My comments here do not assume any time series data ...just a collection of observations that are being scrutinized for anomalies.
An even easier method is to construct an X variable with all zeroes except for the point where the candidate falls. Run a regression (including a constant) and examine the t value for the X variable. If the residuals from this simple regression model are normal and independent then the t value can be interpreted in the standard way.
You can scan the opportunity space by separetely trying different observational points to determine the most significant (if any !) deviant observations form the mean.
I modified my answer to include the concept of scanning in order to rank the observations in terms of exceptional values.
EDITED to illustrate how cross-sectional data is a particular subset of an ARIMAX MODEL
If we specify t=i that b=0 and W(l)=1.0 and delete all reference to I ( the anomalies) and any coloring of the error process we get a model for i observations ..using 1 X ... 29 "0"'s . 1 "1" and 10 "0"'s in my example of 40 observations