Vector Autoregression Models

Stationary multivariate linear models including exogenous predictor variables

A vector autoregression (VAR) model is a system of simultaneous linear equations that describes the evolution of multiple stationary response series. Equations in the system are functions of constants, time trends, lagged responses, and exogenous predictor variables. For an example of an analysis using VAR modeling tools, see VAR Model Case Study.

To convert your VAR model analysis code from using vgx functions to using the varm object and its object functions, see Convert from vgx Functions to Model Objects.

Apps

Econometric Modeler

Analyze and model econometric time series

Functions

expand all

Create Model

varm Create vector autoregression (VAR) model

Fit Model to Data

`estimate`	Fit vector autoregression (VAR) model to data
`infer`	Infer vector autoregression model (VAR) innovations
`summarize`	Display estimation results of vector autoregression (VAR) model

Impulse Response Functions and Granger Causality

`gctest`	Granger causality and block exogeneity tests for vector autoregression (VAR) models
`irf`	Generate vector autoregression (VAR) model impulse responses
`fevd`	Generate vector autoregression (VAR) model forecast error variance decomposition (FEVD)
`gctest`	Block-wise Granger causality and block exogeneity tests
`armairf`	Generate or plot ARMA model impulse responses
`armafevd`	Generate or plot ARMA model forecast error variance decomposition (FEVD)

Convert Between Models

`arma2ar`	Convert ARMA model to AR model
`arma2ma`	Convert ARMA model to MA model
`vec2var`	Convert VEC model to VAR model
`var2vec`	Convert VAR model to VEC model
`vecm`	Convert vector autoregression (VAR) model to vector error-correction (VEC) model

Generate Monte Carlo Simulations

`simulate`	Monte Carlo simulation of vector autoregression (VAR) model
`filter`	Filter disturbances through vector autoregression (VAR) model

Generate Minimum Mean Square Error Forecasts

forecast Forecast vector autoregression (VAR) model responses

Topics

Interactive

Analyze Time Series Data Using Econometric Modeler
Interactively visualize and analyze univariate or multivariate time series data.
Specifying Multivariate Lag Operator Polynomials and Coefficient Constraints Interactively
Specify multivariate lag operator polynomial terms for time series model estimation using Econometric Modeler.
Estimate Vector Autoregression Model Using Econometric Modeler
Interactively fit several multivariate vector autoregression (VAR) models to data. Then, select an estimated model and export it to the command line for further analysis.

Create Model

Create and Adjust VAR Model Using Shorthand Syntax
This example shows how to create a three-dimensional VAR(4) model with unknown parameters using varm and the shorthand syntax.
Create and Adjust VAR Model Using Longhand Syntax
This example shows how to create a three-dimensional VAR(4) model with unknown parameters using varm and the longhand syntax.
Vector Autoregression (VAR) Model Creation
Represent a vector autoregression (VAR) model using a varm object.
Vector Autoregression (VAR) Models
A vector autoregression (VAR) model is a multivariate time series model containing a system of n equations of n distinct, stationary response variables as linear functions of lagged responses and other terms.
Convert from vgx Functions to Model Objects
Convert common tasks that use the vgx functions to the newer functionality.

Fit Model to Data

Format Multivariate Time Series Data
Prepare your data for a multivariate time series analysis.
VAR Model Estimation Overview
Decide on a set of VAR candidates to models, fit each model to the data, choose the model with the best fit, and then determine whether the AR polynomial of the estimated model is stable.
Fit VAR Model to Simulated Data
Simulate data from a known VAR model, then fit a VAR model to the simulated data.
Fit VAR Model of CPI and Unemployment Rate
Estimate a VAR model composed of the consumer price index and unemployment rate.
Implement Seemingly Unrelated Regression
Include exogenous predictors in a VAR model to estimate a regression component along with all other parameters.
Estimate Capital Asset Pricing Model Using SUR
Implement the capital asset pricing model (CAPM) using the Econometrics Toolbox™ VAR model framework.
VAR Model Case Study
Analyze a VAR model.

Impulse Response Functions and Granger Causality

Generate VAR Model Impulse Responses
Generate impulse responses of an interest rate shock on real GDP.
Compare Generalized and Orthogonalized Impulse Response Functions
Demonstrate differences between orthogonal and generalized impulse response functions.

Convert Between Models

Convert VARMA Model to VAR Model
Create a VARMA model, and then convert it to a pure VAR model.

Generate Simulations or Impulse Responses

VAR Model Forecasting, Simulation, and Analysis
Use models to extrapolate the behavior of time series.
Simulate VAR Model Conditional Responses
Forecast CPI growth rates given known values of the unemployment rate using Monte Carlo simulation.
Simulate Responses Using filter
Reproduce the results of simulate using filter.
Simulate Responses of Estimated VARX Model
Estimate a multivariate time series model that contains lagged endogenous and exogenous variables and simulate responses.
Forecast VAR Model Using Monte Carlo Simulation
Generate forecasts from a VAR model using Monte Carlo simulation.

Generate Minimum Mean Square Error Forecasts

Forecast VAR Model
Generate forecasts with error estimates.
Forecast VAR Model Using Monte Carlo Simulation
Generate forecasts from a VAR model using Monte Carlo simulation.
Forecast VAR Model Conditional Responses
Forecast responses given contemporaneous information about other response values in the forecast horizon.
Incorporate Macroeconomic Scenario Projections in Loan Portfolio ECL Calculations
Generate macroeconomic scenarios and perform expected credit loss (ECL) calculations for a portfolio of loans.