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I have the below time series with 361 daily observations (180 observations for year 1 and 181 for year 2). I created the series like this:
arrivals <- ts(X, frequency = 180, start = c(2018, 1)). enter image description here

Seasonal decompostion looks like this after arrivals <- decompose(arrivals): enter image description here

After auto <- auto.arima(arrivals, seasonal = T) f <- forecast(auto, h=50), I got this forecast: enter image description here

Shouldn't the forecast be a little more accurate at least (show hints of seasonality) or my time series analysis is just that trivial? What can I try to get better results?

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    $\begingroup$ What makes you think your forecast is poor or inaccurate? Anyway, ARIMA has a hard time dealing with long seasonality, so it's good it has already picked a seasonal difference. Have you tried a longer term forecast? That should at least be seasonal. Finally, can you make your data available somewhere? $\endgroup$
    – Stephan Kolassa
    Commented Apr 24, 2021 at 14:50
  • $\begingroup$ I don't know I expected the forecast to follow the pattern from the 2 previous years. Try this link for the data link. No matter the value of the h I get the same prediction. $\endgroup$
    – Joseph K
    Commented Apr 24, 2021 at 15:20

1 Answer 1

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I dput() the data at the bottom in case someone wants to take a look.

ARIMA has a hard time dealing with "long" seasonality, especially if you have only observed two seasonal cycles. "Forecasting with long seasonal periods" by Rob Hyndman is very enlightening reading.

Note that the parameter seasonal=TRUE does not force auto.arima() to use a seasonal model, it only allows it. Use D=1 to force a seasonal model (see Seasonality not taken account of in auto.arima()). Here is what happens then:

> model_sarima <- auto.arima(arrivals,D=1)
> model_sarima
Series: arrivals 
ARIMA(2,1,1)(0,1,0)[180] 

Coefficients:
         ar1      ar2      ma1
      0.0627  -0.2052  -0.7837
s.e.  0.0895   0.0827   0.0615

sigma^2 estimated as 116.5:  log likelihood=-686.48
AIC=1380.96   AICc=1381.19   BIC=1393.73
> plot(forecast(model_sarima,h=100),las=1)

As you see, we now have a quite different (and seasonal) model.

SARIMA

Now the forecasts definitely look more, ahem, sophisticated. Whether they are more accurate is doubtful. For one, some of the point forecasts are negative, which you presumably do not want. Actually, the vast prediction intervals give a hint that auto.arima() does not think this forecast is very useful.

Here is an equally dubious stlf forecast:

plot(stlf(arrivals,h=100),las=1)

STLF

An alternative would be to fit a smooth bump function to your two years of history, then extrapolate this forward. But whatever you do, before you forecast you should really think about that conspicuous drop at the end of your series, which is also visible in a seasonplot. Is this some fundamental change, and will your time series go back to normal, or not, and when? That kind of thinking about the drivers of your series can be far more useful than tweaking ARIMA models.

seasonplot(arrivals,col=1:2,pch=19,las=1)
legend("topright",lwd=1,pch=19,col=1:2,legend=2018:2019)

seasonplot

Data:

arrivals <- structure(c(18L, 14L, 13L, 14L, 13L, 10L, 12L, 17L, 12L, 9L, 
17L, 14L, 5L, 17L, 21L, 17L, 20L, 10L, 27L, 8L, 14L, 19L, 15L, 
15L, 14L, 22L, 25L, 16L, 19L, 13L, 17L, 40L, 16L, 16L, 30L, 10L, 
17L, 21L, 25L, 30L, 24L, 21L, 25L, 15L, 22L, 16L, 25L, 13L, 36L, 
29L, 32L, 20L, 24L, 25L, 22L, 36L, 19L, 2L, 24L, 22L, 24L, 11L, 
12L, 21L, 17L, 32L, 24L, 27L, 20L, 31L, 26L, 27L, 23L, 27L, 31L, 
18L, 27L, 36L, 23L, 21L, 28L, 27L, 17L, 23L, 20L, 18L, 23L, 27L, 
25L, 20L, 26L, 36L, 31L, 27L, 29L, 21L, 15L, 29L, 22L, 13L, 24L, 
34L, 23L, 25L, 26L, 25L, 24L, 35L, 23L, 18L, 14L, 25L, 13L, 15L, 
21L, 18L, 8L, 7L, 13L, 25L, 10L, 14L, 13L, 15L, 17L, 22L, 12L, 
18L, 23L, 30L, 26L, 9L, 25L, 24L, 13L, 18L, 28L, 17L, 9L, 22L, 
30L, 31L, 37L, 36L, 18L, 10L, 9L, 24L, 36L, 36L, 28L, 5L, 13L, 
30L, 13L, 12L, 13L, 26L, 26L, 4L, 11L, 9L, 7L, 8L, 16L, 2L, 4L, 
9L, 4L, 4L, 2L, 0L, 6L, 0L, 4L, 1L, 3L, 1L, 13L, 15L, 2L, 3L, 
10L, 7L, 10L, 13L, 26L, 3L, 2L, 18L, 4L, 20L, 29L, 41L, 14L, 
14L, 32L, 30L, 20L, 18L, 33L, 8L, 10L, 22L, 29L, 23L, 28L, 36L, 
12L, 13L, 17L, 10L, 5L, 16L, 33L, 12L, 10L, 17L, 27L, 20L, 26L, 
32L, 6L, 3L, 2L, 8L, 2L, 1L, 17L, 14L, 3L, 30L, 5L, 5L, 8L, 7L, 
6L, 15L, 5L, 6L, 4L, 3L, 15L, 3L, 2L, 0L, 8L, 8L, 33L, 27L, 12L, 
1L, 19L, 14L, 11L, 28L, 24L, 32L, 30L, 12L, 6L, 9L, 5L, 26L, 
7L, 4L, 7L, 15L, 13L, 20L, 20L, 7L, 15L, 7L, 11L, 16L, 24L, 11L, 
26L, 27L, 17L, 17L, 22L, 13L, 9L, 21L, 20L, 23L, 25L, 23L, 28L, 
22L, 11L, 18L, 20L, 13L, 17L, 26L, 24L, 10L, 9L, 6L, 5L, 2L, 
9L, 2L, 1L, 6L, 11L, 19L, 8L, 6L, 8L, 5L, 4L, 4L, 2L, 6L, 4L, 
8L, 3L, 12L, 8L, 2L, 5L, 5L, 4L, 5L, 8L, 3L, 2L, 5L, 8L, 2L, 
5L, 2L, 12L, 0L, 6L, 5L, 2L, 4L, 0L, 4L, 5L, 3L, 0L, 3L, 1L, 
2L, 1L, 0L, 2L, 2L, 0L, 1L, 1L, 1L, 1L, 1L, 1L), .Tsp = c(2018, 
2020, 180), class = "ts")
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  • $\begingroup$ Thank you for your answer. Maybe indeed the data are not sufficient for creating a decent SARIMA model. I had never heard about stacking models before, seems like a quite interesting technique. $\endgroup$
    – Joseph K
    Commented Apr 29, 2021 at 19:03

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