An application of fractional integration to a long temperature series

Abstract

Some recently proposed techniques of fractional integration are applied to a long UK temperature series. The tests are valid under general forms of serial correlation and do not require estimation of the fractional differencing parameter. The results show that central England temperatures have increased about 0.23°C per 100 years in recent history. Attempting to summarize the conclusions for each of the months, we are left with the impression that the highest increase has occurred during the months from October to March.

Long memory, seasonality and time trends in the average monthly temperatures in Alaska

“…(See, e.g. Bloomfield 1992;Smith 1993;Lewis and Ray 1997;Pethkar and Selvam 1997;KoscielnyBunde et al 1998;Pelletier and Turcotte 1999;Percival et al 2004;Maraun et al 2004, Gil-Alana 2003, 2005and Mills 2007). …”

“…In both cases, the coefficients y ð1Þ j and y ð2Þ j tend to zero as j→∞, the rate of decay depending on the magnitudes of d and ρ s in (M1) and of d s and ρ in (M2). 4 This paper differs from others also based on fractional integration (Gil-Alana 2003, 2005 in that we employ a more flexible approach including long-range dependence and seasonality in a unified framework and allowing for long memory in both the zero and the seasonal frequencies of the data.…”

Warming Break Trends and Fractional Integration in the Northern, Southern, and Global Temperature Anomaly Series

“…Moreover, higher the d is, the higher will be the level of association between the observations. Examples of this type of model in meteorological time series data are among others the papers of Bloomfield (1992); Smith (1993); Lewis and Ray (1997); Pethkar and Selvam (1997); Koscielny-Bunde et al (1998);Pelletier and Turcotte (1999);Percival et al (2004);Maraun et al (2004) and Gil-Alana (2003, 2005.…”

Applicatıon of detrended fluctuation analysis to temperature data from Turkey

“…In addition to these studies based on the DFA, there are many other studies based on non-DFA techniques searching the long-term correlation of temperature data (See, e.g. Smith, 1993;Lewis and Ray, 1997;Turcotte, 1997, 1999;Gil-Alana, 2003, 2005.…”