Goodness-of-fit tests for long memory moving average marginal density

This paper addresses the problem of fitting a known density to the marginal error density of a stationary long memory moving average process when its mean is known and unknown. In the case of unknown mean, when mean is estimated by the sample mean, the first order difference between the residual empirical and null distribution functions is known to be asymptotically degenerate at zero, and hence can not be used to fit a distribution up to an unknown mean. In this paper we show that by using a suitable class of estimators of the mean, this first order degeneracy does not occur. We also investigate the large sample behavior of tests based on an integrated square difference between kernel type error density estimators and the expected value of the error density estimator based on errors. The asymptotic null distributions of suitably standardized test statistics are shown to be chi-square with one degree of freedom in both cases of the known and unknown mean. In addition, we discuss the consistency and asymptotic power against local alternatives of the density estimator based test in the case of known mean. A finite sample simulation study of the test based on residual empirical process is also included.     

Asymptotic distributions of some scale estimators in nonlinear models

Often in the robust analysis of regression and time series models there is a need for having a robust scale estimator of a scale parameter of the errors. One often used scale estimator is the median of the absolute residuals s ₁. It is of interest to know its limiting distribution and the consistency rate. Its limiting distribution generally depends on the estimator of the regression and/or autoregressive parameter vector unless the errors are symmetrically distributed around zero. To overcome this difficulty it is then natural to use the median of the absolute differences of pairwise residuals, s ₂, as a scale estimator. This paper derives the asymptotic distributions of these two estimators for a large class of nonlinear regression and autoregressive models when the errors are independent and identically distributed. It is found that the asymptotic distribution of a suitably standardizes s ₂ is free of the initial estimator of the regression/autoregressive parameters. A similar conclusion also holds for s ₁ in linear regression models through the origin and with centered designs, and in linear autoregressive models with zero mean errors.  This paper also investigates the limiting distributions of these estimators in nonlinear regression models with long memory moving average errors. An interesting finding is that if the errors are symmetric around zero, then not only is the limiting distribution of a suitably standardized s ₁ free of the regression estimator, but it is degenerate at zero. On the other hand a similarly standardized s ₂ converges in distribution to a normal distribution, regardless of the errors being symmetric or not. One clear conclusion is that under the symmetry of the long memory moving average errors, the rate of consistency for s ₁ is faster than that of s ₂.     

Examining the success of women of color-owned small and medium-sized enterprises in the United States: A system dynamics perspective

The objective of this study was to unravel the challenges confronting women of color (WoC)-owned small and medium-sized enterprises (SMEs) in the United States. This is based on findings that most WoC-owned SMEs fail within the first few years of establishment. The impact of the global financial crisis resulting from the COVID-19 pandemic on WoC-owned SMEs was also explored. System Dynamics (SD) is a computational modeling approach useful for understanding changes in a system over time and is applied in this study to illustrate WoC entrepreneurs' navigation through the startup and maturation of SMEs. The authors calibrated and validated the model with publicly available data. Findings revealed that more emphasis should be placed on failure reduction in the early years of establishment of these businesses. Also, there is the need for early intervention rather than focusing on the improvement of the successful business exit from the system. Results indicated that the creation of new businesses by WoC after the failure of existing businesses produced an increase in the number of failed enterprises. The authors assert that attention must be paid at the individual level through support to the entrepreneur. This study contributes to the extant literature by providing the first known SD model useful in depicting the SME system for WoC entrepreneurs in the US. The model serves as a potentially useful tool for informing effective policy making, education, and programmatic approaches to support the success of WoC entrepreneurs in the US.