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I have the following data set:

foo <- structure(c(38597, 33009, 38668, 39135, 34384, 36942, 46998, 
49620, 40909, 48973, 38565, 53144, 72367, 53217, 38123, 36383, 
43911, 37028, 34652, 28540, 29421, 27469, 28070, 26377, 26604, 
20390, 23239, 28498, 24818, 21424, 21680, 20077, 22005, 21919, 
17172, 27871, 28113, 20190, 24013, 17036, 16742, 18813, 19793, 
19414, 16653, 16273, 14962, 21602, 16547, 17113, 17767, 18868, 
18858, 19276, 17733, 18835, 18934, 19620, 16831, 17525, 17632, 
15146, 21498, 20677, 17468, 19751, 17536, 16998, 14032, 19719, 
16481, 19048, 20401, 18831, 18602, 24852, 36740, 20814, 44061, 
21532, 22502, 18800, 17510, 32047), .Tsp = c(2010, 2016.91666666667, 
12), class = "ts")

I have splitted it in 72:12, train:test data sets. On train set, manually or using auto.arima() I obtain ARIMA(0,1,2) model, however, taking into account the outliers identified by tsoutliers preferred model becomes ARIMA(1,1,1) which gives the following forecasts for comparing with test data: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2016 17323.90 17887.75 17703.34 17763.65 17743.92 17750.37 17748.26 17748.95 17748.72 17748.80 17748.77 17748.78

If you compare it against test data set you will notice that this forecast is unsatisfactory. Give me please some recommendations for its improvement or justifying bad performances?

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closed as unclear what you're asking by Firebug, kjetil b halvorsen, mdewey, Michael Chernick, COOLSerdash Dec 14 '17 at 20:18

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Here is a plot of your time series:

time series

We note that the beginning of the series obviously behaves very differently from later parts. In addition, there are three large spikes during the last year, i.e., during your test period.

No time series forecasting algorithm will forecast spikes like the last three ones by itself. I would recommend that you investigate what caused these three spikes and include this information in your forecasts. This is far more important than finding a "better" ARIMA model.

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