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I have been asked to develop control charts for my company - or some other means of quickly identifying when ticket sales are "out of control" and not just a random blip. The data we are looking at are seasonal with a positive trend (sales revenue).

It has been suggested that I use an exponentially-weighted moving average (EWMA) chart but my (limited) understanding is that these are only appropriate for use on data with a constant mean.

My gut instinct is to apply an ARIMA model and to assess whether observations fall within confidence limits derived from that... but I'm not confident enough to be sure this is the right approach.

My question therefore is:

  1. Is it appropriate to use control charts to monitor revenue sales
  2. What would be the best model to use

Please bear in mind that it needs to be administered by somebody with undergraduate maths, and explained to true lay people.

Scortchi - Reinstate Monica
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Hal Baggot
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    You're right that you need to use time-series methods to take auto-correlation into account. As well as ARIMA you might want to consider the Holt-Winters algorithm - it's simple & robust. – Scortchi - Reinstate Monica Nov 25 '13 at 16:35
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    you nneed to identify a robust arima model that encompasses any anomalies or level shifts local time trends and/or seasonal pulses that are identifiable. This signal/model can then be useful to detect unusual activity. Stay very clear of any presumed model form but allow the data to speak to the identification of the model form. AUTOBOX (something I have helped develp) would be a good piece of software that would allow you to cut your teeth on this problem and emulate the results. They have 30 day fre trial version that might help you. – IrishStat Nov 25 '13 at 22:00

1 Answers1

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Should is such a dangerous word. I can tell you how I would approach the problem, but like all answers the mileage is likely to vary.

I'm looking at weather, not sales, but it is highly seasonal. enter image description here

What I did was use a smoothing spline (in MatLab). Here is a link to some more descriptive material. hyperlink (see slides 25-32)

Basic approach is:

  • Sweep appropriate range of smoothing parameter
  • At each point measure AIC
  • Find the local best AIC (non-endpoint, look for actual interior local minimum).

There is some good backing for using this, its applicability to exponential family of distributions that envelopes Gaussian/Normal, Binomial, Lognormal, etcetera, but this is not the place. It is derived from the Kullback-Leibler divergence which comes from Shannon's Information Theory.

So you find the historic mean (thick red line), then you subtract it and use good control material on the re-centered data (right side panels).

Here is the canon for SPC, btw:

If that doesn't work for you, and you want to get deeper, consider this:

Best of luck.

EngrStudent
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