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
This paper explores urban temperature in Hong Kong using long-term time series. In particular, the characterization of the urban temperature trend was investigated using the seasonal unit root analysis of monthly mean...This paper explores urban temperature in Hong Kong using long-term time series. In particular, the characterization of the urban temperature trend was investigated using the seasonal unit root analysis of monthly mean air temperature data over the period January 1970 to December 2013. The seasonal unit root test makes it possible to determine the stochastic trend of monthly temperatures using an autoregressive model. The test results showed that mean air temperature has increased by 0.169~ C （10 yr） - 1 over the past four decades. The model of monthly temperature obtained from the seasonal unit root analysis was able to explain 95.9% of the variance in the measured monthly data -- much higher than the variance explained by the ordinary least-squares model using annual mean air temperature data and other studies alike. The model accurately predicted monthly mean air temperatures between January 2014 and December 2015 with a root-mean-square percentage error of 4.2%. The correlation between the predicted and the measured monthly mean air temperatures was 0.989. By analyzing the monthly air temperatures recorded at an urban site and a rural site, it was found that the urban heat island effect led to the urban site being on average 0.865~C warmer than the rural site over the past two decades. Besides, the results of correlation analysis showed that the increase in annual mean air temperature was significantly associated with the increase in population, gross domestic product, urban land use, and energy use, with the R2 values ranging from 0.37 to 0.43.展开更多
A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being l...A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.展开更多
The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of...The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.展开更多
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.
文摘This paper explores urban temperature in Hong Kong using long-term time series. In particular, the characterization of the urban temperature trend was investigated using the seasonal unit root analysis of monthly mean air temperature data over the period January 1970 to December 2013. The seasonal unit root test makes it possible to determine the stochastic trend of monthly temperatures using an autoregressive model. The test results showed that mean air temperature has increased by 0.169~ C （10 yr） - 1 over the past four decades. The model of monthly temperature obtained from the seasonal unit root analysis was able to explain 95.9% of the variance in the measured monthly data -- much higher than the variance explained by the ordinary least-squares model using annual mean air temperature data and other studies alike. The model accurately predicted monthly mean air temperatures between January 2014 and December 2015 with a root-mean-square percentage error of 4.2%. The correlation between the predicted and the measured monthly mean air temperatures was 0.989. By analyzing the monthly air temperatures recorded at an urban site and a rural site, it was found that the urban heat island effect led to the urban site being on average 0.865~C warmer than the rural site over the past two decades. Besides, the results of correlation analysis showed that the increase in annual mean air temperature was significantly associated with the increase in population, gross domestic product, urban land use, and energy use, with the R2 values ranging from 0.37 to 0.43.
基金supported by the NNSF of China(Grant Nos.11971208 and 11601197)the NNSF of China(Grant No.61973145)+5 种基金the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province(Grant No.20224ACB211003)supported by the Science and Technology Research Project of Education Department of Jiangxi Province(Grant No.GJJ200545)the Postgraduate Innovation Project of Jiangxi Province(Grant No.YC2021–B124)NSSF of China(Grant No.21BTJ035)supported by the National Major Social Science Project of China(Grant No.21&ZD152)Natural Science Project of Jiangxi Provincial Department of Science and Technology(Grant No.jxsq2023201048)。
文摘A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.
文摘The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.
