I didnt quite understand why If a time series is a random walk, the best forecast of xt that can be made in period t – 1is xt-1. What does it mean?

It means that if there’s no non-zero drift term, E_{t-1}\left(x_t\right) = x_{t-1}. (Note: E_{t-1} means “the expected value at time *t* − 1 of . . .”.

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Let me see if I understood this - so because we don’t have an actual mean reversion, the best way to predict what will be today is based on what happened yesterday? Cuz for example if the data was covariant stationery, then the value of x1 would have been what the mean reversion calculation would have given us, but in this particular instance where everything is random, we don’t have a way to predict anything, so we just manage it with whatever happened yesterday?

In a word: yup.

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