I would like to predict the average number of days in a year for which two conditions are true:
- daily average temperature is below zero celsius
- the day was preceded by at least four days with daily average temperature below zero celsius
I've historical daily average temperature data for the location available for about 10 years. My initial approach was to use the one sided Chebyshev inequality which can be used to approximate a probability if the distribution is not known. However in this application I am interested in the probability of a special condition, can I use the Chebyshev inequality for a dummy time series as well? I.e.: 1 if condition is fullfilled, otherwise 0, --> the dataset would therefore look something like 0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,1,1,1,etc.
How would you approach a problem like that from a different angle, the data clearly has seasonality, is there any distribution which I could use to have a better estimate than Chebyshev?