*! version 1.0.1 16may2026

Title

ralsdiag -- Diagnostics for the RALS family: non-normality, linearity and rho^2

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Overview |
adf |
lm |
lm-breaks |
f-adf |
f-kss |
battery |
coint |
f-adl |
diag

Syntax

ralsdiag varname [if] [in] [, trend maxlags(#)]

Description

ralsdiag reports the three pre-tests that drive the decision tree in
Yilanci & Ozgur (2025, Figure 3):

1. Skewness, kurtosis, Shapiro-Wilk and Jarque-Bera normality tests on
the residuals of an auxiliary ADF regression. Significant non-normality
implies that the RALS w-augmentation will deliver real power gains.

2. A simple cube-extension linearity test in the spirit of Harvey,
Leybourne & Xiao (2008): an F-test for y^3_ in the ADF equation.

3. The RALS variance ratio rho^2 = sigma^2_RALS / sigma^2_ADF,
estimated directly from a once-run pair of regressions. Smaller values mean
more power gain over the OLS test.

Options

trend include a trend in the auxiliary ADF regression.

maxlags(#) number of Dy_ lags in the auxiliary regression (default 8).

Examples

. ralsdiag close, trend

Stored results

r(skewness) sample skewness of residuals

r(kurtosis) sample kurtosis of residuals

r(sw_W), r(sw_p) Shapiro-Wilk statistic & p-value

r(JB), r(JB_p) Jarque-Bera statistic & p-value

r(HLX_F), r(HLX_p) cube-extension linearity test

r(rho2) estimated rho^2

References

Yilanci, V., Ozgur, O. (2025). Testing Real Interest Rate Parity for EU5 Countries. Politicka Ekonomie 73(3): 528-565.

Im, K.S., Schmidt, P. (2008). More efficient estimation under non-normality when higher moments do not depend on the regressors, using residual augmented least squares. Journal of Econometrics 144(1): 219-233.

See also

Back to overview: rals

Unit-root tests: ralsadf, ralslm, ralslmb, ralsfadf, ralsfkss

Battery (run-all): ralsbattery

Cointegration tests: ralscoint, ralsfadl

Author

Dr Merwan Roudane -- merwanroudane920@gmail.com