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I am not aware of any theoretical work giving minimum or optimum train/test set splits for time series, and I doubt that such general guidelines could be given with any theoretical foundations.
Sales data frequently exhibit seasonality. So one reasonable split would be to hold out the entire last year as a test set, which still gives you more than two years ...
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You want to have as many data points in the test set as possible.
You also want to have as many data points in the training set as possible.
Given a constrain on the total amount of data points, increasing the data points in the test set will reduce the number of data points in the training set.
So you will want to look for an optimum.
Example/...
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I agree with the other answers, there are a lot of things that could go into an 'optimal' train test split for time series such as ensuring that you have complete cycles of seasonality. For example, if you have monthly data and only 28 months you are probably better off doing only a 4 month test split for models that require 2 full seasonal cycles and doing ...
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There is no theoretical optimum for this decision and will be highly problem-dependent.
One option to circumvent this decision is to use an online retraining model. At each point in time, train on previously observed data and test on the next point.
This is illustrated here under the section 'Walk Forward Validation'.
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What can I conclude if model A is better than model B regarding MAE, but model B is better than model B regarding RMSE?
It does not make sense to compare the same predictions from different models using different accuracy metrics, because different metrics elicit different functionals from the (frequently only implicit) predictive distribution:
If you want ...
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I'm not aware of any general framework for comparing the sensitivity to outliers as this usually depends on under/overfitting. I would say that ARIMA will typically not perform well at forecasting values outside of the previously observed range. See a blog post here for some comments on that topic.
The other part of your question relates to metrics that will ...
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However, I thought that the way to find the p was to count the number of times lines crossed the dotted blue line in PACF?
This is wrong.
The following table summarizes the relevant properties of the (theoretical) acfs and pacfs of the ARMA models:
Note that in practice, "zero after lag..." means that the autocorrelations / partial ...
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Hi ColorStatistics: This isn't a mathematical proof but you can use the lag operator as if it was a number. (this is proven in functional analysis and there's a proof if ot somewhere on the net that I'll look for after I write this).
So, suppose you had $\frac{1}{1 - \rho}$ and $\rho$ was less than 1.0.
Then, using the formula for infinite geometric series, ...
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The xreg parameter in forecast::auto.arima is where external regressors and its forecasts are specified (also in TSA::arimax). I never used the pair transfer & xtransf it but seems to be used when the external regressors (covariates) are lagged. For more detail check the online books from the authors: Forecasting: Principles and Practice (3rd edition) or ...
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I would second the recommendation for Hyndman-Athanasopoulos and note that there is a third edition (comment by Mehmet linked to second edition).
Time series forecasting is more of an art than a science sometimes but in general the second pipeline you described is better. The #1 pitfall with time series is look-ahead bias. This is where you use information ...
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Short answer: Yes this is possible (but it relies on a few assumptions being valid).
Assumptions
There is a hidden state (which we can't observe) that is influencing the Food Sales. By definition we can't know what this is but we can use our intuition and give it a name like "Ticket Sales Level" for example. Or like you said it could be "Home ...
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