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I'm trying to build a model to predict reservations up to 15 days in advance.

So, if I want to predict how many reservations there will be tomorrow, I use historical data of how many total reservations there were on two days prior since when using the model to forecast for tomorrow, today won't be finished... Does that make sense?

I think it is an OK and unbiased model, however, it does not use all of the available data, namely, how many reservations for tomorrow have been made today. So, if I want my model to be more 'realtime' and account for current reervations as well, how do I do that? Do I look at reservation data over the course of the day, and just set up a proportion or something? For example, if I use my model at 13:00, find that I have 20 additional reservations, and I know that historically 40% of additional reservations are made by 13:00, do I just take 20+ 20*(60/40) = 50. So now I should 'expect' 50 more on top of what yesterdays total told me? This is all I can think of.

Edit:

" For example if it takes 1 hour to complete three innings at a baseball game you can rest assured that the next 6 innings is going to take a lot longer than 2 hours to complete." Well, what if you knew that historically the first 3 innings accounted for 25% of the time? Sticking with the ballgame example, that's good illustration of my problem which I think you understand Dave, but I'm not sure I've made it clear for the others...

If you wanted to predict the duration of a ball game, you might have some formula based on the current teams, the pitchers, etc.. But, consider a game where you predicted a 2.5 hour game, and you're in the 4th inning, and it's already taken 3 hours, now what do you do?

Dave, I've tried different techniques, involving the seasonal arima methods, etc. I'm not familiar with 'level shifts', although I've seen you mention them in many of your posts. I will do some further web surfing to understand this concept. I'd be very interested in a chat session. Please let me know when you're available, I'm +11 hours EST.

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    $\begingroup$ Sorry, I'm a bit confused. When you say "reservation" you mean something like a restaurant reservation? It sounds like you're predicting when they will OCCUR, as opposed to when they are MADE, right? So reservations made today for tomorrow would enter into tomorrow's forecast along with a prediction based on reservations that occurred yesterday and today? Is this in an AR(2) sort of way? $\endgroup$
    – Wayne
    Sep 22, 2011 at 21:59
  • $\begingroup$ Wayne, sorry I didn't answer this sooner. You are right, I'm not clear in my description. I want to predict how many total paying customers I will have on a particular day. (Call that variable: PAID.) I'm currently doing that as a function of how many reservations there are already for that particular day. (It's not deterministic as there are walk in customers, and cancellations.) (edit -- i hit the enter key or something) When I build my model, to predict tomorrows PAID, I use how many total reservations there are 2 days in advance. $\endgroup$
    – Adam
    Sep 23, 2011 at 4:05
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    $\begingroup$ @Adam Please consider editing your original question instead of posting your updates as answers. Also, your last question about Vista issues with Chrome/IE is better suited for our Meta site, but check whether you don't find anything related in older threads--here or on StackOverflow Meta--before asking. $\endgroup$
    – chl
    Sep 23, 2011 at 8:23
  • $\begingroup$ @adam I am in the EST time zone and am available for the next 7-8 hours . – IrishStat 14 mins ago $\endgroup$
    – IrishStat
    Sep 23, 2011 at 14:08
  • $\begingroup$ @adam If you want you can contact me at dave@autobox.com and then we can arrange for a chat room $\endgroup$
    – IrishStat
    Sep 23, 2011 at 16:03

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Ratio estimates just don't work. For example if it takes 1 hour to complete three innings at a baseball game you can rest assured that the next 6 innings is going to take a lot longer than 2 hours to complete.In order to predict tomorrow given partial information for today and full information for the past NOB days, I suggest the following approach which we implemented for Proctor & Gamble as they had been unable to detect the economic downturn in a timely fashion. Their problem was if we have say 15 days in the current month history and 16 days remain with say 1 holiday and 2 Saturdays ( for example ) we want to compute the probability of achieving total sales of X. We implemented a daily forecasting model that included day-of-the-week;week-of-the-year;month-of-the year effects AND the lead/contemporaneous and lag effects around known events AND any Level Shifts/Time Trends that proved to be statistically significant. The model/approach also included an ARIMA component and validation tests/remedies for constancy of the parameters and variance over time. Furthermore Pulses and Seasonal Pulses ( i.e. significant changes in the day-of-the-week component ) were also entertained in order to develop a robust data generating function (DGF). What you want to do is to also include an hour-of-the-day forecasting model which would in conjunction with the daily forecast/model produce an estimate of the current day's total and the total for the next 15 days. It is imperative that the hourly forecasts and the daily forecasts not only reconcile but be fully integrated where expectations regarding daily totals actually drive the hourly estimates.

If you wished to post your hourly data going back at least 2-3 years , I would be glad to share the results with the list. If for some reason you don't wish to share your data with the list then perhaps we can do a chat room session.

We have also had some experience with a major hotel chain to improve their 60 day forecast for occupancy.

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