# Super Exogeneity (Parameter Invariance) Test

`super.exogeneity.Rd`

This function tests for super exogeneity (parameter invariance) of the model. Parameter invariance is a key component of Super Exogeneity, which
was first introduced in Engle, Hendry, and Richard (1983; Econometrica). This test runs an indicator saturation model for each independent variable
that is present in the `initial.model`

object - these individual models are called the marginal models.
If any outliers or step-shifts are detected using the `isat`

function from the `gets`

package in the marginal models,
then these indicators are added to the initial model, called the conditional model.
Any pre-existing indicators from the initial model are removed, as otherwise the power of the test would be reduced.
The conditional model is then used to run a linear regression
and to obtain an F-Stat statistic to determine whether the shocks detected in the marginal models affect the conditional model.

## Arguments

- initial.model
An object of class

`isat`

(i.e. from the`gets`

package) that contains the initial model- saturation.tpval
The target p-value of the saturation methods (e.g. SIS and IIS, see the 'isat' function in the 'gets' package). Default is 0.01.

- quiet
Logical. Should messages about the forecast procedure be suppressed?

## References

Engle, R. F., Hendry, D. F., & Richard, J. F. (1983). Exogeneity. Econometrica: Journal of the Econometric Society, 73-85.

Engle, R. F., & Hendry, D. F. (1993). Testing superexogeneity and invariance in regression models. Journal of Econometrics, 56(1-2), 119-139.

Hendry, D. F., & Santos, C., 'An Automatic Test of Super Exogeneity', in Bollerslev, T., Russell, J., & Watson, M. (Eds.). (2010). Volatility and time series econometrics: essays in honor of Robert Engle. OUP oxford.

Castle, J. L., Hendry, D. F., & Martinez, A. B. (2017). Evaluating forecasts, narratives and policy using a test of invariance. Econometrics, 5(3), 39.

## Examples

```
#load Hoover and Perez (1999) data:
data(hpdata, package = "gets")
##run isat with step impulse saturation on two lags and a constant 1 percent significance level:
is.model <- gets::isat(
y = hpdata$GCQ,
mxreg = hpdata[,"GYDQ", drop = FALSE],
ar = 1:2,
sis = TRUE,
t.pval = 0.01
)
#>
#> NOTE: quantmod::as.zoo.data.frame() is deprecated
#> Use as.zoo(x, order.by = as.Date(rownames(x))) instead.
#> This note is printed once. To see it for every call, set
#> options(quantmod.deprecate.as.zoo.data.frame = TRUE)
#> Error in charToDate(x): character string is not in a standard unambiguous format
super.exogeneity(is.model)
#> Error in eval(expr, envir, enclos): object 'is.model' not found
```