Additive Or Multiplicative Time Series Model? So i Just have a question,for the time series graph https://gyazo.com/c8246b91ff891fa4177b3d4f22fb4aec (UPDATED)
The time series graph shows the amount of box office sales in $US millions over a 17 year period.
Here is a decomposition graph using additive model: https://gyazo.com/4894ac6b6007145844735fec373ae7a85
Multiplicative model:
https://gyazo.com/5104d911493213b73b864ebaacbe527fc
Would a additive or multiplicative model best fit this graph? In my personal opinion I think a multiplicative model would best fit this graph, as it appears that there is alot of seasonal spikes appear to vary in different size and magnitude. However I am not certain.
 A: Based on the STL decomposition chart I would say the time series exhibits only very mild heteroskedasticity (maybe a little less variance 2004-2008) and this is not associated with periods with a higher or lower mean value. There also don't seem to be any outliers caused by an additive model such as a negative prediction for a strictly non-negative count data. In fact, the mean seems to vary only from 600 to 900 (<20% relative range) and never goes close to zero so the choice between additive and multiplicative is probably not of primary importance. So I would recommend an additive model in this case. 
Just to be clear about the heuristics I'm using to make this recommendation, let's consider a counter example. Let's say the mean had changed from 500 to 20,000 over a few years, and that during the period when the mean was close to 500, the standard error was about 100, while the standard error during the period when the mean was 20,000 was about 4,000. This would show on the residual component of the STL chart as very strong heteroskedasticity. 
Another kind of pathology to look for is interaction of seasonal and trend predictions. Consider these two statements about a website that got 1 million page views a day on average over a period of several years


*

*On Christmas, the number of page views is 1/5 of normal.

*On Christmas, the number of page views is 800,000 


Both fit the historic data. But what if site traffic starts to grow, and we have 2 million in 2017, and 3 million in 2018? Would we still use an adjustment of -800e6 for that day, or would the 1/5 make more sense? What if the site traffic crashes to only half a million a day? Would you then predict negative -300e6 page views? A multiplicative model would instead take trend * seasonal and predict 500e6 * (1/5) = 100e6 for the same day. So if we use the wrong model, we'll see a huge residual spike of with a magnitude of 400e6 for that day. Look for a weak seasonal component outliers in the residuals to indicate we've made a bad choice of multiplicative vs. additive.
