## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 2 (2017), 898-918.

### Evaluation of the cooling trend in the ionosphere using functional regression with incomplete curves

Oleksandr Gromenko, Piotr Kokoszka, and Jan Sojka

#### Abstract

We develop a statistical framework to test the hypothesis of the existence of an ionospheric cooling trend related to the global warming hypothesis; both are attributed to the same driver, namely the increased concentration of greenhouse gases. However, the study of a temporal trend in the ionosphere is easier because there are fewer covariates to be taken into account. The hypothesis that a cooling trend in the ionosphere exists has been an important focus of space physics research for over two decades. A central difficulty in reaching broadly agreed—on conclusions has been the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Complete time series of data that cover several decades exist only in a few separated (industrialized) regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations. We present a statistical analysis that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle spatially indexed curves whose temporal domain depends on location and may contain gaps. The test statistic combines spatial and temporal dependence in the data and is approximately normally distributed. We conclude that a statistically significant cooling trend exists in the Northern Hemisphere. This confirms the hypothesis put forward in the space physics community over two decades ago.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 2 (2017), 898-918.

**Dates**

Received: March 2014

Revised: January 2017

First available in Project Euclid: 20 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1500537728

**Digital Object Identifier**

doi:10.1214/17-AOAS1022

**Mathematical Reviews number (MathSciNet)**

MR3693551

**Zentralblatt MATH identifier**

06775897

**Keywords**

Cooling trend functional regression incomplete time series ionosphere solar activity spatial averaging spatio-temporal modeling

#### Citation

Gromenko, Oleksandr; Kokoszka, Piotr; Sojka, Jan. Evaluation of the cooling trend in the ionosphere using functional regression with incomplete curves. Ann. Appl. Stat. 11 (2017), no. 2, 898--918. doi:10.1214/17-AOAS1022. https://projecteuclid.org/euclid.aoas/1500537728

#### Supplemental materials

- Supplementary material: Evaluation of the cooling trend in the ionosphere using functional regression with incomplete curves. The Supplementary Material contains the code and data used in this paper.Digital Object Identifier: doi:10.1214/17-AOAS1022SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.