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.

Functions

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Estimation

`ar`	Estimate parameters when identifying AR model or ARI model for scalar time series
`arOptions`	Option set for `ar`
`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`	Estimate ODE parameters of linear grey-box model
`nlgreyest`	Estimate nonlinear grey-box model parameters

Models

`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

Response Analysis

`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 identified model K-step-ahead output

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.

Featured Examples

Modeling Current Signal from an Energizing Transformer

The modeling of a measured signal.

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Spectrum Estimation Using Complex Data - Marple's Test Case

Perform spectral estimation on time series data. We use Marple's test case (The complex data in L. Marple: S.L. Marple, Jr, Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ 1987.)

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Forecast Multivariate Time Series

Perform multivariate time series forecasting of data measured from predator and prey populations in a prey crowding scenario. The predator-prey population-change dynamics are modeled using linear and nonlinear time series models. Forecasting performance of these models is compared.

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Classical Pendulum: Some Algorithm-Related Issues

How the estimation algorithm choices may impact the results for a nonlinear grey box model estimation.

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