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The above is just the standard equation for the ADF test. http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test It looks complicated. You might start by reading about the original, simpler, Dickey Fuller Test, before it became 'Augmented'. Suppose interest rates $y(t)$ are mean reverting: when they are high they tend to come down and when low ...

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With ML, you're looking to identify patterns in your inputs that result in your output(s). Thus you collect all the outputs you are hoping to be able to identify later, and the inputs which correspond to those outputs (i.e just before the output was generated), collect as many as possible of these relationships, stick them into a ML model and hope you've ...

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The answer is at least, in part, definitional. The original definition of the process constrains the model to $0<\alpha<1$ to assure a convex combination of the two terms. It assures that the prediction is between the two values at all times. Software to estimate the solution should be properly constrained so that a result of 1.4 cannot happen. The ...

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There are two other possibilities not mentioned in the above answers. Consider the time series $x_{t+1}=\beta{x}_t+\epsilon_{t+1}$. Assume $t\in\{81,82\}$ are missing. The question is why are they missing. Consider three possible cases. The first is that it is a holiday or a similar day where there was no activity. The second is omission as a recording ...

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There is this very good book on forecasting by Rob Hyndman and George Athanasopoulos. There you find very useful tips and R code. Have a look at the chapter on time series decomposition there you find relevant stuff about seasonal time series.

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