Theory of Bilinear Time Series Models

ABSTRACT

In this paper, we prove some theoretic properties of bilinear time series models which are extension of ARMA models. The sufficient conditions for asymptotic stationarity and ivertibility of some types of bilinear models are derived. The structural theory of discussed bilinear models is similar to that of ARMA models. For illustration, a bilinear model has been fitted to the Wolfer sunspot numbers and a substantial reduction in sum of squared residuals is obtained as comparing with Box-Jenkins ARMA model.     

Tabloids

Abstract

Comic books and libraries do not seem to get along, at least not in North American libraries. Aside from a few dozen specialized, noncirculating research collections, retrospective comic book holdings remain virtually unknown as a library resource.1 Browsing collections of current comic books are equally rare in public, school, and college libraries. In a 1984 article, comic book bibliographer Randall Scott observed, “In most communities, if you want to read or refer to a comic book, you have to buy it.” Librarian Doug Highsmith concurred, writing in 1992 that public libraries carrying the latest issues of popular comics titles are “still the exception rather than the rule.” Both statements remain fundamentally true today.     

A new nonlinear unit root test with Fourier function

Abstract

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an exponential smooth threshold autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse and KSS tests.     

Questions from Newbies—Facilitating Communication and Professional Development: A Case Study

Abstract

For new collection managers, it may be intimidating to ask questions about processes that seem to be common knowledge for their more experienced colleagues. To help with this issue, the Collections & Research Strategy department at North Carolina State University Libraries uses a shared document where new collection managers can log questions as they arise. The questions are shared at regular Collections Interest Group meetings and often generate interesting discussions that librarians both new and experienced can benefit from. This case study will provide an overview of the structure of the document, how it is used, and the types of questions that get asked.     

Robust multivariate diagnostics for PLSR and application on high dimensional spectrally overlapped drug systems

ABSTRACT

Statistical methods are effectively used in the evaluation of pharmaceutical formulations instead of laborious liquid chromatography. However, signal overlapping, nonlinearity, multicollinearity and presence of outliers deteriorate the performance of statistical methods. The Partial Least Squares Regression (PLSR) is a very popular method in the quantification of high dimensional spectrally overlapped drug formulations. The SIMPLS is the mostly used PLSR algorithm, but it is highly sensitive to outliers that also effect the diagnostics. In this paper, we propose new robust multivariate diagnostics to identify outliers, influential observations and points causing non-normality for a PLSR model. We study performances of the proposed diagnostics on two everyday use highly overlapping drug systems: Paracetamol–Caffeine and Doxylamine Succinate–Pyridoxine Hydrochloride.     

Regression analysis of interval-censored failure time data with cured subgroup and mismeasured covariates

Abstract

Failure time data occur in many areas and also in various forms and in particular, many authors have discussed regression analysis of failure time data in the presence of interval censoring, a cured subgroup or mismeasured covariates. However, it does not seem to exist an established procedure that can deal with all three issues together. Corresponding to this, we propose a sieve maximum likelihood estimation procedure that takes into account all three issues with the use of the SIMEX algorithm. The asymptotic properties of the proposed estimators are established, and an extensive simulation study is also conducted and suggests that the proposed method works well for practical situations.     

On the problem of model selection in bilinear time series analyses

One of the problems in bilinear time series (BLTS) analysis is that of identification. Unlike linear models, the identification in BLTS modelling is not always based on the autocorrelation function (or spectrum) since it is sometimes misleading, The authors, therefore., derive in this note the autocorrelation function of a function of a bilinear process which can be used for identification as well as for testing the linearity.     

Hellinger distance estimation of general bilinear time series models

In the present paper, minimum Hellinger distance estimates for parameters of a bilinear time series model are presented. The probabilistic properties such as stationarity, existence of moments of the stationary distribution and strong mixing property of the model are well known (see for instance [J. Liu, A note on causality and invertibility of a general bilinear time series model, Adv. Appl. Probab. 22 (1990) 247–250; J. Liu, P.J. Brockwell, On the general bilinear time series model, J. Appl. Probab. 25 (1988) 553–564; D.T. Pham, The mixing property of bilinear and generalised random coefficients autoregressive models, Stoch. Process Appl. 23 (1986) 291–300]). We establish, under some mild conditions, the consistency and the asymptotic normality of the minimum Hellinger distance estimates of the parameters of the model.     

Full Bayesian Significance Test for Zero-Inflated Distributions

ABSTRACT

In this article we propose a new Kolmogorov-Smirnov type test for testing the nonlinearity of time series, based on the one which was originally introduced by An and Cheng. Our simulation study shows that the suggested test performs better than the original test. An associated bootstrap test is also found to outperform remarkably the non-bootstrap test.     

New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study

ABSTRACT

New invariant and consistent goodness-of-fit tests for multivariate normality are introduced. Tests are based on the Karhunen–Loève transformation of a multidimensional sample from a population. A comparison of simulated powers of tests and other well-known tests with respect to some alternatives is given. The simulation study demonstrates that power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests. However, averaged over all of the simulated conditions examined in this article, the Anderson–Darling type and the Cramer–von Mises type tests seem to be the best.     

On the performance of MixTVEM: a simulation study

Abstract

The mixture of time-varying effect model (MixTVEM) was proposed to handle both nonlinearity and heterogeneity in describing the complex patterns of change over time in the analysis of intensive longitudinal data (ILD). We conducted simulation studies to assess the performance of the MixTVEM. We found that in most cases, the MixTVEM could identify correctly the number of latent classes, as well as reveal accurately the coefficient functions. However, the estimation accuracy and feasibility of the computation could be affected by the sample size. Moreover, the MixTVEM is highly intensive computationally, compared with the original TVEM.     

