Define prediction interval for a monthly sales pattern The point of my analysis is to develop an alert system to detect when the sales of the current month are deviating significantly from the monthly forecast and guess whether the month is going to close short/long. My idea was to obtain prediction intervals for the "shape" of the sales curve throughout the month and then compare the current forecast execution rate to those intervals. I've implemented my concept in r with dummy data:
p <- 30 # 30 month days
n <- 12 # 12 month history

data <- matrix(rnorm(p*n, mean = 100, sd = 75), p, n) #dummy data
data <- apply(data, 2, cumsum) #cumulative sales
data <- data %*% diag(1/data[p,]) #cumulative percentage or "execution rate"

mean <- apply(data, 1, mean)
var <- apply(data, 1, var)

sup <- mean + qt(0.975, n-1)*sqrt(var*(1+1/n)) # t-student PI
inf <- mean - qt(0.975, n-1)*sqrt(var*(1+1/n))

matplot(data, type = "l", col = "gray", lty = 1, main="Prediction intervals for monthly sales pattern",
        xlab="day of month", ylab="execution rate") 
lines(mean, col = "red")
lines(sup, col = "blue") 
lines(inf, col = "blue")
abline(0, 1/31)
legend(1, 1, legend=c("mean", "95% PI", "data", "linear"),
       col=c("red", "blue", "gray", "black"), lty=1, cex=0.8)


Is this correct from the statistical point of view?
 A: No. You can't use a CI to detect when normal observations have deviated significantly from the expected trend. This is because the width of the CI approaches 0 as you get more data. Even a prediction interval won't quite solve the problem, since the chances of a false positive declaration of "significant deviation" increase every time you inspect the curve.
The Y-axis doesn't make sense. Is 100% the number of contracts which execute each month? Why would you standardize to that value? If you have to know how many contracts you get in a month to calculate the percentage, then it defeats the purpose of monitoring the ongoing progress.
The tool you are probably looking for is a control chart.
A: We routinely build daily models taking into account day-of-the-week-effects , day-pf-the-month-effects . week-of-the-month effefcts , monthly effects , holiday effects and user-specified predictor series ( if any ) . The whole idea is to compute the probability of making a month-end number as we go through the month.
This is accomplished by creating a probability distribution for each step ahead ( each day ) using error re-sampling (bootstrapping) .The k distributions containing l simulations per period ( k being the # of remaining days) can then be aggregated simulation # by simulation # to obtain a distribution of the sum. 
These simulations can optionally be "infected" by identified pulse anomalies in order to provide realistic limits yielding informative probabilities.
