## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 5, Number 1 (2011), 5-44.

### A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?

Blakeley B. McShane and Abraham J. Wyner

#### Abstract

Predicting historic temperatures based on tree rings, ice cores, and other natural proxies is a difficult endeavor. The relationship between proxies and temperature is weak and the number of proxies is far larger than the number of target data points. Furthermore, the data contain complex spatial and temporal dependence structures which are not easily captured with simple models.

In this paper, we assess the reliability of such reconstructions and their statistical significance against various null models. We find that the proxies do not predict temperature significantly better than random series generated independently of temperature. Furthermore, various model specifications that perform similarly at predicting temperature produce extremely different historical backcasts. Finally, the proxies seem unable to forecast the high levels of and sharp run-up in temperature in the 1990s either in-sample or from contiguous holdout blocks, thus casting doubt on their ability to predict such phenomena if in fact they occurred several hundred years ago.

We propose our own reconstruction of Northern Hemisphere average annual land temperature over the last millennium, assess its reliability, and compare it to those from the climate science literature. Our model provides a similar reconstruction but has much wider standard errors, reflecting the weak signal and large uncertainty encountered in this setting.

#### Article information

**Source**

Ann. Appl. Stat. Volume 5, Number 1 (2011), 5-44.

**Dates**

First available in Project Euclid: 21 March 2011

**Permanent link to this document**

http://projecteuclid.org/euclid.aoas/1300715170

**Digital Object Identifier**

doi:10.1214/10-AOAS398

**Zentralblatt MATH identifier**

05906786

**Keywords**

Climate change global warming paleoclimatology temperature reconstruction model validation cross-validation time series

#### Citation

McShane, Blakeley B.; Wyner, Abraham J. A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?. Ann. Appl. Stat. 5 (2011), no. 1, 5--44. doi:10.1214/10-AOAS398. http://projecteuclid.org/euclid.aoas/1300715170.

#### Supplemental materials

- Supplementary material: Code repository for “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?”. This repository archives all data and code used for “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?” In particular, it contains code to make all figures and tables featured in the paper.