire data sequence for prediction.
Deep Recurrent Neural Network (DRNN): DRNNs, or stacked RNNs, incorporate multiple layers to enhance predictive capabilities. However, their performance may degrade with lengthy input sequences. To address this, attention mechanisms, a significant innovation in deep learning, can be integrated into the model.
Convolutional Neural Networks (CNN): CNNs, widely employed in image processing, consist of convolution, pooling, and fully connected layers. These layers collectively learn features, reduce input size, and perform forecasting. A recent variant, Temporal Convolutional Networks (TCNs), competes with DRNNs in terms of execution time and memory requirements. TCNs utilize dilated convolutions to capture both local and temporal information.
Generative Models: Deep learning research has placed generative models—particularly diffusion models (DMs) and generative adversarial networks (GANs)—at the forefront due to their inventive capacity to produce synthetic images. The capabilities of these models have been expanded to include time series and sequential data.
Applications for GANs and DMs include time series forecasting. GANs comprise a generator and discriminator trained adversarially. GANs in time series forecasting function either for data augmentation or as end-to-end models. In data augmentation, GANs enhance small datasets with synthetic time series, training traditional models such as LSTM on the augmented set.
For end-to-end forecasting, GANs themselves become the forecasting models. Diffusion models, a new generative architecture, excel in various domains. They employ denoising diffusion probabilistic models, score-based generative models, and stochastic differential equations. Recent diffusion-based approaches for short-term time series forecasting, such as TimeGrad and ScoreGrad, showcase the application of these models in capturing underlying data distributions.
Transformers: Transformer models excel in tasks such as natural language processing and computer vision. They are also effective in long-term time series forecasting (LTSF). There are challenges to the prevailing belief in transformer efficacy for LTSF. The baseline model, LTSF-Linear, surprisingly outperforms complex transformer-based models across various benchmarks. The results call into doubt the transformers' temporal modeling capabilities in LTSF and suggest reassessing their applicability for additional time series analysis jobs.
Applications of Time Series Forecasting
The applications of time series forecasting are diverse and impactful. Addressing trends and seasonal patterns in business data is vital for informed decision-making. Time series forecasting is pivotal in estimating future needs, aiding businesses in accurate planning. To underscore the significance of time series prediction, categorize deep-learning research by application domain and prevalent network architectures (LSTM, GRU, BRNN, DFFNN, CNN, and TCN).
Energy and Fuels: The surge in renewable energy usage necessitates precise estimates for enhanced power system planning. Various deep-learning architectures, including LSTM, ENN, GRU, BRNN, and TCN, have proven effective in predicting electricity demand consumption, photo-voltaic energy load, and even soot emission in diesel engines. Hybrid architectures are also employed for applications like forecasting carbon prices and energy consumption.
Image and Video: Extensive research focuses on image and video analysis across diverse domains. Convolution-based networks, particularly CNNs, dominate the literature for forecasting combustion instability, traffic speed, and detecting coronary artery stenosis. TCNs gain prominence for tasks such as estimating density maps from videos or dynamically detecting stress through facial photographs.
Financial: Financial analysis, a longstanding challenge, sees the application of various architectures like CNN, DNN, GRU, and LSTM. Comparative studies analyze the efficacy of these architectures, highlighting the ongoing quest for innovative methodologies to address the complexity of financial problems.
Environmental: Environmental data analysis, a popular research domain, leverages deep-learning techniques for time series forecasting. CNN and LSTM are employed for predicting wind speed and temperature, while TCN and ENN architectures forecast water quality and demand. Deep learning is applied to address diverse environmental challenges, such as carbon dioxide emissions and flood predictions.
Industry: Deep-learning techniques find utility in various industrial tasks, from traffic flow forecasting using TCN and BRNN to LSTM applications in process planning and construction equipment recognition. ENN and GRU networks contribute to forecasting the useful life or degradation of materials.
Health: Although the application of deep-learning architectures in health is widespread, time series prediction in this field faces challenges due to short series and computational costs. Convolution-based architectures, like CNN, are prevalent for tasks such as monitoring sleep stages or forecasting pneumonia incidence rates. LSTM is applied to forecast the status of critical patients.
Miscellaneous: TCN emerges as a versatile architecture for general-purpose time series forecasting. Other architectures, including CNN and RNN, find application in diverse domains such as detecting human activity or anomalies, particularly in cybersecurity.
The volume of generated time series data is experiencing exponential growth daily. Employing time series analysis proves instrumental for businesses, empowering them to enhance decision-making and monitor operations effectively. The literature on time series forecasting explores contemporary deep learning algorithms essential for proficient time series forecasting. It delves into key domains where time series play a pivotal role and is extensively utilized.
References and Further Readings
Torres, J. F., Hadjout, D., Sebaa, A., Martínez-Álvarez, F., and Troncoso, A. (2021). Deep learning for time series forecasting: a survey. Big Data, 9(1), 3-21. DOI: https://doi.org/10.1089/big.2020.0159
Zeng, A., Chen, M., Zhang, L., and Xu, Q. (2023). Are transformers effective for time series forecasting? In Proceedings of the AAAI conference on artificial intelligence (Vol. 37, No. 9, pp. 11121-11128). DOI: https://doi.org/10.1609/aaai.v37i9.26317
Casolaro, A., Capone, V., Iannuzzo, G., and Camastra, F. (2023). Deep Learning for Time Series Forecasting: Advances and Open Problems. Information, 14(11), 598. DOI: https://doi.org/10.3390/info14110598