# Forecasting final sales at end of a period, with similar historical data

I've been working on a forecast that I could use some help on. I saw some similar questions posted before but they seemed too detailed to be helpful in my case.

Question

What is the best way to forecast the final sales numbers over a period given I know the cumulative sales up to a certain day? The products I'm working with are on sale for a total of 30 days and if I'm on day X out of 30 I want to be able to forecast the final sales numbers using the sales figures I already have from day 0 to day X.

Historical data

I have a bunch of historical time series sales data of other similar products sold in the past, which were all on sale for 30 days as well. They all follow very similar growth trends (see below), although some will end up selling more or less due to popularity of the product & growth of the business. I would expect any future product I'm forecasting for to follow these same trends, although they may end up selling more due to growth in the business.

Initial thoughts

I've thought about using very simple ratios to do the forecasting (e.g. on average across all the past products, the final sales numbers on day 30 are 3x the sales we see by day 15, so if I'm on day 15 just multiple the numbers I see by 3 to get an estimate of final). I also thought about just creating a simple linear regression for each day out of the 30. But there must be a more predictive way to model something like this.

I'm struggling to figure out where to start doing some digging into this, so would appreciate any help or ideas about what sort of models I should be looking into for the type of problem/data I have.

Thanks!

• That makes for a good approach. – Michael Chernick Mar 7 '17 at 21:08
• The issue I ran into using the ratio or linear regression is that it wasn't very accurate especially if I'm on an early day like day 4 out of 30. Because it takes a small number (let's say 2000 units) and end up simply multiplying that by something in the range of 20x to get to the final number. So if that ratio is off by a tiny bit the final prediction will vary greatly. Maybe this is just an unavoidable issue in tackling a problem like this, but is there type of model that if I'm on day 4, I can use not just the sales up to day 4 as input, but also the day 1-3 sales to help better forecast? – StSh Mar 8 '17 at 15:10