Estimate a VAR model

Searches through the vector of lag orders to find the best VAR model which has lowest AIC, AICc or BIC value. It is implemented using OLS per equation.

VAR(formula, ic = c("aicc", "aic", "bic"), ...)

Arguments

formula

Model specification (see "Specials" section).

ic

The information criterion used in selecting the model.

...

Further arguments for arima

Value

A model specification.

Details

Exogenous regressors and common_xregs can be specified in the model formula.

Specials

pdq

The AR special is used to specify the lag order for the auto-regression.

AR(p = 0:5)

p	The order of the auto-regressive (AR) terms. If multiple values are provided, the one which minimises ic will be chosen.

xreg

Exogenous regressors can be included in an VAR model without explicitly using the xreg() special. Common exogenous regressor specials as specified in common_xregs can also be used. These regressors are handled using stats::model.frame(), and so interactions and other functionality behaves similarly to stats::lm().

The inclusion of a constant in the model follows the similar rules to stats::lm(), where including 1 will add a constant and 0 or -1 will remove the constant. If left out, the inclusion of a constant will be determined by minimising ic.

xreg(...)

...	Bare expressions for the exogenous regressors (such as log(x))

See also

Forecasting: Principles and Practices, Vector autoregressions (section 11.2)

Examples

lung_deaths <- cbind(mdeaths, fdeaths) %>%
  as_tsibble(pivot_longer = FALSE)

fit <- lung_deaths %>%
  model(VAR(vars(mdeaths, fdeaths) ~ AR(3)))

report(fit)
#> Series: mdeaths, fdeaths 
#> Model: VAR(3) w/ mean 
#> 
#> Coefficients for mdeaths:
#>       lag(mdeaths,1)  lag(fdeaths,1)  lag(mdeaths,2)  lag(fdeaths,2)
#>               0.6675          0.8074          0.3677         -1.4540
#> s.e.          0.3550          0.8347          0.3525          0.8088
#>       lag(mdeaths,3)  lag(fdeaths,3)  constant
#>               0.2606         -1.1214  538.7817
#> s.e.          0.3424          0.8143  137.1047
#> 
#> Coefficients for fdeaths:
#>       lag(mdeaths,1)  lag(fdeaths,1)  lag(mdeaths,2)  lag(fdeaths,2)
#>               0.2138          0.4563          0.0937         -0.3984
#> s.e.          0.1460          0.3434          0.1450          0.3328
#>       lag(mdeaths,3)  lag(fdeaths,3)  constant
#>               0.0250          -0.315  202.0027
#> s.e.          0.1409           0.335   56.4065
#> 
#> Residual covariance matrix:
#>          mdeaths  fdeaths
#> mdeaths 58985.95 22747.94
#> fdeaths 22747.94  9983.95
#> 
#> log likelihood = -812.35
#> AIC = 1660.69	AICc = 1674.37	BIC = 1700.9

fit %>%
  forecast() %>%
  autoplot(lung_deaths)