# Estimate confidence intervals iteratively for time series dataset for hundreds of products

I am working on a retailer data set where I have weekly data for hundreds of products.

ID    Week1     Week2   Week3   Week4   Week5   Week6   Week7
1000    41      618      720    645      573    503      447
1001    4       62        80     67       94    81       65
1002    2       32        10     23       26    26       31
1003    6       22        13     1        28    19       25
1004    1       9          7     9         6     8        4
1005    0       2          9     3         4    14       19


The objective is to detect outliers. So my I have 2 questions:

1. I am trying to make a confidence interval and if the values exist in that interval then its fine otherwise. I would consider the values a outlier. Is this the correct way of detecting outliers for thousands of products ? Or if not then what could be possible and efficient ways of doing this ?

2. If it is a possible way then my current approach is to approximate my sales data with Poisson distribution explained here. But still I can see that there are sales of products which according to human eye should not be outliers but they are coming as outliers even though I am using 99% confidence interval. The reason is that I am taking mean. Any suggestions how can I improve this ?

• Do you have a good reason to think that time between sales are exponential corresponding to a Poisson process? What constitutes an outlier in this context? – Michael Chernick Apr 13 '17 at 14:22
• Actually I didn't know much about the distribution followed by sales. I was initially using normal distribution but got very bad results. Then the article shared showed that it somehow follows poisson distribution. So my question was exactly this. Am I following the correct approach or what approach should I use to detect outliers ? – muazfaiz Apr 13 '17 at 14:35