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Decomposition
Decomposition is a technique used to break down time series data into its fundamental components—trends, seasonal, cyclic, and remainder—making it easier to analyze the underlying patterns and interpret data.
Decomposing a time series data set into long-term trends, seasonal patterns, and the remainder using the Singular Spectrum Analysis algorithm implemented via the trenddecomp function. (See MATLAB code.)
Model Selection and Fitting
Model selection finds the most suitable model to capture the underlying data patterns based on characteristics such as seasonality, trend, and stationarity. Model fitting focuses on training the selected model to minimize the difference between observed data and predictions, ensuring it generalizes well to new data.
Model Prediction and Forecasting
In model prediction and forecasting, the model trained in the previous step is applied to new data to generate future data points based on historical patterns.
Model Evaluation
Model evaluation involves assessing how well a model performs and the accuracy of its predictions. It comprises of three key components:
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Performance metrics: Metrics such as root mean squared error (RMSE) calculate the differences between predicted and actual values, providing a measure of the accuracy of a model.
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Validation techniques: Cross-validation, backtesting, and other techniques assess the reliability of a model by evaluating its performance in making predictions on new data sets.
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Interpretability methods: Techniques such as local interpretable model-agnostic explanations (LIME) and Shapley additive explanations (SHAP) help with understanding model predictions, making the model’s decisions more transparent.
 Visualizing the distribution of RMSE values for new data to identify anomalous sequences. (See MATLAB code.) |
 Visualizing the distribution of RMSE values for new data to identify anomalous sequences. (See MATLAB code.) |
Common Approaches to Time Series Modeling
Three common approaches to modeling time series data are traditional forecasting models, machine learning models, and deep learning models.
Traditional Forecasting Models
Traditional forecasting models use statistical techniques to identify and model underlying data patterns and trends.
The auto regressive integrated moving average (ARIMA) statistical model predicts future values by analyzing historical data. It captures trends and seasonality, making it applicable for both stationary and nonstationary data sets and suitable for short- to medium-term forecasting, such as stock prices and sales.
The exponential smoothing model applies exponentially decreasing weights to past observations, prioritizing more recent data. This method effectively smooths short-term fluctuations while capturing underlying trends and patterns in time series data. It is particularly useful for data with trends or seasonality.
Machine Learning Models
Machine learning models can capture the complex patterns in data that traditional models might miss. Random forest models build multiple decision trees and combine their outputs to improve prediction accuracy in time series analysis. They handle large, high-dimensional data sets and are robust to overfitting. By using past data as predictors, they capture nonlinear relationships and interactions, making them well-suited for modeling irregular patterns. Support vector machines (SVMs) are supervised learning models used for classification and regression. In time series analysis, they can model nonlinear relationships and handle high-dimensional data, especially with small, complex data sets. For example, SVMs can forecast energy demand by capturing nonlinear interactions between historical consumption, weather, and economic indicators. 
Plot showing classification of ECG signals using signal processing, wavelet-based feature extraction, and a support vector machine (SVM) classifier to distinguish between arrhythmia (ARR), congestive heart failure (CHF), and normal sinus rhythm (NSR). (See MATLAB code.)
Deep Learning Models
Deep learning enhances time series analysis by automatically learning patterns and dependencies directly from data. These models capture both short-term fluctuations and long-term trends, making them ideal for forecasting and anomaly detection
Long short-term memory (LSTM) models are a specialized type of recurrent neural network (RNN) designed to overcome the limitations of traditional RNNs by using memory cells and gating mechanisms. This design enables them to capture long-term dependencies effectively, making LSTMs particularly useful for time series analysis tasks such as forecasting and sequence prediction.
Using a simple long short-term memory (LSTM) network for closed-loop forecasting to predict time series data. (See MATLAB code.)
Convolutional neural networks (CNNs) are used in time series analysis as they can automatically extract features from data using convolutional layers. They identify local patterns and hierarchies, making them effective for identifying short-term dependencies for tasks such as multivariate time series classification.
Types of Time Series Analysis
Time series analyses can be classified into categories that describe, explain, forecast, and optimize data trends and patterns effectively:
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Descriptive analysis summarizes the key features of a data set. It helps in understanding the underlying patterns, trends, and seasonal variations in the data.
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Explanatory analysis aims to understand the relationships and causal effects within the data. It seeks to explain why certain patterns or trends occur by examining the underlying factors and correlations.
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Predictive analysis uses historical data, statistical models, and machine learning algorithms to predict future trends and patterns.
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Prescriptive analysis provides recommendations and actions based on predictive insights. It suggests optimal decisions by evaluating different scenarios and their potential outcomes.
Challenges in Time Series Analysis
Certain types of obstacles are typical of time series analysis. During data acquisition, it’s common for sensors or instruments to record data at inconsistent intervals, a problem for many time series models designed to handle monotonically increasing data. Preparing the data may include handling missing data, outliers, noise, and other irregularities as well as resampling the data to create uniform intervals. Exploratory data analysis techniques discussed above can help in mitigating these issues. Additionally, the inherent seasonality and cyclical patterns in time series data can complicate the process of choosing and fitting models. A solid understanding of the data set and applicable modeling options is a great starting point. The outlined modeling approaches, along with cross-validation and other established model verification techniques, will be helpful in these cases.
Why Time Series Analysis Is Important
Time series analysis can be used to model and predict future trends in various domains, such as stock prices, weather conditions, sales, and demand forecasting. This approach enhances the accuracy of planning and supports strategic decision-making by anticipating upcoming developments. Examples of applications that benefit from time series analysis include:
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Economic and financial analysis: Understand economic indicators and financial markets, providing insights for risk management and strategic planning. |
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Environmental monitoring: Perform continuous environmental monitoring and assess climate risks, which helps in understanding long-term trends and risks. |
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Predictive maintenance: Anticipate equipment failures and optimize maintenance schedules, reducing downtime and operational costs. |
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Signal processing: Interpret signals from IoT devices, sensors, and health systems to enhance performance, detect anomalies, and improve reliability. |
Examples of Time Series Analysis
Time series analysis involves techniques for understanding and forecasting data that evolves over time. The examples below illustrate various applications, highlighting unique methods and tools for extracting meaningful insights from complex data sets.
Time Series Analysis with MATLAB
MATLAB® enables engineers to perform time series analysis in applications such as signal processing, control systems, and predictive maintenance.
Prepare Data for Time Series Analysis with Timetables
If you plan to use time-based operations, either before or after preprocessing tasks such as handling missing values and managing outliers, you need to convert the data into a format suitable for time series analysis. The timetable function is designed for timestamped data, associating a time with each row and storing column-oriented variables with the same number of rows. It simplifies time series analysis by providing time-specific functions for aligning, combining, and calculating data, as well as features such as synchronization and resampling.
MATLAB provides specialized toolboxes to help with your complete workflows depending on your specific application area.
Common Time Series Analysis Applications and Next Steps
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Comparative forecasting analysis for predator-prey populations using ARMA, Polynomial AR, Gaussian process (GP), and grey-box models. (
Comparison of instantaneous frequency in normal and atrial fibrillation (AFib) ECG signals. (
