Doubts on ARIMA models forecast to account for an exponential trend only later in time

I have a 10 years daily data series, with no indicative trend on the first 8 years but seemingly exponential growth in the last 2.

I’m using R with forecast package.

auto.arima recommends:

ARIMA(0,0,2)SARIMA(2,1,0,)[12]+drift=0.25

Note that no first difference is recommended. I worry that my future forecast (using this model) will not fairly account for the exponential growth witnessed for the past 2 years, since the drift=0.25 is an under representation of trend? Is my worry unfounded because differencing effectively remove trend. Otherwise please advise what can I do about it?

It’s not a structural break, but perhaps a “time varying parameter” (according to Prof. Rob Hyndman – but how can I do that? http://robjhyndman.com/hyndsight/structural-breaks/ – any easy solutions/references to this?) P.s. I could only answer this question if my mathematics is good enough…thanks in advance.

• post your data. – Tom Reilly Sep 29 '16 at 22:07
• – Hu Shanxiong Sep 30 '16 at 16:07
• Note that I have averaged the daily series into monthly data, that's why seasonality is shown as 12. My primary concern is whether the drift recommended by the model (which took account of the data structure of the full 10 years) actually under-represents the seemingly exponential growth in the last 2 years. I'm confused because with the coefficients weights in MA(2) and drift, the exponential trend should be accounted for right? (or if the data has been first differenced instead, the exponential trend should also be accounted for as well right?). My residuals are stationary. – Hu Shanxiong Sep 30 '16 at 16:14