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First of all, unless you're rather confident that the three time series exhibit the exact same patterns/dynamics, then I would advise against training a single model on all 3. You should do separate ones - since there are presumably different patterns to learn. To your main question, though - how to compare prediction errors? Unless there's some larger ...

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The parameters of the ARIMA model are defined as follows: p: The number of lag observations included in the model, also called the lag order. d: The number of times that the raw observations are differenced, also called the degree of differencing. q: The size of the moving average window, also called the order of moving average. How do we decide these ...

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2nd raw moment as sum of variance and mean Any 2nd raw moment can be decomposed into the mean and central 2nd moment. $$E[q^2] = E[q]^2 + E[(q-E[q])^2]$$ When the quantity $q$ is a difference between two quantities, $q = \hat{f}-f$, then you get $$E[(\hat{f}-f)^2] = E[\hat{f}-f]^2 + E[(\hat{f}-f-E[\hat{f}-f])^2]$$ These two terms have a simple meaning in ...

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The biggest difference is that residuals is a term used in statistics and "idiosyncratic errors" isn't. In statistics there is a distinction between error and residuals, where in the model $$y = f(x) + \varepsilon$$ $\varepsilon$ is the error term, while $$r = y - \hat y$$ where $\hat y$ is the fitted value, is the residual. I did a quick ...

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As whuber discusses in his comments, this is simply notation to denote that the empirical loss $L_S(h) = \frac{1}{m} \sum_i 1_{h(x_i) \neq f(x_i)}$ is the same as the expected value of the true loss, that is: $L_S(h) = \mathop{\mathbb{E}}_S[L_{D (\text{uniform over S)}}(h)]$.

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