I've the following regression problem. I'm forecasting a random variable $X$ for every day of a month, represented as $X_{ij}$ where $i$ is the day of the month and $j$ is the month number. I care if the total at the end of the month is within what was committed (say $C_{0j}$). I get the $X_{ij}$ values in sequence, i.e. every day ${X_{0j}, X_{1j}...}$. I also have historical values of $X_{ij}$ and $C_{0j}$ to train on. I needed help in understanding if I've set up my data right for training a machine learned model. My current set up is to use 31 models, each for a day into the month and to use MSE as loss function. For e.g. model $M_3$ would train on data
$X_{train} = {X_{1j}, X_{2j}, X_{3j}}$ and $Y_{train} = (\sum_{4}^{30}X_{ij}) - C_{0j}$ $\forall j$ using MSE as loss function.
Likewise for $M_4$ the set up would look like
$X_{train} = {X_{1j}, X_{2j}, X_{3j}, X_{4j}}$ and $Y_{train} = (\sum_{5}^{30}X_{ij}) - C_{0j}$ $\forall j$ using MSE as loss function, and so on...
Could someone help validate if this set up is right? I'm unsure of the right loss function. For e.g. why not RMSE or MAE ?