How to approximate MAE of monthly values from MAE of daily values? Suppose I have the Mean Absolute Error (MAE) of daily values for a period of, say, 1 year. Assume the errors are normally distributed.
The value for a month is equal to the sum of the values for each day in that month.
Can I approximate the MAE of what the monthly values would be given the MAE of the daily values?
Based on how we can scale variance to bigger time periods, I believe it may be doable by multiplying the daily MAE by $\sqrt{30}$, assuming 30 days per month. Would this be valid? Why/Why not?

I've assumed that when you say the errors are normally distributed you mean the daily values (and so the monthly values) are normally distributed. I've also assumed that by MAE you mean the mean difference between each value and the mean of the values distribution,(i.e. the mean absolute deviation or MAD), rather than the mean difference between each value and an estimate of the value.
If these assumptions are correct, then your method of estimating the monthly MAE (or MAD) is valid. According to Wolfram MathWorld, the MAD of the normal distribution is $\sqrt{\frac 2 \pi} \sigma$, so as $\sigma_m = \sqrt{30} \sigma_d$ (where $\sigma_d$ and $\sigma_m$ are the standard deviations of your daily and monthly distributions, respectively), $MAD_m$ will also be $\sqrt{30} MAD_d$.
