Today’s email brought this one:
I was wondering if I could get your opinion on a particular problem that I have run into during the reviewing process of an article.
Basically, I have an analysis where I am looking at a couple of time-series and I wanted to know if, over time there was an upward trend in the series. Inspection of the raw data suggests there is, but we want some statistical evidence for this.
To achieve this I ran some ARIMA (0,1,1) models including a drift/trend term to see if the mean of the series did indeed shift upwards with time and found that it did. However, we have run into an issue with a reviewer who argues that differencing removes trends and may not be a suitable way to detect trends. Therefore, the fact that we found a trend despite differencing suggest that differencing was not successful. I know there are a few papers and textbooks that use ARIMA (0,1,1) models as ‘random walks with drift’-type models so I cited them as examples of this procedure in action, but they remained unconvinced.
Instead it was suggested that I look for trends in the raw undifferenced time-series as these would be more reliable as no trends had been removed. AT the moment I am hesitant to do this as I was sort of taught that even pure random walks could give you significant trends. Moreover, given that the raw time-series is not stationary I was worried that an ARIMA (0,0,1) model as it would be might not actually be appropriate.
There’s nothing like running into ignorant reviewers who want you to do things that make no sense. (more…)