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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.

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    $\begingroup$ 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. $\endgroup$ – Alexis Mar 23 '15 at 5:27
  • $\begingroup$ 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. $\endgroup$ – conjectures Feb 23 '16 at 16:41
  • $\begingroup$ @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. $\endgroup$ – Aksakal Nov 17 '16 at 21:14
  • $\begingroup$ Which area/country is this for? It should be possible to obtain good predictor variables, do you have some? $\endgroup$ – kjetil b halvorsen Mar 2 '17 at 14:29
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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.

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  • $\begingroup$ Thanks for your answer! Could you comment on what you mean by 'Appropriate Arima component to deal with interdependence of observations' ? You mean I should expect to need an autoregressive term in my model, along with potential dummyvars for calendar effects? $\endgroup$ – user3817704 Oct 26 '14 at 11:48
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    $\begingroup$ Yes you might need autoregressive effects (ARIMA) and potential dummy variables for deterministic effects. The ARIMA structure is an optimization/generalization of your time window as it incorporates the optimal lag structure and the optimal weights for each lag. $\endgroup$ – IrishStat Oct 26 '14 at 11:54
  • $\begingroup$ The first few sentences were promising, and then I ran into "Please review all my previous posts" which was not. $\endgroup$ – rolando2 Feb 15 '15 at 16:50
  • $\begingroup$ which was not ???? $\endgroup$ – IrishStat Feb 15 '15 at 18:30

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