# Testing Randomness in day of year values

I have airline booking data (no. of bookings vs day of year).

Day of year is a vector, taking values from 1 to 365, with stepwise increments of 1.

We can have one data-set where booking exists for 300 days; while another data-set where booking exists in only 20 days. Examples:

Sample 1 (1,2,3,4,....100,125,126,127......200,230,231,....364,365) --> 312 values
Sample 2 (10,20,71,72,73,199,200,201,202,280,287,288, 345,346,360) --> 15 values


There are hundreds of such samples. I am trying to find out if there is a way to tell if these sample data-sets are Random or not.

I need to find a way to separate random and non-random data for further computations in the mathematical model I am working on. Any suggestion/ literature reference is most welcome.

Editing to provide clarification


I am working on the estimation module of an airline yield generation, forecast and dynamic pricing prototype.For every booking curve (no. of bookings vs day of year)- corresponding to different origin and destination, fare families, timeslot etc. we use Fast fourier transform to capture dominant frequencies and use those in our day of year seasonality calculations.

The problem is not every booking curve has seasonality. There might be a booking curve with just 10 bookings over the year. So, my task is to isolate such cases in the time domain and not applying FFT or seasonality calculations on those.

My idea was to find out if a particular day of year data has randomness or not. If yes, then there is no seasonality.

I had previously used the seasonal decompose package of Python statsmodel. The issue is that it detects seasonality in every booking curve except for the case where there is a constant no. of bookings every day in the year. So that does not work for me. Seasonal decompose, of course, took both variables (day of year and bookings).

Therefore, I had the idea to test the randomness in day of year (x-axis: time) values only. I am open to any new ideas.

From the comments, there are already a couple of ideas. I would like to know how to test if there is no correlation between the values; or if every day (1-365) is equally likely to occur.

• Random as in coming from a uniform distribution? That is each day is equally likely? – user2974951 Dec 24 '18 at 12:10
• Or random in not having autocorrelation or other structure? Please clarify your question! – kjetil b halvorsen Dec 24 '18 at 14:28
• Provided some clarifications. Please let me know if I could add something further. – rahul Dec 25 '18 at 13:27