Standard post-estimation tests should be used to check that the underlying assumptions are appropriate for all types of macro models. The set of appropriate tests should be based on best practices in the relevant field / literature. The model development documentation should clearly indicate (i) the chosen test for each property, (ii) the nature of the H0 hypothesis, (iii) the cut-off values chosen upfront to determine the rejection or non-rejection.
5.8.2
In the context of time series regression, regression coefficients should be significant and residuals should be tested for autocorrelation and normality. The table below indicates properties that should be tested, at a minimum. Other tests may be considered, if necessary.
Table 9: Typical statistical tests for models based on time series regression
Property to be tested
Description of the property to be rejected
Suggested test (others may exist)
Stationarity
Absence of stationarity in each time series
Augmented Dickey-Fuller (ADF)
Co-integration
Absence of stationarity in a linear combination of the dependent variable and each independent variable
Engle-granger two-step method
Multicolinearity
High correlation between the independent variables
Variance Inflation Factor
Coefficient significance
The coefficients are not statistically significantly different from zero
Coefficient p-value on a t-distribution
Autocorrelation
High correlation between the error terms of the model
Ljung-Box test
Heteroscedasticity
Absence of relationship between independent variables and residuals