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I understand that you have weekly product sales over 2 years with up to 30 categorical grouping variables, and you want to predict future sales using a mixed effects model. You can try to use a mixed effects model for prediction/forecasting, although I personally would advise caution. You would include the weekly sales as the outcome/response, and any ...


2

Without values for X1 and X2 (the predictors), you cannot compute predicted values for gross sales using the linear model. As far as the training/test set, this procedure is used more for assessing model fit and predictive power and will not help you in this situation. You still need known values for your predictors. If you have the means to estimate your ...


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For getting (4), first substitute (2), then (1): $$x_t=Fx_{t-1}+g(y_t-\hat y_{t|t-1})=Fx_{t-1}+gy_t-g(w'x_{t-1})=(F-gw')x_{t-1}+gy_t$$ For (5): $$\begin{align}x_t&=Dx_{t-1}+gy_t\\&=D(Dx_{t-2}+gy_{t-1})+gy_t\\&=D^2x_{t-2}+(Dgy_{t-1}+gy_t)\\&=D^2(Dx_{t-3}+gy_{t-2})+(Dgy_{t-1}+gy_t)\\&=D^3x_{t-3}+(D^2gy_{t-2}+Dgy_{t-1}+gy_t)\\&=D^3x_{t-...


1

I'm not sure what you mean by "fixed accuracy" in this context. A fixed accuracy would imply that since the accuracy is always the same (and known after the first few forecasting) we can adjust for the accuracy rate to recover the original value of the time series and we end up with a perfect forecast instead. I assume what you really want is to simulate ...


1

Similarities between countries would be based upon examination of models thus build the models first. Trend analysis is at best a vague concept . Trends can be deterministic or stochastic (as part of an arima model). Either trend detection needs to be concerned with level shifts ( which are not trends ) . see ML preprocess to achieve stationarity and ...


1

First off, yes, doing a rolling weekly forecast and identifying VAR or ARIMA orders on a yearly basis only is certainly an admissible approach. You can fix orders and parameters for all time, or fix orders on a yearly basis and refit the parameters weekly, or change both of them every week, etc. These are all admissible as long as you base the choice of ...


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Note that different accuracy measures (such as the MAPE or the RMSE) are minimized in expectation by different functionals of the unknown future distribution. See Kolassa (2020, International Journal of Forecasting) for an explanation. The MAPE in particular rewards a biased forecast: What are the shortcomings of the Mean Absolute Percentage Error (MAPE)? ...


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Take a look at https://autobox.com/pdfs/regvsbox-old.pdf to get some idea about how to do regression with time series data . Ordinary regression procedures requires independent ( i.e. non-time series ) data. In terms of predicting the predictors use arima and MAKE SURE THAT THE UNCERTAINTY IN THE PREDICTORS IS incorporated into the uncertainty of Y .


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Since my similar question was flagged as duplicate (good debate in the comments!), I came across Simon Kuttruf's explanation on Medium: for integer orders of differencing only a (small) finite set of past values is reflected in the resulting differenced series: the preceding value in first order differencing, two preceding values for second order ...


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