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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.

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.

Learn how to analyze time series 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 polynomial AR and ARMA models for time series data at the command line and in the app.

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 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.