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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

Atime seriesis 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 theSystem Identificationapp 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, seeWhat Are Time Series Models?

You can use the identified models to predict model output at the command line, in the app, or in Simulink®。在命令行上,您还可以预测模型outputs beyond the time range of the measured data.

Functions

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ar Estimate parameters when identifying AR model or ARI model for scalar time series
arOptions Option set forar
arx Estimate parameters of ARX, ARIX, AR, or ARI model
armax Estimate parameters of ARMAX, ARIMAX, ARMA, or ARIMA model using time-domain data
ivar AR model estimation using instrumental variable method
ssest Estimate state-space model using time-domain or frequency-domain data
n4sid Estimate state-space model using subspace method with time-domain or frequency-domain data
spa Estimate frequency response with fixed frequency resolution using spectral analysis
spafdr Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution
etfe Estimate empirical transfer functions and periodograms
nlarx Estimate parameters of nonlinear ARX model
greyest Linear grey-box model estimation
nlgreyest Estimate nonlinear grey-box model parameters
idpoly Polynomial model with identifiable parameters
idss State-space model with identifiable parameters
idfrd Frequency response data or model
idnlarx Nonlinear ARX model
idgrey Linear ODE (grey-box model) with identifiable parameters
idnlgrey Nonlinear grey-box model
spectrum Plot or return output power spectrum of time series model or disturbance spectrum of linear input/output model
forecast Forecast identified model output
predict Predict K-step-ahead model output

Topics

About Time Series Models

Estimate Models

Forecast Model Output