statsmodels - How exactly BIC in Augmented Dickey–Fuller test work in Python? -

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this question on augmented dickey–fuller test implementation in statsmodels.tsa.stattools python library - adfuller().

in principle, aic , bic supposed compute information criterion set of available models , pick best (the 1 lowest information loss).

but how operate in context of augmented dickey–fuller?

the thing don't get: i've set maxlag=30, bic chose lags=5 informational criterion. i've set maxlag=40 - bic still chooses lags=5 information criterion have changed! why in world information criterion same number of lags differ maxlag changed?

sometimes leads change of choice of model, when bic switches lags=5 lags=4 when maxlag changed 20 30, makes no sense lag=4 available.

when request automatic lag selection in adfulller, function needs compare models given maxlag lags. comparison need use same observations models. because lagged observations enter regressor matrix loose observations initial conditions corresponding largest lag included.

as consequence autolag uses nobs - maxlags observations models. calculating test statistic adfuller itself, don't need model comparison anymore , can use observations available chosen lag, i.e. nobs - best_lag.

more general, how treat initial conditions , different number of initial conditions not clear cut, autocorrelation , partial autocorrelation largely based on using available observations, full mle ar , arma models uses stationary model include initial conditions, while conditional mle or least squares drops them necessary.


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