In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown ...In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.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
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
This study tests the hysteresis hypothesis of unemployment in fifteen OECD countries by using panel unit root tests which allow for structural breaks. We apply annual unemployment rates covering 1985-2008 periods. We ...This study tests the hysteresis hypothesis of unemployment in fifteen OECD countries by using panel unit root tests which allow for structural breaks. We apply annual unemployment rates covering 1985-2008 periods. We test whether unemployment rates are stationary by using second generation tests which allow cross section dependency among series and panel unit root test based on structural break advanced by Carrion-i-Silvestre, Barrio-Castro and Lopez-Bazo （2005）. We find series as a stationary process with structural breaks according to Carrion-i Silvestre et al. （2005） test, while we find series as unit root process with second generation panel unit root test. According to the Carrion-i Silvestre et al. （2005） test, we find the evidence of absence of hysteresis in analyzed countries. As a result, temporary shocks have temporary effects on unemployment instead of permanent effect. Structural factors can affect the natural rate of unemployment and, therefore, unemployment would be stationary around a process that is subject to structural breaks. So, there still exists a unique natural rate of unemployment to which the economy eventually will converge.展开更多
Concession contracts in highways often include some kind of clauses （for example, a minimum traffic guarantee） that allow for better management of the business risks. The value of these clauses may be important and ...Concession contracts in highways often include some kind of clauses （for example, a minimum traffic guarantee） that allow for better management of the business risks. The value of these clauses may be important and should be added to the total value of the concession. However, in these cases, traditional valuation techniques, like the NPV （net present value） of the project, are insufficient. An alternative methodology for the valuation of highway concession is one based on the real options approach. This methodology is generally built on the assumption of the evolution of traffic volume as a GBM （geometric Brownian motion）, which is the hypothesis analyzed in this paper. First, a description of the methodology used for the analysis of the existence of unit roots （i.e., the hypothesis of non-stationarity） is provided. The Dickey-Fuller approach has been used, which is the most common test for this kind of analysis. Then this methodology is applied to perform a statistical analysis of traffic series in Spanish toll highways. For this purpose, data on the AADT （annual average daily traffic） on a set of highways have been used. The period of analysis is around thirty years in most cases. The main outcome of the research is that the hypothesis that traffic volume follows a GBM process in Spanish toll highways cannot be rejected. This result is robust, and therefore it can be used as a starting point for the application of the real options theory to assess toll highway concessions.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
This study investigates the convergence hypothesis and stochastic dynamics of agricultural land use and ecological balance across 13 major agricultural countries from 1992 to 2022.The study's concentrated samples ...This study investigates the convergence hypothesis and stochastic dynamics of agricultural land use and ecological balance across 13 major agricultural countries from 1992 to 2022.The study's concentrated samples are Russia,the United States,the Netherlands,Brazil,Germany,China,France,Spain,Italy,Canada,Belgium,Indonesia,and India.The research uncovers notable variations in ecological balance by utilizing a comprehensive set of advanced panel unit root tests(Panel CIPS,CADF,Panel-LM,Panel-KPSS,and Bahmani-Oskooee et al.’s Panel KPSS Unit Root Test).The findings highlight significant improvements in Canada,contrasting with declines in the Netherlands,France,Germany,and the United States.The results indicate convergence in ecological balance among these countries,suggesting that agricultural practices are progressively aligning with sustainability objectives.The considered countries can determine and enact joint and collective policy actions addressing cropland sustainability.However,the univariate outcome also shows that the cropland ecological balance of Germany,China,France,Indonesia,and India does contain a unit root and stationary which means the presence of the constant-mean.The univariate actions from the mentioned governments will not promote persistent impact.Therefore,joint actions determined by the countries considered are recommended for the mentioned countries.However,the rest of the countries also enact local policies.The insights gained are critical for informing global sustainability strategies and aiding policymakers in developing effective measures to enhance agricultural practices and mitigate environmental impacts.This research provides a data-driven foundation for optimizing agricultural sustainability and supports international efforts to achieve long-term ecological stability.展开更多
This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly...This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly correlated with returns.To this end,we propose a robust test which can capture empirical phenomena such as heavy tails,stationary,and local to unity.Moreover,we develop related asymptotic results without the second-moment assumption between the predictive variable and returns.To make the proposed test reasonable,we propose a generalized correlation and provide theoretical support.To illustrate the applicability of the test,we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon.Finally,we provide an empirical study for further illustration,to which the proposed test is applied to a U.S.equity data set.展开更多
A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is ...A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the Jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside the unit circle and hence on the unit circle is directly determined from the proposed single modified Jury tabulation and the sign criterion. The proposed scheme is simple and the examples are given to bring out the merits of the proposed scheme which is also applicable for the singular and non-singular cases.展开更多
基金Supported by the National Natural Science Foundation of China(10801118)Specialized Research Fund for the Doctor Program of Higher Education(200803351094)
文摘In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.
