This paper establishes various results involving functions of integrated processes. Two theorems -that improve similar results by Park and Phillips -are proven for averages of functions of an integrated process that has not been rescaled by the square root of sample size. In addition, two results are given that characterize asymptotic behavior of averages of non-integrable functions of rescaled integrated processes; the observations close to the pole take over asymptotic behavior in that case. Throughout, we make the assumption that the innovations of the integrated process are a linear process.

This study explores the relationship between Asian dust storms (ADSs), asthma hospital admissions and average medical cost discharge. We adopt the hospitalisation data from the Taiwan National Health Insurance research database covering the period from 2000 to 2009. The autoregressive integrated moving average with exogenous variables (ARIMAX) analyses were performed to explore the relationship between ADS and asthma hospital admissions, adjusting for temperature, air pollutants and season dummy. The results show that ADS events do generate a critical influence upon the occurrences of asthma on post-ADS events from days 1 through 3, with an average of 17-20 more hospitalised admissions, and have stronger effects on preschool children, middle-aged people and the elderly. From the perspective of medical expenses, the cost of hospitalised admissions for asthma substantially rises daily, on average, by NT$634,698 to NT$787,407 during ADS event days. This study suggests that government should establish a forecast and alert system and release warnings about dust storms, so that the individuals predisposed to asthma can take precautionary measures to reduce their outdoor exposure. Consequently, personal risk and medical expenditure could be reduced significantly, especially for preschool children, middle-aged people and the elderly with asthma.

The current study illustrated the time variance of turning points in the relationship between carbon emissions and income to resolve heated debate on the different responsibility to climate change with 1950–2010 data of five development diversity countries—three developed countries (Germany, Italy, and Japan) and one developing country (India) and one newly industrialized economy (Taiwan). The article also examines the impact of the crisis on emission. The time-varying patterns in the turning points on environmental Kuznets curves (EKCs) were observed by a rolling regression technique with 1950–2010 data regarding the per capita CO2 emissions caused by fossil fuel combustion and the incomes of the countries. Several empirical findings were revealed from this analysis. Per capita CO2 emissions commonly decreased with varying magnitudes in the five countries over time. The EKC hypothesis regarding the CO2 emissions is affirmed again in this study. The announcement effects associated with the Kyoto Protocol was evidenced. As indicated by the occurring GDP of the turning point, there is a strong reduction trend in the income level of the turning points right before the years of Kyoto Protocol; and this decreasing trend nearly ended as the Kyoto protocol approached its end, except in Germany, where the occurring income of the turning points continued to have a decreasing trend. Although the global financial crisis had its effects in the world, the impacts on carbon dioxide emissions vary across countries.

To clarify the effects of generalized capitals and energy footprint on aggregate incomes and total carbon dioxide emissions, a cross-country panel analysis is applied in the present study. The generalized capitals included in this study are human capital, manufacture capital, natural capitals (as rents of fossil fuels, forest, and minerals). The energy footprint is represented by the primary energy consumption to index the overall domestic energy use. A Cobb–Douglas production function is used to empirically study on a panel of 21 European Union countries. Annual data of rents of natural capitals are used to represent the economic value of natural capitals that flows to the economy. The following are the main findings of this study: (1) Employing human and manufactural capital makes contributions to income growth and carbon reduction. This study’s evidence guides to clarify the misunderstanding of capital and capitalism. Innovations through well-developed and well-managed human and manufactured capital can help sustain income and reduce carbon dioxide emissions. (2) Energy footprint is the vital determinant to total carbon dioxide emissions and hence the most important part of climate policy. (3) The value currently commeasured by monetary terms and compiled by the World Bank is evidenced, not persistently contributed to the income, rather contributed to total carbon dioxide emissions, for the sake of the energy-intensive attributes in the resource-extracting industry. The natural capitals represented by the rent of extracting endowed natural resources can only represent part of the value of natural capitals to human beings. The virtue values of natural capitals in terms of amenity and life supporting are inevitable, but intangible and hence incommensurable. This value is still ignored and unable to enter the contemporary gate of monetary national accounting system.

This paper presents some new results for the nonlinear transformations of the fractional integration process. Specifically, this paper reviews the weight fractional integration process with the Hurst parameter, 3/2 <i>> d ></i> 5/6 , and investigates the asymptotics of asymptotically homogeneous functional transformations of weight fractional integration process. These new results improve upon the earlier research of Tyurin and Phillips [1]