Solved – stl() gives seasonal component, but ets() and auto.arima() choose nonseasonal models

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I'm completely new to forecasting so please correct me if I'm wrong.

I'm trying to forecast sales data using R. My main concern is that when I decompose the data using stl() from stats package, it shows a seasonal component whereas when I use ets() or auto.arima() commands, they do not take a seasonal component into account. Can anyone please suggest to me where I am going wrong? Which method should I prefer?

I would like to do forecast for Aug15-Dec15.

My data are as follows:

Month      Year Amount January    2010 7632 February   2010 6686 March      2010 3442 April      2010 4556 May        2010 7796 June       2010 1534 July       2010 1466 August     2010 3535 September  2010 2503 October    2010 7534 November   2010 1197 December   2010 5861 January    2011 8846 February   2011 7219 March      2011 5066 April      2011 13177 May        2011 7833 June       2011 5585 July       2011 6392 August     2011 5787 September  2011 13488 October    2011 9413 November   2011 7610 December   2011 11301 January    2012 14912 February   2012 13578 March      2012 12091 April      2012 14628 May        2012 10703 June       2012 7373 July       2012 13638 August     2012 10794 September  2012 12186 October    2012 8137 November   2012 7874 December   2012 7707 January    2013 11569 February   2013 13446 March      2013 10339 April      2013 19086 May        2013 15201 June       2013 11741 July       2013 19368 August     2013 15755 September  2013 12214 October    2013 13859 November   2013 13096 December   2013 14548 January    2014 16191.1 February   2014 23122.3 March      2014 21421.6 April      2014 20904.5 May        2014 19711.5 June       2014 9481.9 July       2014 18699 August     2014 21271.9 September  2014 19515.5 October    2014 19890.6 November   2014 16789 December   2014 31409.3 January    2015 21917.2 February   2015 24911.4 March      2015 26072.4 April      2015 23919.3 May        2015 26980.8 June       2015 41661.2 July       2015 27065.4 August     2015  September  2015  October    2015  November   2015  December   2015

My R code:

x.ts <- structure(c(7632, 6686, 3442, 4556, 7796, 1534, 1466, 3535,     2503, 7534, 1197, 5861, 8846, 7219, 5066, 13177, 7833, 5585, 6392,      5787, 13488, 9413, 7610, 11301, 14912, 13578, 12091, 14628, 10703,      7373, 13638, 10794, 12186, 8137, 7874, 7707, 11569, 13446, 10339,      19086, 15201, 11741, 19368, 15755, 12214, 13859, 13096, 14548,      16191.1, 23122.3, 21421.6, 20904.5, 19711.5, 9481.9, 18699, 21271.9,      19515.5, 19890.6, 16789, 31409.3, 21917.2, 24911.4, 26072.4,      23919.3, 26980.8, 41661.2, 27065.4, NA, NA, NA, NA, NA),   .Tsp = c(2010, 2015.91666666667, 12), class = "ts")  fit <- stl(x.ts,na.action = na.omit,s.window = "periodic",robust = T) plot(fit) summary(ets(x.ts))  fit2 <- auto.arima(x = x.ts, stepwise = F, approximation = F) summary(fit2)

EDIT:

ets(x.ts)$aicc [1] 1404.23     ETS       AICc      AAN    1404.26631    ANN    1404.23046    MNN    1411.95791    MAN    1404.40096    MMN    1400.49486
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Best Answer

Let's load your data (this is why dput is useful):

x.ts <- structure(c(7632, 6686, 3442, 4556, 7796, 1534, 1466, 3535,     2503, 7534, 1197, 5861, 8846, 7219, 5066, 13177, 7833, 5585, 6392,      5787, 13488, 9413, 7610, 11301, 14912, 13578, 12091, 14628, 10703,      7373, 13638, 10794, 12186, 8137, 7874, 7707, 11569, 13446, 10339,      19086, 15201, 11741, 19368, 15755, 12214, 13859, 13096, 14548,      16191.1, 23122.3, 21421.6, 20904.5, 19711.5, 9481.9, 18699, 21271.9,      19515.5, 19890.6, 16789, 31409.3, 21917.2, 24911.4, 26072.4,      23919.3, 26980.8, 41661.2, 27065.4, NA, NA, NA, NA, NA),   .Tsp = c(2010, 2015.91666666667, 12), class = "ts")

Here is a plot:

plot(x.ts)

time series

Now, a trend is rather obvious in your data. To look for seasonality, a seasonplot is useful:

library(forecast) seasonplot(x.ts,year.labels=TRUE,col=rainbow(6))

seasonplot

We again see the increasing trend quite nicely. However, there is no obvious seasonality.

And this is why ets() and auto.arima() do not choose seasonal models.

stl() will do a season-trend-level decomposition whether or not seasonality or a trend are present. It does not do statistical tests for these, or compare seasonal vs. non-seasonal models on information criteria or anything like this.

This earlier question and answer may be helpful: Seasonality not taken account of in auto.arima(). In addition, I very much recommend this free online forecasting textbook.

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