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.
文摘This study tests the hysteresis hypothesis of unemployment in fifteen OECD countries by using panel unit root tests which allow for structural breaks. We apply annual unemployment rates covering 1985-2008 periods. We test whether unemployment rates are stationary by using second generation tests which allow cross section dependency among series and panel unit root test based on structural break advanced by Carrion-i-Silvestre, Barrio-Castro and Lopez-Bazo （2005）. We find series as a stationary process with structural breaks according to Carrion-i Silvestre et al. （2005） test, while we find series as unit root process with second generation panel unit root test. According to the Carrion-i Silvestre et al. （2005） test, we find the evidence of absence of hysteresis in analyzed countries. As a result, temporary shocks have temporary effects on unemployment instead of permanent effect. Structural factors can affect the natural rate of unemployment and, therefore, unemployment would be stationary around a process that is subject to structural breaks. So, there still exists a unique natural rate of unemployment to which the economy eventually will converge.
文摘Concession contracts in highways often include some kind of clauses （for example, a minimum traffic guarantee） that allow for better management of the business risks. The value of these clauses may be important and should be added to the total value of the concession. However, in these cases, traditional valuation techniques, like the NPV （net present value） of the project, are insufficient. An alternative methodology for the valuation of highway concession is one based on the real options approach. This methodology is generally built on the assumption of the evolution of traffic volume as a GBM （geometric Brownian motion）, which is the hypothesis analyzed in this paper. First, a description of the methodology used for the analysis of the existence of unit roots （i.e., the hypothesis of non-stationarity） is provided. The Dickey-Fuller approach has been used, which is the most common test for this kind of analysis. Then this methodology is applied to perform a statistical analysis of traffic series in Spanish toll highways. For this purpose, data on the AADT （annual average daily traffic） on a set of highways have been used. The period of analysis is around thirty years in most cases. The main outcome of the research is that the hypothesis that traffic volume follows a GBM process in Spanish toll highways cannot be rejected. This result is robust, and therefore it can be used as a starting point for the application of the real options theory to assess toll highway concessions.
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This study investigates the convergence hypothesis and stochastic dynamics of agricultural land use and ecological balance across 13 major agricultural countries from 1992 to 2022.The study's concentrated samples are Russia,the United States,the Netherlands,Brazil,Germany,China,France,Spain,Italy,Canada,Belgium,Indonesia,and India.The research uncovers notable variations in ecological balance by utilizing a comprehensive set of advanced panel unit root tests(Panel CIPS,CADF,Panel-LM,Panel-KPSS,and Bahmani-Oskooee et al.’s Panel KPSS Unit Root Test).The findings highlight significant improvements in Canada,contrasting with declines in the Netherlands,France,Germany,and the United States.The results indicate convergence in ecological balance among these countries,suggesting that agricultural practices are progressively aligning with sustainability objectives.The considered countries can determine and enact joint and collective policy actions addressing cropland sustainability.However,the univariate outcome also shows that the cropland ecological balance of Germany,China,France,Indonesia,and India does contain a unit root and stationary which means the presence of the constant-mean.The univariate actions from the mentioned governments will not promote persistent impact.Therefore,joint actions determined by the countries considered are recommended for the mentioned countries.However,the rest of the countries also enact local policies.The insights gained are critical for informing global sustainability strategies and aiding policymakers in developing effective measures to enhance agricultural practices and mitigate environmental impacts.This research provides a data-driven foundation for optimizing agricultural sustainability and supports international efforts to achieve long-term ecological stability.
基金The research of WONG Hsin-Chieh is partially supported by the NSTC(111-2118-M-305-004-MY2)the research of PANG Tian-xiao is partially supported by the National Social Science Foundation of China(21BTJ067)。
文摘This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly correlated with returns.To this end,we propose a robust test which can capture empirical phenomena such as heavy tails,stationary,and local to unity.Moreover,we develop related asymptotic results without the second-moment assumption between the predictive variable and returns.To make the proposed test reasonable,we propose a generalized correlation and provide theoretical support.To illustrate the applicability of the test,we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon.Finally,we provide an empirical study for further illustration,to which the proposed test is applied to a U.S.equity data set.
文摘A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the Jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside the unit circle and hence on the unit circle is directly determined from the proposed single modified Jury tabulation and the sign criterion. The proposed scheme is simple and the examples are given to bring out the merits of the proposed scheme which is also applicable for the singular and non-singular cases.
