People count regression analysis

Question

I have data of number of customers entering a business and number of customers leaving a business every 15 minutes. I need to predict the number of people that will be entering and leaving the business on the next 15 and 30 minutes. I can also save old data for 2-3 weeks.

I want a simple model with a high success rate. I read about linear regression and also read that this might not be the best model cause of negative values and Poisson regression might suit better.

I would be happy to read recommendations regarding my situation.

Answer 1

You probably have seasonality, or more precisely multiple-seasonalities, since you may have intra-daily patterns, and these may differ by the day of week.

In addition, your data are count-data. Unless you have large numbers (rule of thumb: more than 30 in each 15 minute bucket), you should address this and not use a normal distribution approximation.

I would recommend a Poisson regression with predictors accounting for the seasonalities, e.g., using harmonics or bump functions. Two weeks of historical data is very little to capture seasonalities, though, especially differing patterns by day of week. Try to get more data.

Be sure to use a good accuracy measure for evaluating your forecasts, e.g., the rmse. If you use the mae, your forecasts may be biased, or you may "find" that a flat zero forecast is "best":

• Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)?
• Why does minimizing the MAE lead to forecasting the median and not the mean?

Alternatively, and even better, use proper scoring-rules to assess your forecasts. I have written a little paper (Kolassa, 2016, IJF) on this that you may find interesting.