R help - Oct 2015 - Time Series Daily Frequency Part of a Year

My data consist of daily sales figures for multiple products but only for a
3 month period each year (Oct., Nov., Dec). The goal is to forecast the
daily sales figures for the following year *by day* (the following Oct.,
Nov., Dec.) So, I'd like to forecast what sales for product X will be on
Nov. 12th of the next year (and each day of those three months), for
example.

I am just conceptually stuck on the fact that the time series is
"yearly"
in one sense but the daily observations only occur for those 3 months. The
rest of the year is not really 0 -- the products are not even for sale the
rest of the year (these are tickets for events). The frequency seems like
it should be 92 days.

Hoping someone can just point me in the right direction conceptually.

Thanks,

Zodran

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I have made no attempt to think deeply about this, but it seems to me 
that the structure of your data does not fit into any "standard" time 
series model.

You would appear to have a number (how many?) of *intrinsically finite* 
time series.  In a sense you have a number of "multivariate" 
observations, where the dimension of your observations is 92.

You may be able to model the covariance structure of your data in some 
time-series-ish way (ARMA, I guess).

Is it reasonable to assume that your observations are iid over years
(i.e. that the mean level or trend is the same from year to year)?

I'm pretty sure that you will need to assume that the covariance 
structure is the same from year to year, in order to get anywhere.

There *may* be material on models for this sort of data somewhere in the 
literature.  Googling "multiple short time series" turned up a number
of
hits, some of which could be useful to you.  If not, then you've got a 
bit of a research project on your hands.

Almost surely you will have to write your own fitting code to fit a 
model to such data.

Good luck!

cheers,

Rolf Turner

-- 
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

On 08/10/15 10:23, zod jones wrote:
> My data consist of daily sales figures for multiple products but only for a
> 3 month period each year (Oct., Nov., Dec). The goal is to forecast the
> daily sales figures for the following year *by day* (the following Oct.,
> Nov., Dec.) So, I'd like to forecast what sales for product X will be
on
> Nov. 12th of the next year (and each day of those three months), for
> example.
>
> I am just conceptually stuck on the fact that the time series is
"yearly"
> in one sense but the daily observations only occur for those 3 months. The
> rest of the year is not really 0 -- the products are not even for sale the
> rest of the year (these are tickets for events). The frequency seems like
> it should be 92 days.
>
> Hoping someone can just point me in the right direction conceptually.

Thanks for the reply. I thought I'd find more on this by searching for
course enrollment forecasting because the events I'm dealing with are
essentially like courses that need to be compared year on year (over many
years). But the info I found relating to models for enrollment were only
aggregated (university enrollment overall and not specific courses only for
one term or semester compared year on year by date, etc.) I think maybe the
"date" part is just throwing me off -- they are really 92 data points
and
not part of normal time series. That is my guess, anyway.

I'll do more research on multiple short time series and see where I get.
Thanks! Zodran

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