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Luis A. Gil-Alana

Abstract

This paper deals with the estimation of time trends in temperature anomaly series. However, instead of imposing that the estimated residuals from the time trends are covariance stationary processes with spectral density that is positive and finite at the zero frequency [I(0)], the author allows them to be fractionally integrated. In this context, a new procedure for testing fractional integration with segmented trends is applied to the northern, southern, and global temperature anomaly series. The results show that the three series are fractionally integrated, and the warming effects are substantially higher after the break in all cases.

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Luis A. Gil-Alana

Abstract

This paper looks at the analysis of U.K. monthly rainfall data from a long-term persistence viewpoint. Different modeling approaches are considered, taking into account the strong dependence and the seasonality in the data. The results indicate that the most appropriate model is the one that presents cyclical long-run dependence with the order of integration being positive though small, and the cycles having a periodicity of about a year.

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Luis A. Gil-Alana

Abstract

The temperatures in the Northern Hemisphere from 1854 to 1999 have been analyzed in this article by means of a testing procedure that permits one to consider fractional degrees of integration. The tests are valid under general forms of serial correlation and deterministic trends and do not require estimation of the fractional differencing parameter. The results show that the series follows a fractionally integrated process with the order of integration higher than zero and thus implying long memory behavior. The series was decomposed into four different subsamples, and it was observed that the degree of dependence between the observations substantially increased during the twentieth century.

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Luis A. Gil-Alana, Manuel Monge, and María Fátima Romero Rojo

Abstract

This paper addresses analysis of the global monthly sea surface temperatures using a reconstructed dataset that goes back to 1884. We use fractional integration methods to examine features such as persistence, seasonality, and time trends in the data. The results show that seasonality is a relevant issue, finding evidence of seasonal unit roots. With the seasonal component removed, persistence is also very significant, and, when looking at the data month by month, evidence of significant linear trends is detected in all cases. According to these results, monthly sea surface temperatures increase by between 0.07° and 0.11°C every 100 years.

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Luis A. Gil-Alana, OlaOluwa S. Yaya, Oladapo G. Awolaja, and Lorenzo Cristofaro

Abstract

This paper focuses on the analysis of the time series behavior of the air quality in the 50 U.S. states by looking at the statistical properties of particulate matter (PM10 and PM2.5) datasets. We use long daily time series of outdoor air quality indices to examine issues such as the degree of persistence as well as the existence of time trends in data. For this purpose, we use a long-memory fractionally integrated framework. The results show significant negative time trend coefficients in a number of states and evidence of long memory in the majority of the cases. In general, we observe heterogeneous results across counties though we notice higher degrees of persistence in the states on the west with respect to those on the east, where there is a general decreasing trend. It is hoped that the findings in the paper will continue to assist in quantitative evidence-based air quality regulation and policies.

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