Calculating confidence intervals for monthly data


I am currently working with monthly data and I try to calculate confidence intervals for the monthly average. I have data from from 2010 to 2019 and there seems to be some seasonality.

The statement I want to make, is: In december 2020, we expect a value of x which lies with a certainty of 95% between y and z.

For the expected value x, I use the average december values of 2010 to 2019.

For the confidence interval, I am not sure:

My initial guess was to use all months (Jan-Dec) to calculate the standard deviation for the entire dataset to get the confidence intervals (assuming normal distribution of the data). -> One standard deviation for the entire data set.

However, on second thought, I was wondering whether I should use only the data for the month of December to estimate the confidence interval of that month.-> 12 standard deviations, one for each month.

Can somebody help me to figure out which approach is correct?

Thank you very much for your help!


Fortran must die
Before you do anything you have to make the decision of what the distribution is. That was the problem for ESM (time series) models for many years, they had no known distribution.

I am not sure it is reasonable with time series data to assume normality.