In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distri...In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average processes.Finally,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.展开更多
In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test s...In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.展开更多
A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheopt...A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheoptimality of the bound.Applications to Student’s statistic and autoregressive process are also discussed.展开更多
Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased ...Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased by 0.6°C - 0.8°C during the 20th century, along with changes in the hydrological cycle. This has alerted the international community and brought great interest to climate scientists leading to several studies on climate trend detection at various scales. This paper examines the long-term modification of the near surface air temperature in Rwanda. Time series of near surface air temperature data for the period ranging from 1958 to 2010 for five weather observatories were collected from the Rwanda National Meteorological Service. Variations and trends of annual mean temperature time series were examined. The cumulative sum charts (CUSUM) and bootstrapping and the sequential version of the Mann Kendall Rank Statistic were used for the detection of abrupt changes. Regression analysis was performed for the trends and the Mann-Kendall Rank Statistic Test was used for the examination of their significance. Statistically significant abrupt changes and trends have been detected. The major change point in the annual mean temperature occurred around 1977-1979. The analysis of the annual mean temperature showed for all observatories a not very significant cooling trend during the period ranging from 1958 to 1977-1979 while a significant warming trend was furthermore observed for the period after the 1977-1979 where Kigali, the Capital of Rwanda, presented the highest values of the slope (0.0455/year) with high value of coefficient of determination (R2 = 0.6798), the Kendall’s tau statistic (M-K = 0.62), the Kendall Score (S = 328) with a two-sided p-value far less than the confidence level α of 5%). This is most likely explained by the growing population and increasing urbanization and industrialization the country has experienced, especially the Capital City Kigali, during the last decades.展开更多
基金Supported by the NNSF of China(11701004,11801003)NSSF of China(14ATJ005)+1 种基金NSF of Anhui Province(1808085QA03,1808085QA17,1808085QF212,2008085MA14)Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0006,KJ2019A0021).
文摘In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average processes.Finally,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.
基金National Natural Science Foundation of China(1047112610671176).
文摘In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.
基金This research was supported by National Natural Science Foundation of China(10371074)RGC Competitive Earmarked Research Grants(HKUST6183/03E and HKUST6232/04E).
文摘A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite moments.The bound coincides with the classical Berry–Esseenboundforstandardizedmartingales.Anexampleisgiventoshowtheoptimality of the bound.Applications to Student’s statistic and autoregressive process are also discussed.
文摘Climate change and global warming are widely recognized as the most significant environmental dilemma the world is experiencing today. Recent studies have shown that the Earth’s surface air temperature has increased by 0.6°C - 0.8°C during the 20th century, along with changes in the hydrological cycle. This has alerted the international community and brought great interest to climate scientists leading to several studies on climate trend detection at various scales. This paper examines the long-term modification of the near surface air temperature in Rwanda. Time series of near surface air temperature data for the period ranging from 1958 to 2010 for five weather observatories were collected from the Rwanda National Meteorological Service. Variations and trends of annual mean temperature time series were examined. The cumulative sum charts (CUSUM) and bootstrapping and the sequential version of the Mann Kendall Rank Statistic were used for the detection of abrupt changes. Regression analysis was performed for the trends and the Mann-Kendall Rank Statistic Test was used for the examination of their significance. Statistically significant abrupt changes and trends have been detected. The major change point in the annual mean temperature occurred around 1977-1979. The analysis of the annual mean temperature showed for all observatories a not very significant cooling trend during the period ranging from 1958 to 1977-1979 while a significant warming trend was furthermore observed for the period after the 1977-1979 where Kigali, the Capital of Rwanda, presented the highest values of the slope (0.0455/year) with high value of coefficient of determination (R2 = 0.6798), the Kendall’s tau statistic (M-K = 0.62), the Kendall Score (S = 328) with a two-sided p-value far less than the confidence level α of 5%). This is most likely explained by the growing population and increasing urbanization and industrialization the country has experienced, especially the Capital City Kigali, during the last decades.
