On the Robustness of Ljung-Box and McLeod-Li Q Tests: A Simulation Study

In financial time series analysis, serial correlations and the volatility clustering effect of asset returns are commonly checked by Ljung-Box and McLeod-Li Q tests and filtered by ARMA-GARCH models. However, this simulation study shows that both the size and power performance of these two tests are not robust to heavily tailed data. Further, these Q tests may reject processes without ARMA-GARCH structures simply because of nonlinearity and conditionally heteroskedastic higher-order moments. These results imply that, to avoid misleading interpretations on time series data, these two tests should be used with care in practical applications.ARMA-GARCH

A Generalized Jarque-Bera Test of Conditional Normality

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test

Laser scanner jitter characterization, page content analysis for optimal rendering, and understanding image graininess

In Chapter 1, the electrophotographic (EP) process is widely used in imaging systems such as laser printers and office copiers. In the EP process, laser scanner jitter is a common artifact that mainly appears along the scan direction due to the condition of polygon facets. Prior studies have not focused on the periodic characteristic of laser scanner jitter in terms of the modeling and analysis. This chapter addresses the periodic characteristic of laser scanner jitter in the mathematical model. In the Fourier domain, we derive an analytic expression for laser scanner jitter in general, and extend the expression assuming a sinusoidal displacement. This leads to a simple closed-form expression in terms of Bessel functions of the first kind. We further examine the relationship between the continuous-space halftone image and the periodic laser scanner jitter. The simulation results show that our proposed mathematical model predicts the phenomenon of laser scanner jitter effectively, when compared to the characterization using a test pattern, which consists of a flat field with 25% dot coverage However, there is some mismatches between the analytical spectrum and spectrum of the processed scanned test target. We improve experimental results by directly estimating the displacement instead of assuming a sinusoidal displacement. This gives a better prediction of the phenomenon of laser scanner jitter. ^ In Chapter 2, we describe a segmentation-based object map correction algorithm, which can be integrated in a new imaging pipeline for laser electrophotographic (EP) printers. This new imaging pipeline incorporates the idea of object-oriented halftoning, which applies different halftone screens to different regions of the page, to improve the overall print quality. In particular, smooth areas are halftoned with a low-frequency screen to provide more stable printing; whereas detail areas are halftoned with a high-frequency screen, since this will better reproduce the object detail. In this case, the object detail also serves to mask any print defects that arise from the use of a high frequency screen. These regions are defined by the initial object map, which is translated from the page description language (PDL). However, the information of object type obtained from the PDL may be incorrect. Some smooth areas may be labeled as raster causing them to be halftoned with a high frequency screen, rather than being labeled as vector, which would result in them being rendered with a low frequency screen. To correct the misclassification, we propose an object map correction algorithm that combines information from the incorrect object map with information obtained by segmentation of the continuous-tone RGB rasterized page image. Finally, the rendered image can be halftoned by the object-oriented halftoning approach, based on the corrected object map. Preliminary experimental results indicate the benefits of our algorithm combined with the new imaging pipeline, in terms of correction of misclassification errors. ^ In Chapter 3, we describe a study to understand image graininess. With the emergence of the high-end digital printing technologies, it is of interest to analyze the nature and causes of image graininess in order to understand the factors that prevent high-end digital presses from achieving the same print quality as commercial offset presses. We want to understand how image graininess relates to the halftoning technology and marking technology. This chapter provides three different approaches to understand image graininess. First, we perform a Fourier-based analysis of regular and irregular periodic, clustered-dot halftone textures. With high-end digital printing technology, irregular screens can be considered since they can achieve a better approximation to the screen sets used for commercial offset presses. This is due to the fact that the elements of the periodicity matrix of an irregular screen are rational numbers, rather than integers, which would be the case for a regular screen. From the analytical results, we show that irregular halftone textures generate new frequency components near the spectrum origin; and these frequency components are low enough to be visible to the human viewer. However, regular halftone textures do not have these frequency components. In addition, we provide a metric to measure the nonuniformity of a given halftone texture. The metric indicates that the nonuniformity of irregular halftone textures is higher than the nonuniformity of regular halftone textures. Furthermore, a method to visualize the nonuniformity of given halftone textures is described. The analysis shows that irregular halftone textures are grainier than regular halftone textures. Second, we analyze the regular and irregular periodic, clustered-dot halftone textures by calculating three spatial statistics. First, the disparity between lattice points generated by the periodicity matrix, and centroids of dot clusters are considered. Next, the area of dot clusters in regular and irregular halftone textures is considered. Third, the compactness of dot clusters in the regular and irregular halftone textures is calculated. The disparity of between centroids of irregular dot clusters and lattices points generated by the irregular screen is larger than the disparity of between centroids of regular dot clusters and lattices points generated by the regular screen. Irregular halftone textures have higher variance in the histogram of dot-cluster area. In addition, the compactness measurement shows that irregular dot clusters are less compact than regular dot clusters. But, a clustered-dot halftone algorithm wants to produce clustered-dot as compact as possible. Lastly, we exam the current marking technology by printing the same halftone pattern on different substrates, glossy and polyester media. The experimental results show that the current marking technology provides better print quality on glossy media than on polyester media. With above three different approaches, we conclude that the current halftoning technology introduces image graininess in the spatial domain because of the non-integer elements in the periodicity matrix of the irregular screen and the finite addressability of the marking engine. In addition, the geometric characteristics of irregular dot clusters is more irregular than the geometric characteristics of regular dot clusters. Finally, the marking technology provides inconsistency of print quality between substrates

An Empirical Study of Language Use and Code-mixing in Amis

This study investigates Amis language use and Amis-Chinese code-mixing using naturally occurring data and inferential statistics. The results indicate that there is a statistically significant difference between age and language use. The younger an Amis person is, the less Amis he or she speaks. This shift becomes apparent from the birth cohort of 1961 to 1970, and their language ability in Amis and their frequency of speaking Amis sharply deteriorates as age decreases. Among all types of code-mixing defined by Muysken (2000), insertion is the most common among Amis-Chinese bilinguals, irrespective of their age or generation. This is typical for two typologically different languages as Amis and Chinese. The insertion of Chinese into Amis structure is more prevalent than inserting Amis into Chinese structure, and a significant difference is found between age and preferred structure. The most typical elements used in noun phrases referring to things, followed by name, time, and kinship