Fractional order estimation and testing, application to Swedish temperature data

Abstract

SUMMARYHere we introduce a concept of periodogram roughness, which we use for estimating the roughness (variation) of spectral density. Periodogram roughness is used for several estimation and testing purposes. With the help of a spectral compensator factor it can be used to estimate fractional order as well as the autoregressive parameters or the moving average. The periodogram roughness is asymptotically normal when sample size increases. We applied our methods to temperature measurements in 10 network stations throughout Sweden to estimate the fractional order. The cycle pattern in temperature measurements has been tested. It shows long range dependency structure.

Uncertainties in Global Warming Temperature-Trend and Their Impacts on Agricultural Production: an Econometric Evaluation

“…Many studies have been carried out on detecting and modeling long memory in various areas such as climate change (e.g. Hussain and Elbergali, 1999;Haslett and Raftery, 1989), economic and financial fields (e.g. Lo, 1991;Meade and Maire, 2003).…”

Space‐time modelling of trends in temperature series

“…Beran, 1994), a commonly used noise model is the long memory process (e.g. Hussain and Elbergali, 1999, Craigmile et al., 2004, Koutsoyiannis, 2003, Cohn and Lins, 2005). In particular, in the context of a single time series analysis, Craigmile et al.…”

“…Beran, 1994), a commonly used noise model is the long memory process (e.g. Hussain and Elbergali, 1999, Craigmile et al, 2004, Koutsoyiannis, 2003, Cohn and Lins, 2005. In particular, in the context of a single time series analysis, Craigmile et al (2004) provided estimates of trend, confidence regions, and significance tests when a trend is observed in the presence of a classical long memory noise such as the fractional differenced (FD) process (Granger and Joyeux, 1980;Hosking, 1981).…”

A simple method for detecting fractional cointegration relation: an application to Finnish data

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