São Paulo City is getting 2 $$^{\circ }$$C hotter in the last 50 years: regression model with autoregressive errors or with lagged temperatures?

Abstract

This study presents two time series models to estimate the mean increase in the monthly mean temperature in Sao Paulo City from 1960 to 2017. The basic model consists of a linear regression model including trend and sine and cosine functions to consider seasonality. As the errors are supposed to be autocorrelated for time series, we can include in the regression model the lagged temperatures or autoregressive errors. The first approach is often used in practice, but the trend parameter estimator is biased to estimate the long-run trend effect. The unbiased trend effect estimator is presented with its variance and confidence interval. The second approach provides directly the unbiased trend estimator. Finally, there is evidence that the temperature trend effect is constant over time and both models lead to a significant increase of $$1.9{\,}^{\circ }$$ C in the last 50 years in Sao Paulo City. The 95% confidence interval is equal to [1.6; 2.2] for the model with autoregressive errors, which is beyond the limits announced in the Paris Agreement of 2015.