1

I have the following time series of count data:

x <- ts(c(21337, 56994, 95497, 138829, 146346, 157182, 128136,
          104615, 103659, 102082, 109968, 113945, 118067, 93867, 54930))

To which I have associated the following model

> library(forecast)
...
> ets(x)
ETS(A,N,N) 

Call:
 ets(y = x) 

  Smoothing parameters:
    alpha = 0.9999 

  Initial states:
    l = 105466.6663 

  sigma:  32125.45

     AIC     AICc      BIC 
355.9429 356.9429 357.3590

Which gives me negative prediction boundaries at 95% confidence:

> forecast(ets(x), level = .95)
   Point Forecast       Lo 95    Hi 95
16       54933.94   -8030.795 117898.7
17       54933.94  -34107.138 143975.0
18       54933.94  -54116.824 163984.7
...

Since we're dealing with count data, I've decided to hide the negative values from my final plot:

plot(forecast(ets(x), level = .95), ylim = c(0, 260e3))

plot

My questions are:

  1. How many Statistics professors have I just aggravated with that procedure?
  2. How could I get away with such a model without having to resort to transforming my data (I'm trying to avoid the back-and-forth of log-transformation)?

Related questions:

Community
  • 1
Waldir Leoncio
  • 2,637
  • 4
    Your prediction intervals are predicated on a distributional assumption that doesn't seem to hold; ignoring the distributional assumption, even the mean-variance relationship in the model won't hold. – Glen_b Aug 19 '15 at 22:13
  • 2
    Try using lambda=0 in your call to ets. – Rob Hyndman Aug 19 '15 at 22:31
  • @Glen_b, does this mean that I should never use such models on count data, even if the prediction intervals are always positive ("always" as in "up to a reasonable confidence level like .95")? – Waldir Leoncio Aug 20 '15 at 19:37
  • 1
    I wouldn't say "never", if the mean is never close to zero and the mean doesn't vary much (so the variance mis-specification won't cause you too much problem), it probably would be okay. – Glen_b Aug 20 '15 at 19:40
  • @RobHyndman, I've tried using it before, but I'm glad you've prompted me to try again. On my first try, I ended up dismissing lambda = 0 because I thought plot(ets()) and forecast(ets()) were giving me log values. Now I see they actually don't (right?). I'll study Box-Cox transformations in order to understand better what's going on there, but this seems like a better approach than what I was using. Thanks! – Waldir Leoncio Aug 20 '15 at 19:40
  • Alternatively if you didn't need any tests or intervals (or used methods suited to heteroskedastic situations, and sample sizes were large) then you could tolerate more variation in the mean (but you'd still want it to stay away from 0). – Glen_b Aug 20 '15 at 21:47

0 Answers0