AUTHOR=Hasan Mahmud , Wathodkar Gauree , Muia Mathias 

TITLE=ARMA model development and analysis for global temperature uncertainty

JOURNAL=Frontiers in Astronomy and Space Sciences

VOLUME=Volume 10 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2023.1098345

DOI=10.3389/fspas.2023.1098345

ISSN=2296-987X

ABSTRACT=Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time series temperature uncertainty model which is the Auto-regressive Moving Average (ARMA)(1, 1) model. The model was developed for observed annual mean temperature anomaly X(t) which
is a combination of true (latent) global anomaly Y (t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t) which was decomposed to Land Surface Temperature (LST) uncertainty, Sea Surface Temperature (SST) uncertainty, and the corresponding source of uncertainty. The ARMA model was analyzed and compared with Auto-regressive (AR), and Auto-regressive integrated moving average (ARIMA) for the data taken from NASA, Goddard Institute for space studies Surface Temperature Analysis. The statistical analysis of the Auto-correlation function
(ACF), Partial auto-correlation function (PACF), Normal quantile-quantile (Normal Q-Q) plot, the density of the residuals, and variance of normal variable w(t) show that ARMA(1, 1) fits better than AR(1) and ARIMA(1, d, 1) for d = 1, 2.