9

You have fallen victim to the renewal paradox, a.k.a. inspection paradox, a.k.a. length-biased sampling. $F_{\Delta}$ is the distribution of service time for the kth customer, but it is NOT the distribution of service time for the customer being served at a preselected time $T$. The very manner of selecting the customer based on observing at a preselected ...


8

For time series, it is better to think about the $\alpha_t$ terms (supposed to be an independent mean zero series) as innovations, not errors. They are not modeling errors of measurements, but the really new information that arrives in the series, not predictable from the history of the series. So a pure AR series depends on former values, while a pure MA ...


6

If the 1200 products are closely related, so that trend (if any) and noise are likely to be correlated across products, a single model might make sense. If they are loosely related (so that they might share a common trend but separate noise processes), you might consider fitting a single trend model (linear regression on time?), "detrending" the data, then ...


4

Note: This answer is intended to show what I have learned from the valuable answer provided by @Mark L.Stone. His post answered my question of why the simulation is biased. Hence, this post provides only additional insight. I chose to post it as an answer and not an edit due to the original question already being lengthy. What has been learned comes from ...


4

This problem is a multivariate (simply when you have more than one time-dependent variables) time series for which you can use Vector Auto Regression (VAR) technique among some others. Explanation and Python implementation of this technique has been discussed in details in here. This technique is also considered the dependencies between various time-...


4

Kjetil's answer is very good, and the distinction between errors and innovations are important to understand. But there are also applications where measurement issues do result in MA-type errors. For example, statistical time series are often collected from a rotating sample panel. In something like an employment survey, households might be selected for the ...


4

I have never encountered a problem like this in literature, but here is one possible way of formulating the problem as a MIP. Notation: $n$: length of the number series $l$: desired length of the subsequence $q_i$: number at position $i$ in the original number series ($i \in I = \{1,\ldots,n\}$) $r_j$: number at position $j$ in the subsequence ($j \in J = \{...


3

The demand of 1200 product will often be related. There might be common events (Christmas, some large accident, ...) that influence all or many of the demands, substitution effects, ... or there may be relations imposed by the cost function (inventory control ...) These can be tackled by some common model, and this is often hierarchical forecasting. There ...


Only top voted, non community-wiki answers of a minimum length are eligible