This note shows, however, that the disturbances of the log-transformed model are heteroskedastic
and the mean varies with time.
Hansen (1992) shows that OLS estimates of heteroskedastic
cointegration models are consistent, and he concludes that the dominant property (requirement) of the cointegrating residuals is mean stationarity.
The White procedure corrects for problems arising from the variance of the error term being heteroskedastic
as well as correlated with the regressors.
Switching the positions of [Delta]ln[m.sub.t] and [Delta]ln[P.sub.t] and re-estimating yields a statistically unstable, autocorrelated, and heteroskedastic
Model 1-8: Box-Cox heteroskedastic
model with interaction terms.
consistent standard errors are reported in parentheses.
The error term for each cross section is assumed to have the characteristics normally assumed with OLS with the exception that the error terms, while being mutually exclusive, are heteroskedastic
. Across time, the errors are assumed to be autoregressive for a given state.
The error term in these estimates was heteroskedastic
with its variance proportional to the square of the price of the vehicle.
In other words, the first entry of w must be heteroskedastic
in order for g to be difference stationary as is assumed.
We note finally that the estimable form given by (3), which utilizes total sales per state as the dependent variable, is almost certain to exhibit heteroskedastic
errors since sales can vary by orders of magnitude between large and small states.
Engle |1982~ introduced the concept of ARCH (autoregressive conditional heteroskedastic
) models with a specific application to inflation expectations.
When the scatter of the errors is different, varying depending on the value of one or more of the independent variables, the error terms are heteroskedastic
. Namely the distribution law of errors remains normal with a mathematical expectation equal to zero, but the errors of the model are a function of the values of the independent variables: [epsilon] ~ N(0,f(X)), where f(X) is a function that describes the change in the variance of errors as a function of the values of the independent variables.