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From what I understand, SARIMAX models exogenous variables are not lagged, i.e. to estimate $y_t$ value, you need $x_t$ exogenous variables, not $x_{t-i}$.

I could do a workaround by creating lagged variables to trick the model. Is this a correct approach or are there other better models for these kind of situations?

BTW: I'm trying to see if I can improve fruits prices (high seasonality) predictions by adding local weather and foreign exchange data.

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    $\begingroup$ Nothing says that your $X_t$ series cannot be lagged. So, yeah, the trick would work. $\endgroup$
    – ColorStatistics
    Commented Nov 11, 2021 at 22:28

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Here's gedankenexperiment for you: what if you created a new variable $z_t\equiv x_{t-1}$, and used it in your regressions instead of $x_t$? Surely SARIMAX would work with $z_t$ variable. There's your answer

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  • $\begingroup$ Sure, that is what i meant with: "I could do a workaround by creating lagged variables to trick the model". But I wanted to know if for these situations other TS models are more suitable. $\endgroup$
    – Oliver Mohr Bonometti
    Commented Nov 12, 2021 at 11:27

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