I have reduced my original forecasting problem (Short context : I need to forecast hotel bookings and checkins for the next 3 months. I already have a reasonable forecast for bookings and need to derive the checkin forecast from those bookings. These checkins will happen x days from the day of booking )to the following problem :
I look at 'days to checkin' as my target variable and look at the past distribution of bookings by 'days to checkin' .
I intend to estimate this curve (using KDE) and then and use this distribution to get checkins that wil be made +0 day, +1 day ... +x days from booking date (essentially being able to split my bookings forecast to checkin forecast in the future). However I have a couple of questions :
This distribution will be different depending on which day the booking is made. e.g. bookings made in the summer will probably be last minute and hence checkin will be close to the creation date. I should thus estimate this curve for every day of year . However I have 5 years of history , which means 5 curves as my sample data for the KDE to forecast for every single date in the future . Which one should I use , is there a way to combine the 5 - or have a weighted distribution , giving curves from recent year more weight ?
I also need to factor in any recent change in behavior of the booker (which might not be day of year related).e.g. this year bookers are probably largely booking close to the checkin. So I need to factor in this YoY change in distribution as well. How do I factor this in my estimation of the curve? If I take the curve only from the recent past dates then I am not capturing the day of year peculiarity properly. Should I then combine curves from past years (for same day of year that I am forecasting for) as well as recent data (which is naturally not the same day of year as I am forecasting for ) to get both - the impact that the day of year has on the distribution as well as the recent booker behavior has? If there are other alternatives , I 'd be very happy to learn about them. Thanks !
