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Time Series Analysis

Analyze time series data by identifying linear and nonlinear models such as AR, ARMA, state-space, and grey-box models, performing spectral analysis, and forecasting model outputs

A time series is data that contains one or more measured output channels but no measured input. A time series model, also called a signal model, is a dynamic system that is identified to fit a given signal or time series data. The time series can be multivariate, which leads to multivariate models. You can identify time series models in the System Identification app or at the command line. System Identification Toolbox™ enables you to create and estimate four general types of time series model.

  • Linear parametric models — Estimate parameters in structures such as autoregressive models and state-space models.

  • Frequency-response models — Estimate spectral models using spectral analysis.

  • Nonlinear ARX models — Estimate parameters in the nonlinear ARX structure.

  • Grey-box models — Estimate the coefficients of the ordinary differential or difference equations that represent your system dynamics.

Parametric time series model identification requires uniformly sampled time-domain data, except for the ARX model, which can handle frequency-domain signals. Spectral analysis algorithms support time-domain and frequency-domain data. Your data can have one or more output channels and must have no input channel. For more information on time series models, see What Are Time Series Models?

You can use the identified models to predict model output at the command line, in the app, or in Simulink®. At the command line, you can also forecast model outputs beyond the time range of the measured data.


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arEstimate parameters of AR model or ARI model for scalar time series
arOptionsOption set for ar
arxEstimate parameters of ARX, ARIX, AR, or ARI model
armaxEstimate parameters of ARMAX, ARIMAX, ARMA, or ARIMA model using time-domain data
ivarAR model estimation using instrumental variable method
ssestEstimate state-space model using time-domain or frequency-domain data
n4sidEstimate state-space model using subspace method with time-domain or frequency-domain data
spaEstimate frequency response with fixed frequency resolution using spectral analysis
spafdrEstimate frequency response and spectrum using spectral analysis with frequency-dependent resolution
etfeEstimate empirical transfer functions and periodograms
nlarxEstimate parameters of nonlinear ARX model
greyestLinear grey-box model estimation
nlgreyestEstimate nonlinear grey-box model parameters
idpolyPolynomial model with identifiable parameters
idssState-space model with identifiable parameters
idfrdFrequency response data or model
idnlarxNonlinear ARX model
idgreyLinear ODE (grey-box model) with identifiable parameters
idnlgreyNonlinear grey-box model
spectrumPlot or return output power spectrum of time series model or disturbance spectrum of linear input-output model
forecastForecast identified model output
predictPredict K-step-ahead model output


About Time Series Models

What Are Time Series Models?

A time series model, also called a signal model, is a dynamic system that is identified to fit data that includes only output channels and no input channels.

Analyze Time-Series Models

Learn how to analyze time series models.

Estimate Models

Identify Time Series Models at the Command Line

Simulate a time series and use parametric and nonparametric methods to estimate and compare time-series models.

Estimate AR and ARMA Models

Estimate polynomial AR and ARMA models for time series data at the command line and in the app.

Estimate ARIMA Models

Estimate autoregressive integrated Moving Average (ARIMA) models.

Estimate State-Space Time Series Models

Estimate state-space models for time series data at the command line.

Estimate Time-Series Power Spectra

Estimate power spectra for time series data at the command line and in the app.

Estimate Coefficients of ODEs to Fit Given Solution

Estimate model parameters using linear and nonlinear grey-box modeling.

Forecast Model Output

Forecast Output of Dynamic System

Workflow for forecasting time series data and input-output data using linear and nonlinear models.

Time Series Prediction and Forecasting for Prognosis

Create a time series model and use the model for prediction, forecasting, and state estimation.

Introduction to Forecasting of Dynamic System Response

Understand the concept of forecasting data using linear and nonlinear models.

Featured Examples