# I sense a pattern in this (seasonal) data; would using an X-11-ARIMA forecast method be appropriate?

TL;DR: based on the chart below, would forecasting via X-11-ARIMA be appropriate?

I'm hoping this question (and any subsequent answers) could provide valuable insight into any other analyst considering using time-series forecasting in their work.

Long version:

I have data regarding the units of my company's product vs. when each product was sold. It's fair to say that the sales in my company are cyclical, which is why I'm considering using an X-11-ARIMA model.

Is this an appropriate instance to use an X-11-ARIMA model? My understanding is that the X-11 takes seasons "into consideration," but does that mean that I'll end up further from the true forecast if the model removes the effect of seasonality?

Here is the chart I have:

Some clarifications:

1. The dates are not spaced out precisely equally. I could try to fix this, though, using two methods: (i) eliminating all weekend dates (which I'll end up doing anyway- sales on weekends won't be considered) and then indexing each business day to a "Day_n" value, or (ii) keeping all dates, and simply averaging the sales counts for any day that's missing (which I'm not crazy about doing).

2. By looking at the chart, one could find little spikes/outliers that happen on a reasonably consistent basis. These are "end of the month" values and I'm likely to use them in a different chart altogether, as usually a bulk of sales happen on the last day of the month.

3. The data shown in my plot spans the time from January 1st, 2014, through April 30th, 2017. Is 3+ years too much data for projecting values into one month from now?

• p.s.- if this question is better suited for the "Data Science" StackOverflow, I'd be happy to migrate it there- but I noticed that on Stats.SE, there were tags for forecasting and ARIMA, so I thought I'd post it here. – daOnlyBG May 23 '17 at 20:28

Haha, "too much" data? Have you ever heard anyone complain about having too much data?

In principle, yes, you could use X-11-ARIMA to model and forecast this. Note that using the correct term ("X-11-ARIMA", not "ARIMA X-11") will make finding literature easier. And the current version is already X-13-ARIMA-SEATS.

However, I don't think either of these are really useful. You have : intra-year (obvious in your plot), intra-month (the end-of-month spikes you mention) and possibly also intra-week. X-13-ARIMA-SEATS doesn't model multiple seasonalities. I'd much rather recommend a model that explicitly does this, like , which is available in the forecast package in R. Plus, ARIMA models don't really play well with daily data, since you need to look at a lot of lags.

Keep the weekend dates. Set them to NA if there were really no "true" sales on those days, because your store or whatever was closed. The TBATS model should be able to deal with this.

And no, three years of data is certainly not too much to forecast a month out. Especially since you seem to have a trend, which your model might only pick up, given all the seasonalities involved, if you have enough data.

• Thanks for the detailed and insightful response- I'll get to checking out the tbats method promptly. – daOnlyBG May 23 '17 at 21:16
• The bit about tbats is correct, but to add some detail about X-11: this is a non-parametric algorithm for estimating/adjusting (single) seasonality. In particular, it does not define any dynamics for the seasonality, and so cannot forecast it. The newer algorithm X-12-ARIMA involves first forecasting with a simple regression with (seasonal) ARIMA errors model, and then applying X-11, but X-11 has nothing to do with the forecast. – Chris Haug May 23 '17 at 23:23
• @StephanKolassa If you'd like to answer my follow up question (and you know, earn points and help out a novice like myself) I have one here: stats.stackexchange.com/q/283072/67220 – daOnlyBG Jun 1 '17 at 21:20