# Time Series Analysis

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.

## Functions

## Topics

### 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.