Time series with correlated observations: How to start analysis? We have a time series dataset: Daily arrivals of asylum seekers. 
Goal is to model this variable. In particular we would like to attempt Arima modeling and/or fitting a distribution.
Before we get to questions of stationarity, constant variance and such, we are at a loss about correlatedness of observations: In case of a holiday, the next day will see more people coming in. What are standard methods for taking such interdependence between observations into account?
We may group per week or per month. Per week still gives this problem however. Per month leaves us with rather little observations and loss of information. 
Currently we make prediction by one-sided moving average. But the time window is chosen arbitrary, we want to obtain more statistical foundation for our predictions.
 A: Use daily data to develop a useful model. You can then accumulate the forecasts into weekly or monthly buckets as you wish. The daily model could contain structure like day-of-the-week ,day-of-the-month, week-of-the-month, week-of-the-year , month-of-the-year, pre and post holiday effects, long weekend effects after or before a holiday, level shifts , local time trends and of course pulse effects to deal with non-recurring one-time effects. For guidance in this area you might want to read my earlier posts (and others !) on daily data analysis. Please review all my previous posts as that is the only subject I know anything about thus the only one I comment about. You might find some of material informative as you try to forge a practical software solution . As you said you need to make sure your software solution deals with non-constant error variance and parameter transiency over time and incorporates these considerations as needed. An appropriate ARIMA component in your model will deal with the interdependence of your observations.
