Removing the influence of the serial correlation on the Mann-Kendall test

Abstract

The Pre-Whitening (PW), the Trend-Free Pre-Whitening (TFPW) and the Modified Trend-Free PreWhitening (MTFPW) were developed to remove the influence of serial correlations on the MannKendall trend test. The main purpose of this study was to compare the performance of these algorithms for evaluating trends in auto-correlated series. The PW, TFPW and MTFPW were also applied to the monthly values of the rainfall (Pre), minimum (Tmin) and maximum (Tmax) air temperature data obtained from the weather station of Ribeirão Preto, State of São Paulo, Brazil. Sets of Monte Carlo simulations were carried out to evaluate the occurrence of the type I and the type II errors obtained from these three algorithms. The TFPW has the highest power. However, it also presented the highest occurrence of type I errors. The PW clearly limits the influence of serial correlation on the occurrence of type I errors. Nevertheless, this feature is accomplished at a cost of a great reduction of its ability to detect trends. The MTFPW leads to a better balance between the probabilities of both statistical errors. It was also concluded that the hypothesis of the presence of no climate change in the location of Ribeirão Pareto cannot be accepted. Keywords: Trends, climate change, auto-correlation. RESUMO: REMOÇÃO DA INFLUÊNCIA DA CORRELAÇÃO SERIAL SOBRE O TESTE DE MANN-KENDALL Os procedimentos denominados de Pre-Whitening (PW), Trend-Free Pre-Whitening (TFPW) eModified Trend-Free Pre-Whitening (MTFPW) foram desenvolvidos para remover a influência da correlação serial no teste de tendência de Mann-Kendall. O objetivo principal desse estudo foi comparar o desempenho desses três algoritmos para avaliar a presença de tendências em séries auto-correlacionadas. O PW, o TFPW e o MTFPW também foram aplicados nos dados mensais de precipitação pluvial e das temperaturas mínima e máxima do ar registrados em Ribeirão Preto, SP. Foram realizadas simulações de Monte Carlo para quantificar a ocorrências dos erros tipo I e II associados à esses procedimentos. Embora o TFPW tenha apresentado o menor número de erros tipo II, o mesmo associou-se a maior frequência de ocorrência de erros tipo I. O PW limitou a influência da correlação serial sobre a ocorrência do erro tipo I. Entretanto, essa última característica é atingida ao custo de uma importante redução em sua habilidade de detectar reais tendências. O MTFPW leva a um melhor equilíbrio entre as probabilidades de ocorrência desses dois erros estatísticos. Concluí-se também que a hipótese da ausência de tendências climáticas na localidade de Ribeirão Preto não pode ser aceita. Palavras-chave: Tendências, mudança climática, auto-correlação. 162Gabriel Constatino Blain.Volume 29 (2)

Determining Changes in Land Use Structure in Małopolska Using Statistical Methods

“…The test has been widely applied for detection of monotonic land use changes [41][42][43]. It is also a very popular method in environmental studies [44][45][46][47]. If the sample is {y 1 ,…,y n }, then the MannKendall (MK) statistic has the following form:…”

“…The MK test revealed a decrease of the power in the presence of autocorrelation [23,[47][48][49][50], which means that the existing trend can be undetected by the test if the series contains autocorrelated data. The decrease of power results Preliminary calculations revealed that all data series were serially correlated in this study because by using the Ljung-Box test [53] the autocorrelation function ACF was revealed to be significant for certain lags.…”

Analysis of the Qinghai-Xizang Plateau Monsoon Evolution and Its Linkages with Soil Moisture

“…The main methods applied in this study are the nonparametric Mann-Kendall (MK) test and correlation analysis [34,35]. The MK trend test and Sequential Mann-Kendall (SQMK) test, which is widely applied in the areas of meteorology and hydrology, is commonly utilized to detect trends and abrupt changes in plateau monsoon indices.…”

“…Positive (negative) Z values indicate the presence of significant increasing (decreasing) trends in plateau monsoons ifˇˇZˇˇě Z 1´α{2 (α representing the significance level) in a two-sided trend test [34,35].…”

“…If UF and UB intersect and the point is located between the corresponding critical lines, then the point corresponds to the time when the abrupt change begins. In this study, the hypothesis tests were performed at the 5% significance level [34,35].…”