Engle-Granger two-step cointegration test

Step 1 regresses y1 on y2 by OLS; step 2 runs an augmented Dickey-Fuller regression without deterministic terms on the step-1 residuals, choosing the number of augmentation lags in 1..max_lag by AIC on a common sample. The ADF step is computed natively and reproduces urca::ur.df(type = "none", lags = max_lag, selectlags = "AIC") exactly; no external package is used. The statistic is compared with the Engle-Granger (two-variable, constant) critical values -3.90 / -3.34 / -3.04, not the plain Dickey-Fuller ones, and p_value is a coarse bracket from them.

Usage

morie_eg_coint(y1, y2, max_lag = NULL)

Arguments

y1

Numeric, first series.

y2

Numeric, second series.

max_lag

Max ADF augmentation lags. Default floor(12*(n/100)^0.25).

Value

Named list with adf_statistic, p_value, beta, critical_values, n, method.

References

Engle, R. F. and Granger, C. W. J. (1987). Co-integration and error correction. Econometrica 55, 251-276.

Examples

set.seed(1)
morie_eg_coint(y1 = rnorm(100), y2 = rnorm(100))
#> $adf_statistic
#> [1] -6.40701
#> 
#> $p_value
#> [1] 0.005
#> 
#> $beta
#> [1]  0.1088521158 -0.0009323697
#> 
#> $critical_values
#>    1%    5%   10% 
#> -3.90 -3.34 -3.04 
#> 
#> $n
#> [1] 100
#> 
#> $method
#> [1] "Engle-Granger 2-step cointegration (Engle & Granger 1987)"
#>