A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite...A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite order invertible moving average of order q (MA(q)) is equivalent to an infinite order autoregressive (AR) process. The purpose of this paper is to demonstrate that the concept is not universally true. Thus, a finite order stationary autoregressive process of order p (AR(p)) can be written as an finite order moving average process and a finite order moving average process of order q (MA(q)) can be written as a finite order stationary autoregressive process. The regions of breakdown of concept of duality were determined for p = q = 1,2 using method of moments. The method involves equating non-zero autocovariances of the stationary AR(p) to the equivalent non-zero autocovariances of the invertible MA(p) to determine the region of non-duality. In such region of breakdown in duality, 1) both the Autocorrelation function and the Partial Autocorrelation function of the AR process and MA process cuts off after equal lags 2) a finite AR model can be adequately represented by a finite MA model of equal order and conversely with the same error variance and 3) negative values of the parameters of the AR process are equal in magnitude but opposite in direction to the parameters of the equivalent MA process and conversely. Empirical examples (simulation and real life examples) were used to illustrate these. Therefore, it has been recommended that caution should be exercised in using the concept of duality in time series analysis until future research proves otherwise.展开更多
Reflecting back on higher or world religions in history,the tenets of their doctrines have been male dominating,and they have been characterized by androcentrism.Under a male-dominating religious order,women are often...Reflecting back on higher or world religions in history,the tenets of their doctrines have been male dominating,and they have been characterized by androcentrism.Under a male-dominating religious order,women are often excluded from essential rituals or hierarchy,their role consequently dwindling gradually.Behind this negative view of women,we can find the dichotomous thinking of male practitioners,the distinctions of the holy and secular,spirit and body,reason and emotion,male and female,and good and evil.The sacred world which male priests sought was separated from the secular world,and the purity of their souls could not coexist with their bodies.Men were regarded as having an existence that was pure,sacred,spiritual,good and reasonable,while women were seen as being worldly,fleshly,unwholesome and emotional.The former and the latter could not be compatible or mixed.The former were primary,while the latter were secondary and the object of control or elimination by the former.In this presentation I will introduce a new paradigm based on the practices of Won Buddhism for the development of egalitarian society.展开更多
文摘A widely held view in time series analysis is the concept of duality that a finite order stationary autoregressive process of order p (AR(p)) is equivalent to an infinite order moving average (MA) process and a finite order invertible moving average of order q (MA(q)) is equivalent to an infinite order autoregressive (AR) process. The purpose of this paper is to demonstrate that the concept is not universally true. Thus, a finite order stationary autoregressive process of order p (AR(p)) can be written as an finite order moving average process and a finite order moving average process of order q (MA(q)) can be written as a finite order stationary autoregressive process. The regions of breakdown of concept of duality were determined for p = q = 1,2 using method of moments. The method involves equating non-zero autocovariances of the stationary AR(p) to the equivalent non-zero autocovariances of the invertible MA(p) to determine the region of non-duality. In such region of breakdown in duality, 1) both the Autocorrelation function and the Partial Autocorrelation function of the AR process and MA process cuts off after equal lags 2) a finite AR model can be adequately represented by a finite MA model of equal order and conversely with the same error variance and 3) negative values of the parameters of the AR process are equal in magnitude but opposite in direction to the parameters of the equivalent MA process and conversely. Empirical examples (simulation and real life examples) were used to illustrate these. Therefore, it has been recommended that caution should be exercised in using the concept of duality in time series analysis until future research proves otherwise.
文摘Reflecting back on higher or world religions in history,the tenets of their doctrines have been male dominating,and they have been characterized by androcentrism.Under a male-dominating religious order,women are often excluded from essential rituals or hierarchy,their role consequently dwindling gradually.Behind this negative view of women,we can find the dichotomous thinking of male practitioners,the distinctions of the holy and secular,spirit and body,reason and emotion,male and female,and good and evil.The sacred world which male priests sought was separated from the secular world,and the purity of their souls could not coexist with their bodies.Men were regarded as having an existence that was pure,sacred,spiritual,good and reasonable,while women were seen as being worldly,fleshly,unwholesome and emotional.The former and the latter could not be compatible or mixed.The former were primary,while the latter were secondary and the object of control or elimination by the former.In this presentation I will introduce a new paradigm based on the practices of Won Buddhism for the development of egalitarian society.
