Computational Aspects of Maximum Likelihood Estimation of Autoregressive Fractionally Integrated Moving Average Models

We discuss computational aspects of likelihood-based estimation of univariate ARFIMA (p,d,q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.Long memory, Bias, Modified profile likelihood, Restricted maximum likelihood estimator, Time-series regression model likelihood

Multimodality in the GARCH Regression Model

Several aspects of GARCH(p,q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model is presented, and it is shown how these can then be implemented by parameter transformations. It is argued that these conditions may also be too restrictive, and a simpler alternative is introduced which is formulated in terms of the unconditional variance. Finally, examples show that multimodality is a real concern for models of the £/$ exchange rate, especially when p>2.Dummy variable, EGARCH, GARCH, Multimodality.

Outlier Detection in GARCH Models

We present a new procedure for detecting multiple additive outliers in GARCH(1,1) models at unknown dates. The outlier candidates are the observations with the largest standardized residual. First, a likelihood-ratio based test determines the presence and timing of an outlier. Next, a second test determines the type of additive outlier (volatility or level). The tests are shown to be similar with respect to the GARCH parameters. Their null distribution can be easily approximated from an extreme value distribution, so that computation of p-values does not require simulation. The procedure outperforms alternative methods, especially when it comes to determining the date of the outlier. We apply the method to returns of the Dow Jones index, using monthly, weekly, and daily data. The procedure is extended and applied to GARCH models with Student-t distributed errors.

Multimodality and the GARCH Likelihood

We investigate several aspects of GARCH models which are relevant for empirical applications. In particular, we note that the inclusion of a dummy variable as regressor can lead to multimodality in the GARCH likelihood. This makes standard inference on the estimated coefficient impossible. Next, we investigate the implementation of different restrictions on the GARCH parameter space. We present a small refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model, and show how these can be implemented by parameter transformations. We argue that these conditions are also too restrictive, and consider restrictions which are formulated in terms of the unconditional variance. These are easier to work with and understand. Finally, we show that multimodality is a real concern for models of the pound/dollar exchange rate, and should be taken account of, especially when p>=2.

The global fight against trans fat: the potential role of international trade and law

Non-communicable diseases in general and cardiovascular diseases in particular are a leading cause of death globally. Trans-fat consumption is a significant risk factor for cardiovascular diseases. The World Health Organization’s ‘REPLACE’ action package of 2018 aims to eliminate it completely in the global food supply by 2023. Legislative and other regulatory actions (i.e., banning trans-fat) are considered as effective means to achieve such a goal. Both wealthier and poorer countries are taking or considering action, as shown by the United States food regulations and Cambodian draft food legislation discussed in this paper. This paper reviews these actions and examines public and private stakeholders’ incentives to increase health-protecting or health-promoting standards and regulations at home and abroad, setting the ground for further research on the topic. It focuses on the potential of trade incentives as a potential driver of a ‘race to the top’. While it has been documented that powerful countries use international trade instruments to weaken other countries’ national regulations, at times these powerful countries may also be interested in more stringent regulations abroad to protect their exports from competition from third countries with less stringent regulations. This article explores practical and principled considerations on how such a dynamic may spread trans-fat restrictions globally. It argues that trade dynamics and public health considerations within powerful countries may help to promote anti-trans-fat regulation globally but will not be sufficient and is ethically questionable. True international regulatory cooperation is needed and could be facilitated by the World Health Organization. Nevertheless, the paper highlights that international trade and investment law offers opportunities for anti-trans-fat policy diffusion globally

The Principal Element of a Frobenius Lie Algebra

We introduce the notion of the \textit{principal element} of a Frobenius Lie algebra \f. The principal element corresponds to a choice of F\in \f^* such that $F[-,-]$ non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to \sl_n, its eigenvalues are integers and are independent of $F$. For certain ``small'' functionals $F$, a simple construction is given which readily yields the principal element. When applied to the first maximal parabolic subalgebra of \sl_n, the principal element coincides with semisimple element of the principal three-dimensional subalgebra. We also show that Frobenius algebras are stable under deformation.Comment: 10 page

An Hourly Periodic State Space Model for Modelling French National Electricity Load

We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for each hour of the day. Dependence between the equations is introduced by covariances between disturbances that drive the time-varying processes. The equations are estimated simultaneously. Our model consists of components that represent trends, seasons at different levels (yearly, weekly, daily, special days and holidays), short-term dynamics and weather regression effects including nonlinear functions for heating effects. The implementation of our forecasting procedure relies on the multivariate linear Gaussian state space framework and is applied to national French hourly electricity load. The analysis focuses on two hours, 9 AM and 12 AM, but forecasting results are presented for all twenty-four hours. Given the time series length of nine years of hourly observations, many features of our model can be readily estimated including yearly patterns and their time-varying nature. The empirical analysis involves an out-of sample forecasting assessment up to seven days ahead. The one-day ahead forecasts from fourty-eight bivariate models are compared with twenty-four univariate models for all hours of the day. We find that the implied forecasting function strongly depends on the hour of the day

Evaluation of Labeling Strategies for Rotating Maps

We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with one corner to its respective point. We require that each label remains horizontally aligned during the map rotation and our goal is to find a set of mutually non-overlapping active labels for every rotation angle $\alpha \in [0, 2\pi)$ so that the number of active labels over a full map rotation of 2$\pi$ is maximized. We discuss and experimentally evaluate several labeling models that define additional consistency constraints on label activities in order to reduce flickering effects during monotone map rotation. We introduce three heuristic algorithms and compare them experimentally to an existing approximation algorithm and exact solutions obtained from an integer linear program. Our results show that on the one hand low flickering can be achieved at the expense of only a small reduction in the objective value, and that on the other hand the proposed heuristics achieve a high labeling quality significantly faster than the other methods.Comment: 16 pages, extended version of a SEA 2014 pape