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I am trying to build a regression model for two time series x (independent) and y (dependent) to get y=f(x).

I read from other posts saying you have to pre-whitening your time series for both x and y and then make regression on the stationary data (e.g.Forecast time series data with external variables). But there are also people who said it is not necessary. I am very confused because if the trend in y can be explained by the trending in x, why do we still need to do that pre-whitening? And what is exactly the right procedure to do it?

I would really appreciate it if you could give me some guidance on this.

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