If my daily default rate is distributed as a normal I can say that my annual default rate is distributed as a normal? A study of daily default rates allows me to conclude that they are distributed as a normal one. Previously, I had to eliminate some of the effects of stationarity.
I have following two questions:
How can it be justified that if the daily default rate is normal, then the annual default rate will also follow a Normal distribution? or this assumption is not possible at all?
Eliminating the stationarity effect implies the normal distribution assumption is not right?
Add:My daily default rate for a 3 year sample is normal, regardless of the summer months and weekends. My problem is that I do not know if it is possible to increase the temporality of the variable rate of default and assume that it is normal, because it is another variable.   
 A: Sum of two normally distributed independent random variables is always normally distributed. I suggest you simulate some data and see for yourself. So if your daily values are normally distributed yearly values will be as well.
EDIT:
Let's use simulation to see this. We used two extremely separated normal distributions to prove the point:

a<-rnorm(n,0,1)
b<-rnorm(n,6,0.5)
hist(a+b)

When n tends to infinity, a+b tends to normality.
A: It depends. For example Let's suppose you collect data on Monday and you run the descriptive stats for that day and found out the skewness and kurtosis. From that you arrived at a conclusion that data for Monday is normal. 
Now on Tuesday you again collected data found out the skewness,kurtosis and concluded that data for Tuesday is normal. 
Similarly you collected data for all seven days of a week and after collecting data for all seven days you again ran a test.To your surprise it was not normal
ALERT:The daily normal distribution is local whereas week distribution is a superposition of them.
In simpler words Mean,St.Dev on Monday can be 50 and 2,whereas on Tuesday it can be 100,2. Even if you superpose these two days data it is still not normal.
