Econometrics Toolbox

Key Features

  • Univariate ARMAX/GARCH composite models, including EGARCH, GJR, and other variants
  • Multivariate simulation and forecasting of VAR, VEC, and cointegrated models
  • State-space models and Kalman filters for parameter estimation
  • Tests for unit root (Dickey-Fuller, Phillips-Perron) and stationarity (Leybourne-McCabe, KPSS)
  • Statistical tests, including likelihood ratio, LM, Wald, Engle’s ARCH, and Ljung-Box Q
  • Cointegration tests, including Engle-Granger and Johansen
  • Diagnostics and utilities, including AIC/BIC model selection and partial-, auto-, and cross-correlations
  • Hodrick-Prescott filter for business-cycle analysis

 

Introduction to Econometrics Toolbox 26:17
In this webinar, we’ll demonstrate selected features of Econometrics Toolbox. Econometrics Toolbox lets you perform Monte Carlo simulation and forecasting with linear and nonlinear stochastic differential equations (SDEs) and build univariate ARMAX/G

Time-Series Modeling

Econometrics Toolbox facilitates the multistep process of identifying and testing univariate and multivariate time-series models for financial and econometric data. The toolbox supports the full model development and analysis workflow:

  • Data analysis and preprocessing
  • Model identification
  • Parameter estimation
  • Simulation
  • Forecasting
econometrics-hodrickprescott
Business Cycle Analysis Using Hodrick-Prescott Filter
Use the Hodrick-Prescott filter to analyze GNP cyclicality.

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)

Introduction to Econometrics Toolbox 6:26
Create a predictive time-series model of a stock index.

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)
econometrics-useconomy
Modeling the United States Economy
Develop a small macroeconomic model in the style of Smets and Wouters.

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
Testing of NASDAQ Composite Index price series and returns for autocorrelation and partial autocorrelation.

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).

State-Space Modeling and Parameter Estimation

Econometrics Toolbox includes functions for creating state-space models and tools for estimating parameters based on these and other model types.

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

Parameter Estimation

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

Interactively developing a GARCH(1,1) model and estimating the model parameters for NASDAQ daily returns in the command window.

Developing a GARCH(1,1) model and estimating the model parameters for NASDAQ daily returns in the command window.

Estimating state-space model parameters using a Kalman filter.
Estimating state-space model parameters using a Kalman filter.

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 ARMAX/GARCH composite models,multivariate VARMAX models, and state-space models.

Forecast results using Monte Carlo simulation with the garchsim function.

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

Forecasting

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.

Modeling the U.S. economy with forecasts for Real GDP.

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).

econometrics-useconomy
Modeling the United States Economy
Develop a small macroeconomic model in the style of Smets and Wouters.

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.

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.

Estimating market risk using bootstrapping and filtered historical simulation technique.
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).
econometrics-marketrisk
Evaluating Market Risk Using Extreme Value Theory and Copulas
Model the market risk of a hypothetical global equity index portfolio using Monte Carlo simulation.

Try Econometrics Toolbox

Get trial software

Concevez et testez des stratégies de trading algorithmique

View webinar