Comment on state space modeling of multiple time series

This paper raises some interpretative issues that arise from univariate trend–cycle decompositions with correlated disturbances. In particular, it discusses whether the interpretation of a negative correlation as providing evidence for the prominence of real, or supply, shocks, can be supported.

For this purpose it determines the conditions under which correlated components may originate from the underestimation of the cyclical component in an orthogonal decomposition; from the presence of a growth rate cycle, rather than a deviation cycle; or alternatively, as a consequence of the hysteresis phenomenon. Finally, it considers interpreting correlated components in terms of permanent–transitory decompositions, where the permanent component has richer dynamics than a pure random walk.

The consequences for smoothing and signal extraction are discussed: in particular, it is documented that a negative correlation implies that future observations carry most of the information needed to assess cyclical stance. As a result, the components will be subject to underestimation in real time and thus to high revisions. The overall conclusion is that the characterization of economic fluctuations in macroeconomic time series largely remains an open issue.     

Statistical comparisons of methods for interpolating the output of a numerical air quality model

This paper compares Models-3/Community Multiscale Air Quality (CMAQ) outputs at multiple resolutions by interpolating from coarse resolution to fine resolution and analyzing the interpolation difference. Spatial variograms provide a convenient way to investigate the spatial character of interpolation differences and, importantly, to distinguish between naive (nearest neighbor) interpolation and bilinear interpolation, which takes a weighted average of four neighboring cells. For example, when the higher resolution is three times the lower, the variogram of the difference between naive interpolation of the lower resolution output and the higher resolution output shows a depression at every third lag. This phenomenon is related to the blocky nature of naive interpolation and demonstrates the inferiority of naive interpolation to bilinear interpolation in a way that pixelwise comparisons cannot. Theoretical investigations show when one can expect to observe this periodic depression in the variogram of interpolation differences. Naive interpolation is in fact used widely in a number of settings; our results suggest that it should be routinely replaced by bilinear interpolation.     

Large-Scale Replication Projects in Contemporary Psychological Research

ABSTRACT

Replication is complicated in psychological research because studies of a given psychological phenomenon can never be direct or exact replications of one another, and thus effect sizes vary from one study of the phenomenon to the next—an issue of clear importance for replication. Current large-scale replication projects represent an important step forward for assessing replicability, but provide only limited information because they have thus far been designed in a manner such that heterogeneity either cannot be assessed or is intended to be eliminated. Consequently, the nontrivial degree of heterogeneity found in these projects represents a lower bound on the true degree of heterogeneity. We recommend enriching large-scale replication projects going forward by embracing heterogeneity. We argue this is the key for assessing replicability: if effect sizes are sufficiently heterogeneous—even if the sign of the effect is consistent—the phenomenon in question does not seem particularly replicable and the theory underlying it seems poorly constructed and in need of enrichment. Uncovering why and revising theory in light of it will lead to improved theory that explains heterogeneity and increases replicability. Given this, large-scale replication projects can play an important role not only in assessing replicability but also in advancing theory.     

Recursive estimation of bilinear time series models

In this paper we are concerned with the recursive estimation of bilinear models. Some methods from linear time invariant systems are adapted to suit bilinear time series models. The time-varying Kalman filter and associated parameter estimation algorithm is carried on the bilinear time series models. The methods are illustrated with examples.     

SOME REMARKS ON THE INFORMATION GEOMETRY OF THE GAMMA DISTRIBUTION

ABSTRACT

Bounds for the Fisher information metric associated with the Gamma statistical model are found in terms of Poincaré type metric. This results in the determination of bounds for the Rao distance, that is the Riemannian distance induced by the information metric, between Gamma distributions, and of bounds for the Gaussian curvature of the Gamma model. The bounds seem to be sharp, where the lower and upper Rao distance bounds are Poincaré distances with Gaussian curvatures ?1/4 and ?1/2, respectively. In addition, the sign of the Gaussian curvature of the Gamma model is shown to be negative which means, in particular, that the geometry of the model is hyperbolic.     

Data-Informed Collection Decisions Using R

ABSTRACT

Collection decisions can seem daunting to a librarian who is new to the job. In charge of many new-to-her subject fund codes, the author wanted to understand what had been previously purchased using these funds and how to effectively manage a custom ebook collection. The author used the R programming language to clean and merge purchase and usage data. This article will provide an overview of tasks in R that can be leveraged for making data-informed collection decisions and for sharing information with colleagues.     

XML

Abstract

XML offers some significant enhancements and functionality over what can be achieved with HTML. Among them:

o ? XML is a language for defining markup languages. It is not restricted in scope to the fixed tags defined in HTML. Document types can be created that are customized to the application, type of data, and user community for which it is intended.

? Information content can be richer and easier to use, both because of the richer flexibility of tags and the hypertext linking abilities of XML are greater than those offered in HTML.

? Information should be more usable and accessible. Because of the nature of XML, communities will be able to create applications customized to their needs, rather than being restricted to software provided by major vendors as has become the case with HTML.

? XML files are valid SGML. They can be used in SGML environments outside of the Web. At the same time XML has removed many of the complexities inherent in SGML, providing a more simple model and thus making it easier to develop XML applications that would be the case for SGML.

     

Conditional Quantile Estimation for Truncated and Associated Data

Abstract

In survival or reliability studies, it is common to have data which are not only incomplete but weakly dependent too. Random truncation and censoring are two common forms of such data when they are neither independent nor strongly mixing but rather associated. The focus of this paper is on estimating conditional distribution and conditional quantile functions for randomly left truncated data satisfying association condition. We aim at deriving strong uniform consistency rates and asymptotic normality for the estimators and thereby, extend to association case some results stated under iid and α-mixing hypotheses. The performance of the quantile function estimator is evaluated on simulated data sets.