Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?
Article first published online: 24 AUG 2006
Journal of the Royal Statistical Society: Series A (Statistics in Society)
Volume 170, Issue 1, pages 83–94, January 2007
How to Cite
Mills, T. C. (2007), Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170: 83–94. doi: 10.1111/j.1467-985X.2006.00443.x
- Issue published online: 24 AUG 2006
- Article first published online: 24 AUG 2006
- [Received October 2005. Final revision March 2006]
- Long memory;
- Northern hemisphere temperatures;
- Segmented trends;
- Smooth transitions;
- Time series
Summary. The time series properties of the temperature reconstruction of Moberg and co-workers are analysed. It is found that the record appears to exhibit long memory characteristics that can be modelled by an autoregressive fractionally integrated moving average process that is both stationary and mean reverting, so that forecasts will eventually return to a constant underlying level. Recent research has suggested that long memory and shifts in level and trend may be confused with each other, and fitting models with slowly changing trends is found to remove the evidence of long memory. Discriminating between the two models is difficult, however, and the strikingly different forecasts that are implied by the two models point towards some intriguing research questions concerning the stochastic process driving this temperature reconstruction.