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I've read a portion of "Time Series Analysis and Forecasting" by Brockwell and Davis and I feel like I've gained some theoretical background and intuition.

I'm planning on applying for positions where there's supposed to be some Time Series modelling interview problem. Unfortunately I feel like my theoretical experience with the subject would not be enough for the matter.

I'm looking for some resources with example problems with Time Series modelling and predictions, preferably with example solutions in R.

Thanks in advance! Apologies if this has been asked before.

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You asked 'I am looking for some resources with example problems with Time Series modelling and predictions"

I answer .. look no fUrther that SE... don't limit your scholarly pursuit to a language or a free set of often inadequate tools but pursue "the city on the top of the hill" .

Look for creative/trend-setting examples . There are many on this site and I have been involved in a few that you might find illuminating . Pursue https://stats.stackexchange.com/users/3382/irishstat for a few interesting and educational discussions that I have been involved in.

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