Key Features

  • Econometric Modeler app for time series modeling
  • Univariate ARIMAX/GARCH composite models, including EGARCH and GJR
  • Multivariate simulation and forecasting of VAR, VEC, and cointegrated models
  • State-space models and Kalman filters for parameter estimation
  • Bayesian linear regression models and robust regression estimators
  • Tests for unit root, stationarity, cointegration, and structural change
  • Statistical tests, including likelihood ratio, LM, Wald, Engle’s ARCH, and Ljung-Box Q
  • Diagnostics and utilities, including AIC/BIC model selection and partial-, auto-, and cross-correlations


Econometric Modeler App for Time Series Modeling

The Econometric Modeler app supports time series modeling workflows, including data preprocessing, data visualization, model identification, and parameter estimations. You can select various econometric models, such as ARMA, ARIMA, ARIMAX, GARCH, EGATRCH, GJR, and other regression models, and compare them for the best fit to the data. Moreover, you can export the model to MATLAB® or generate MATLAB code to capture and reuse the tasks performed interactively. You can then use MATLAB to work on other tasks, including simulation and forecasting using the model.

Econometric Modeler app for time series modeling.

Univariate Time Series Modeling

Time series modeling capabilities in Econometrics Toolbox™ are designed to capture characteristics commonly associated with financial and econometric data, including data with fat tails, volatility clustering, and leverage effects.

Supported conditional mean models include:

  • Autoregressive moving average (ARMA)
  • Autoregressive moving average with exogenous inputs (ARMAX)
  • Autoregressive integrated moving average (ARIMA) with exogenous inputs (ARIMAX)
  • Regression with ARIMA error terms

Supported conditional variance models include:

  • Generalized autoregressive conditional hetreroscedasticity (GARCH)
  • Glosten-Jagannathan-Runkle (GJR)
  • Exponential GARCH (EGARCH)

Multiple Time Series Modeling

Econometrics Toolbox supports multivariate time series analysis by extending capabilities for univariate models. Supported models include:

  • Vector autoregressive (VAR)
  • Vector moving average (VMA)
  • Vector autoregressive moving average (VARMA)
  • Vector autoregressive moving average with exogenous inputs (VARMAX)
  • Vector error-correction (VEC)
Develop a small macroeconomic model in the style of Smets and Wouters.

Parameter Estimation

With Econometrics Toolbox, you can perform parameter estimation (also known as model calibration) of univariate ARIMAX/GARCH composite models, multivariate VAR/VARX models, multivariate VEC models, and state-space models.

Estimate model parameters for a GARCH(1,1) model using the garch function to define the model structure and the estimate function to fit the model to data.

Model Identification and Analysis

With Econometrics Toolbox, you can select and test models by specifying a model structure, identifying the model order, estimating parameters, and evaluating residuals. A variety of pre- and post-estimation diagnostics and tests support these analyses, including:

  • Likelihood ratio, Wald, and Lagrange multiplier tests for model specification
  • Akaike and Bayesian information criteria for model order selection
  • Engle’s test for the presence of ARCH/GARCH effects
  • Sample autocorrelation, cross-correlation, and partial autocorrelation functions
  • Ljung-Box Q (portmanteau) test for autocorrelation
  • Dickey-Fuller and Phillips-Perron unit root tests
  • KPSS and Leybourne-McCabe stationarity tests
  • Engle-Granger and Johansen tests for cointegration
  • Variance ratio test for random walks
  • Structural change detection (chowtest, cusumtest, and recreg functions)
  • Robust regression estimators (HAC and FGLS)

Testing of NASDAQ Composite Index price series and returns (left) for autocorrelation and partial autocorrelation. The raw return series does not have any correlation (top right), and correlation is present in the squared return (bottom right).

Bayesian Linear Regression

A standard, frequentist approach to multiple linear regression models generally treats the regression coefficients as fixed but unknown quantities and model disturbances as random variables. A Bayesian approach treats both the coefficients and disturbances as random variables, allowing the coefficients to change as new observations become available. Econometrics Toolbox provides functions for estimating and simulating Bayesian linear regression models, including Bayesian lasso regression. You can create a model object that best describes your prior assumptions on the joint distribution of the regression coefficients and disturbance variance. Then, using the model and data, you can estimate characteristics of the posterior distributions, simulate from the posterior distributions, or forecast responses using the predictive posterior distribution.

Fitting a robust Bayesian linear regression model to data with outliers.

State-Space Modeling

Econometrics Toolbox provides functions for modeling time-invariant or time-varying, linear, Gaussian state-space models. You can create state-space models with known parameter values, perform Monte Carlo simulations, and generate forecasts from the model. For models with unknown parameter values, you can perform parameter estimation from full data sets or from data sets with missing data using the Kalman filter.

Implementing the Diebold Li model, including estimating the parameters of the model with a Kalman filter using the ssm model.

Monte Carlo Simulation

Econometrics Toolbox lets you perform Monte Carlo simulations to generate forecast distributions of both single and multiple time series models, including univariate ARIMAX/GARCH composite models, multivariate VARX models, and state-space models.

Forecast results using Monte Carlo simulation. Time series plots of historical NASDAQ Index value and daily returns (left) are inputs to the garch function, which is used to generate a 30-day ahead forecast distribution with 100 possible paths through Monte Carlo simulation (right).


You can forecast market trends to make budgeting, planning, investing, and policy decisions. Financial Toolbox™ provides the foundation for working with financial time series data; performing regression and parameter estimation with or without missing data; and simulating different scenarios to estimate risk. Econometrics Toolbox extends this foundation with advanced capabilities that account for nonuniform variance across time.

Develop a small macroeconomic model in the style of Smets and Wouters.

Modeling the U.S. economy. Plots show economic indicators for developing a model of U.S real GDP (top left); model calibration results and forecasts for indicators (bottom left); and forecast results for real GDP (right).

Cointegration Modeling

Econometrics Toolbox provides Engle-Granger and Johansen methods for cointegration testing and modeling. The Engel-Granger method tests for individual cointegrating relationships and estimates their parameters. Johansen methods test for multiple cointegrating relationships and estimate parameters in corresponding vector error-correction (VEC) models. Johansen methods also test linear restrictions on error-correction speeds and the space of cointegrating vectors, and they estimate restricted model parameters.

Cointegration testing and modeling on the term structure of interest rates.

Volatility Modeling

Econometrics Toolbox has a complete set of tools for building on time-varying volatility models. The toolbox supports several variants of univariate GARCH models, including standard ARCH/GARCH models, as well as asymmetric EGARCH and GJR models designed to capture leverage effects in asset returns. The toolbox also supports the simulation of stochastic volatility models.

Model the market risk of a hypothetical global equity index portfolio using Monte Carlo simulation.
Estimating market risk using bootstrapping and filtered historical simulation technique. Plots show filtered residuals and volatility of portfolio returns from an AR(1)/EGARCH(1,1) model (top right), the simulated portfolio returns over a one-month horizon (left), and the probability distribution function (bottom right).