# 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.

• You write "Before we get to questions of stationarity" and then in the very same sentence "we are at a loss about correlatedness of observations": yet non-stationarity is memory (e.g. $y_{t} = f(y_{<t}) + \text{other stuff}$, implying correlated observations) in a time series variable. If you care about whether observations are correlated, you care about stationarity. – Alexis Mar 23 '15 at 5:27
• Modelling daily arrivals of asylum seekers with ARIMA seems like a hopeless task; particularly e.g. if this is related to the Syrian conflict. Flows of people are hugely dependent on political and military events, i.e. not recurring seasonal trends. – conjectures Feb 23 '16 at 16:41
• @conjectures, I'm pretty sure there's huge seasonality. I remember reading a newspaper report about the impact of Turkish deal. The author was mentioning something about fewer migrants in the winter due to the weather, and how the deal will really be tested summer time. also, the migrants tend to move in flocks, once they figure out the weak point in the EU borders they'll be pounding it in numbers. hence, you've got to see strong autocorrelation if you count them at any particular border point. – Aksakal Nov 17 '16 at 21:14
• Which area/country is this for? It should be possible to obtain good predictor variables, do you have some? – kjetil b halvorsen Mar 2 '17 at 14:29