This paper analyzes the problem of testing for parameters change in ARCH errors models with deterministic trend based on residual cusum test. It is shown that the asymptotically limiting distribution of the residual c...This paper analyzes the problem of testing for parameters change in ARCH errors models with deterministic trend based on residual cusum test. It is shown that the asymptotically limiting distribution of the residual cusum test statistic is still the sup of a standard Brownian bridge under null hypothesis. In order to check this, we carry out a Monte Carlo simulation and examine the return of IBM data. The results from both simulation and real data analysis support our claim. We also can explain this phenomenon from a theoretical viewpoint that the variance in ARCH model in mainly determined by its parameters.展开更多
It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing b...It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing between a null hypothesis of unifractal fractionally integrated processes and an alternative hypothesis of other processes which display the long memory property. The procedure is based on a pair of empirical, but consistently defined, statistics namely the number of breaks reported by Atheoretical Regression Trees (ART) and the range of the Empirical Fluctuation Process (EFP) in the CUSUM test. The new procedure establishes through simulation the bivariate distribution of the number of breaks reported by ART with the CUSUM range for simulated fractionally integrated series. This bivariate distribution is then used to empirically construct a test which rejects the null hypothesis for a candidate series if its pair of statistics lies on the periphery of the bivariate distribution determined from simulation under the null. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average and show that the rejection rate of the null is higher than if either statistic was used as a univariate test.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
In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics construct...In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge. The test statistics are evaluated by some empirical results.展开更多
On testing for no effect of a predictor on response variable, some tests have been proposed in the literature. In this paper, one of them being a cusum test proposed by Buckley[1] is studied further. This test can be ...On testing for no effect of a predictor on response variable, some tests have been proposed in the literature. In this paper, one of them being a cusum test proposed by Buckley[1] is studied further. This test can be extended to treating the non-normal and time series cases. A Kolmogonov- Smirnov type test is suggested and studied too. The main observation is the link between the statistic and the Brownian bridge. Some small sample experiments are conducted to examine the power of the tests. In some non-normal cases the power is encouraging.展开更多
To detect and estimate a shift in either the mean and the deviation or both for the preliminary analysis, the statistical process control (SPC) tool, the control chart based on the likelihood ratio test (LRT), is the ...To detect and estimate a shift in either the mean and the deviation or both for the preliminary analysis, the statistical process control (SPC) tool, the control chart based on the likelihood ratio test (LRT), is the most popular method. Sullivan and woodall pointed out the test statistic lrt(n1, n2) is approximately distributed as x2(2) as the sample size n,n1 and n2 are very large, and the value of n1 = 2,3,..., n - 2 and that of n2 = n - n1. So it is inevitable that n1 or n2 is not large. In this paper the limit distribution of lrt(n1, n2) for fixed n1 or n2 is figured out, and the exactly analytic formulae for evaluating the expectation and the variance of the limit distribution are also obtained. In addition, the properties of the standardized likelihood ratio statistic slr(n1, n) are discussed in this paper. Although slr(n1, n) contains the most important information, slr(i, n)(i≠n1) also contains lots of information. The cumulative sum (CUSUM) control chart can obtain more information in this condition. So we propose two CUSUM control charts based on the likelihood ratio statistics for the preliminary analysis on the individual observations. One focuses on detecting the shifts in location in the historical data and the other is more general in detecting a shift in either the location and the scale or both. Moreover, the simulated results show that the proposed two control charts are, respectively, superior to their competitors not only in the detection of the sustained shifts but also in the detection of some other out-of-control situations considered in this paper.展开更多
基金the National Natural Science Foundation of China (Nos.60375003 60972150)the Science and Technology Innovation Foundation of Northwestern Polytechnical University (No.2007KJ01033)
文摘This paper analyzes the problem of testing for parameters change in ARCH errors models with deterministic trend based on residual cusum test. It is shown that the asymptotically limiting distribution of the residual cusum test statistic is still the sup of a standard Brownian bridge under null hypothesis. In order to check this, we carry out a Monte Carlo simulation and examine the return of IBM data. The results from both simulation and real data analysis support our claim. We also can explain this phenomenon from a theoretical viewpoint that the variance in ARCH model in mainly determined by its parameters.
文摘It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing between a null hypothesis of unifractal fractionally integrated processes and an alternative hypothesis of other processes which display the long memory property. The procedure is based on a pair of empirical, but consistently defined, statistics namely the number of breaks reported by Atheoretical Regression Trees (ART) and the range of the Empirical Fluctuation Process (EFP) in the CUSUM test. The new procedure establishes through simulation the bivariate distribution of the number of breaks reported by ART with the CUSUM range for simulated fractionally integrated series. This bivariate distribution is then used to empirically construct a test which rejects the null hypothesis for a candidate series if its pair of statistics lies on the periphery of the bivariate distribution determined from simulation under the null. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average and show that the rejection rate of the null is higher than if either statistic was used as a univariate test.
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.
基金supported by National Natural Science Foundation of China(Grant Nos.10901100 and 11071045)
文摘In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge. The test statistics are evaluated by some empirical results.
基金the National Natural Sciences Foundation of China a Grant from the United College of Chinese University of Hong Kong
文摘On testing for no effect of a predictor on response variable, some tests have been proposed in the literature. In this paper, one of them being a cusum test proposed by Buckley[1] is studied further. This test can be extended to treating the non-normal and time series cases. A Kolmogonov- Smirnov type test is suggested and studied too. The main observation is the link between the statistic and the Brownian bridge. Some small sample experiments are conducted to examine the power of the tests. In some non-normal cases the power is encouraging.
基金This work was supported by the Natural Science Foundation of Tianjin (Grant No. 033603111).
文摘To detect and estimate a shift in either the mean and the deviation or both for the preliminary analysis, the statistical process control (SPC) tool, the control chart based on the likelihood ratio test (LRT), is the most popular method. Sullivan and woodall pointed out the test statistic lrt(n1, n2) is approximately distributed as x2(2) as the sample size n,n1 and n2 are very large, and the value of n1 = 2,3,..., n - 2 and that of n2 = n - n1. So it is inevitable that n1 or n2 is not large. In this paper the limit distribution of lrt(n1, n2) for fixed n1 or n2 is figured out, and the exactly analytic formulae for evaluating the expectation and the variance of the limit distribution are also obtained. In addition, the properties of the standardized likelihood ratio statistic slr(n1, n) are discussed in this paper. Although slr(n1, n) contains the most important information, slr(i, n)(i≠n1) also contains lots of information. The cumulative sum (CUSUM) control chart can obtain more information in this condition. So we propose two CUSUM control charts based on the likelihood ratio statistics for the preliminary analysis on the individual observations. One focuses on detecting the shifts in location in the historical data and the other is more general in detecting a shift in either the location and the scale or both. Moreover, the simulated results show that the proposed two control charts are, respectively, superior to their competitors not only in the detection of the sustained shifts but also in the detection of some other out-of-control situations considered in this paper.
