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Detection of Trend Types in Surface Air Temperature in China

Detection of trend types in temperature data, by distinguishing between deterministic and stochastic trends, has important implications for understanding climate change. The Unit root tests (URTs) have been widely used for detecting trend types, but they do not consider the possibility of fractional integration and its influences. In this study, we detected the trend types of surface air temperature observed during the period 1960– 2019 at 558 stations across China, by considering fractional integration. The whole period was divided into three sub-periods by two structural breakpoints (denoted as SBP1 and SBP2). The fractional differencing parameter d was estimated by the Local Whittle (LW) function, and then the Phillips-Perron (PP), Kwiatkowski-Phillips- Schmidt-Shim, (KPSS) and Zivot and Andrews (ZA) tests were used to detect trend types in these temperature data. The results indicated that the de-seasoned monthly temperature (DMT) series are fractionally integrated and, thus, exhibit long-range dependence characteristics, which have significant influence on the estimation of trend slopes and detection of trend types. Compared with the LW function, the ordinary least squares yielded biased estimation of trend slopes, as it cannot handle the long-range dependence of DMT series, which generates pseudo trends and contaminates true trends of temperature. The DMT series with weak long-range dependence or anti-persistent characteristic were accurately detected as deterministic trends during 1960–SBP1, SBP1–SBP2, SBP2–2019. However, the DMT series with strong long-range dependence were detected as stochastic trend by KPSS test during SBP1–2019 and 1960–2019, which results from the oscillatory components from long-range dependence. Considering the fractional integration of time series and URTs together, therefore, is more appropriate to reliably detect trend types in temperature data. Following this, temperature over short periods in China were detected as having deterministic trends, but those at long periods were detected as having a combination of long-range dependence and deterministic trends.

temperature variability; deterministic trend; stochastic trend; unit root test; fractional integration; long-range dependence