Categorical variable as predictor/regressor in ARIMA I apply ARIMA and I want to consider weekly seasonality as a dayOfWeek predictor (1, 2, ..., 7).
How do I deal with dayOfWeek as a categorical variable?
 A: Weekly seasonality:
There are ~ 52,1429 weeks per year. This is not an integer number. ARIMA is only designed for seasonalities with integer numbers.

Daily seasonality:
Every year has 365,25 days. Every month has 28-31 days (or an other number cultural regions which depend on the moon calendar and not the Gregorian calender). Every weeks has 7 days. You will likely observe multiple seasonalities. Some pattern recur every monday, some pattern recur always at the beginning of the month and some pattern recur always at the beginning of the year. ARIMA is not designed for multiple seasonalities. 

A general advice about categorical regressors:
Take on category, i.e. day as 0-level and the other ones as 1-6. You "save" on independent variable and avoid multicollinearity.

Solution:
ARIMA is not designed for multiple seasonalities and uneven seasonalities. You can try another model like tbats instead.

Bibliography:
The original tbats model.
De Livera, A., Hyndman, R., Snyder, R. (2012). Forecasting Time Series with Complex seasonality patterns using exponential smoothing.  Journal of the American Statistical Association. p. 1513-1527
You can also have a closer look at the question with the tags tbats or multipleseasonalities
A: I'm interpreting this question as "how do I go about coding my variables" or "how do I make categorical predictors into quantitative ones?"
One way to do it is to make 6 predictors $X_{i,1}, X_{i,2}, \ldots, X_{i,6}$ where 


*

*$X_{i,1}$ is set to one if observation $i$ falls on a Monday

*$X_{i,2}$ is set to one if observation $i$ falls on a Tuesday

*$X_{i,3}$ is set to one if observation $i$ falls on a Wednesday

*$X_{i,4}$ is set to one if observation $i$ falls on a Thursday

*$X_{i,5}$ is set to one if observation $i$ falls on a Friday

*$X_{i,6}$ is set to one if observation $i$ falls on a Saturday


For any row $i$, at most one of these new columns will have a $1$. And sometimes, on Sundays, you won't have any $1$s. If you have a categorical variable with $p$ levels, you generally need $p-1$ dummy variable predictors.
R has model.matrix() which is pretty cool:
yt <- rnorm(21) 
x.cat <- as.factor(rep(c("sunday", "monday", "tuesday", "wednedsay", "thursday", "friday", "saturday"),3))
x.quant <- model.matrix(~x.cat)
x.quant <- x.quant[,-1] #remove intercept column 
mod <- arima(yt, order=c(1,1,0), xreg=x.quant)

Eh, if you really want your baseline to be Sunday, like in my example, replace the second line with x.quant <- model.matrix(~., data = as.data.frame(x.cat)).
A: You can plug the weekly seasonality dummy and it'll work fine. The question is whether it's the best way to deal with seasonality. This may work for things like Web site load, where the loads may be spiking on weekends and the customer behavior is persistent. 
