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
Self inversion issue and excess capacitance phenomenon were observed for the first time in relatively thick silicon dioxide (SiO2) in the form of MOS (metal(Al)/SiO2/p type crystalline silicon) structure. Both phenome...Self inversion issue and excess capacitance phenomenon were observed for the first time in relatively thick silicon dioxide (SiO2) in the form of MOS (metal(Al)/SiO2/p type crystalline silicon) structure. Both phenomena were based on minority carriers (electrons in this case) and studied through DC current-applied bias voltage (I-V) and AC admittance measurements in dark/light condition as a function of ambient temperature (295 - 380 K). Either of the cases was the departure of traditional MOS analysis, manifesting themselves in the inversion regime of MOS diode. Increase in frequency/temperature/light intensity within dark and light conditions led to weaken the maxima of hump in C-V curves and finally turned into deep depletion mode after exceeding threshold value of frequency/temperature/light intensity. In resumed conditions, supplementary I-V measurements were carried out to describe the generation and conduction mechanism(s) for minority carriers (electrons).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.
基金This work is financially supported by Yildiz Technical University projects under a contract of 2012-01-01-DOP04 and 2011-01-01-KAP03.
文摘Self inversion issue and excess capacitance phenomenon were observed for the first time in relatively thick silicon dioxide (SiO2) in the form of MOS (metal(Al)/SiO2/p type crystalline silicon) structure. Both phenomena were based on minority carriers (electrons in this case) and studied through DC current-applied bias voltage (I-V) and AC admittance measurements in dark/light condition as a function of ambient temperature (295 - 380 K). Either of the cases was the departure of traditional MOS analysis, manifesting themselves in the inversion regime of MOS diode. Increase in frequency/temperature/light intensity within dark and light conditions led to weaken the maxima of hump in C-V curves and finally turned into deep depletion mode after exceeding threshold value of frequency/temperature/light intensity. In resumed conditions, supplementary I-V measurements were carried out to describe the generation and conduction mechanism(s) for minority carriers (electrons).
