Search results

A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m, eigenvalue restrictions have been proposed as necessary and sufficient restrictions for existence of a unique mth moment of the output of a univariate GARCH process or, equivalently, the 2mth moment of the underlying variable. However, proofs in the literature that an eigenvalue restriction is necessary and sufficient for existence of unique 4th or higher even moments of the underlying variable, are either incorrect, incomplete, or unnecessarily long. Thus, the paper contains a short and general proof that an eigenvalue restriction is necessary and sufficient for existence of a unique 4th moment of the underlying variable of a univariate GARCH process. The paper also derives an expression for computing the 4th moment in terms of the GARCH parameters, which immediately implies a necessary and sufficient inequality restriction for existence of the 4th moment. Because the inequality restriction is easily computed in a finite number of basic arithmetic operations on the GARCH parameters and does not require computing eigenvalues, it provides an easy means for computing “by hand” the 4th moment and for checking its existence for low-dimensional GARCH processes. Finally, the paper illustrates the computations with some GARCH(1,1) processes reported in the literature.

The editors are pleased to offer the following papers to the reader in recognition and appreciation of the contributions to our literature made by Robert Engle and Sir Clive Granger, winners of the 2003 Nobel Prize in Economics. Please see the previous dedication page of this volume. This part of Volume 20 of Advances in Econometric focuses on volatility models. The contributions cover a variety of topics and are organized into three broad categories to aid the reader. The first five papers focus broadly on multivariate Generalised auto-regressive conditional heteroskedasticity (GARCH) models. The first four papers propose new models that enhance existing models, while the final paper proposes a test for multivariate GARCH in the models with non-stationary variables. The next three papers examine topics related to high frequency-data. The first of these papers compares asymptotically mean square error (MSE)-equivalent sampling frequencies and window lengths, while the other two papers in this group consider the problem of estimating volatility in the presence of microstructure noise. The last five papers are contributions relevant primarily to univariate volatility models. Of course, we are also pleased to include Rob's and Clive's remarks on their careers and their views on innovation in econometric theory and practice that were given at the third annual Advances in Econometrics Conference held at Louisiana State University, Baton Rouge, on November 5–7, 2004.

We analyze the sizes of standard cointegration tests applied to data subject to linear interpolation, discovering evidence of substantial size distortions induced by the interpolation. We propose modifications to these tests to effectively eliminate size distortions from such tests conducted on data interpolated from end-of-period sampled low-frequency series. Our results generally do not support linear interpolation when alternatives such as aggregation or mixed-frequency-modified tests are possible.

Communications regarding this column should be addressed to Mrs. Cheney, Peabody Library School, Nashville, Term. 37203. Mrs. Cheney does not sell the books listed here. They are available through normal trade sources. Mrs. Cheney, being a member of the editorial board of Pierian Press, will not review Pierian Press reference books in this column. Descriptions of Pierian Press reference books will be included elsewhere in this publication.

The purpose of this paper is to analyse the 2016 elections for Police and Crime Commissioners (PCCs) and to compare them with those that took place in 2012. It seeks to evaluate the background of the candidates who stood for office in 2016, the policies that they put forward, the results of the contests and the implications of the 2016 experience for future PCC elections.

This paper is based around several key themes – the profile of candidates who stood for election, preparations conducted prior to the contests taking place, the election campaign and issues raised during the contests, the results and the profile of elected candidates. The paper is based upon documentary research, making particular use of primary source material.

The research establishes that affiliation to a political party became the main route for successful candidates in 2016 and that local issues related to low-level criminality will dominate the future policing agenda. It establishes that although turnout was higher than in 2012, it remains low and that further consideration needs to be devoted to initiatives to address this for future PCC election contests.

The research focusses on the 2016 elections and identifies a number of key issues that emerged during the campaign affecting the conduct of the contests which have a bearing on future PCC elections. It treats these elections as a bespoke topic and does not seek to place them within the broader context of the development of the office of PCC.

The research suggests that in order to boost voter participation in future PCC election contests, PCCs need to consider further means to advertise the importance of the role they perform and that the government should play a larger financial role in funding publicity for these elections and consider changing the method of election.

The rationale for introducing PCCs was to empower the public in each police force area. However, issues that include the enhanced importance of political affiliation as a criteria for election in 2016 and the social unrepresentative nature of those who stood for election and those who secured election to this office in these contests coupled with shortcomings related to public awareness of both the role of PCCs and the timing of election contests threaten to undermine this objective.

The extensive use of primary source material ensures that the subject matter is original and its interpretation is informed by an academic perspective.

A distinction must be drawn between a dismissal on the one hand, and on the other a repudiation of a contract of employment as a result of a breach of a fundamental term of that contract. When such a repudiation has been accepted by the innocent party then a termination of employment takes place. Such termination does not constitute dismissal (see London v. James Laidlaw & Sons Ltd (1974) IRLR 136 and Gannon v. J. C. Firth (1976) IRLR 415 EAT).