A Mixture Multiplicative Error Model for Realized Volatility

Long-term electricity load forecasting plays a vital role for utilities and planners in terms of grid development and expansion planning. An overestimate of long-term electricity load will result in substantial wasted investment on the construction of excess power facilities, while an underestimate of the future load will result in insufficient generation and inadequate demand. As a first of its kind, this research proposes the use of a multiplicative error model (MEM) in forecasting electricity load for the long-term horizon. MEM originates from the structure of autoregressive conditional heteroscedasticity (ARCH) model where conditional variance is dynamically parameterized and it multiplicatively interacts with an innovation term of time-series. Historical load data, as accessed from a United States (U.S.) regional transmission operator, and recession data, accessed from the National Bureau of Economic Research, are used in this study. The superiority of considering volatility is proven by out-of-sample forecast results as well as directional accuracy during the great economic recession of 2008. Historical volatility is used to account for implied volatility. To incorporate future volatility, backtesting of MEM is performed. Two performance indicators used to assess the proposed model are: (i) loss functions in terms of mean absolute percentage error and mean squared error (for both in-sample model fit and out-of-sample forecasts) and (ii) directional accuracy.

Introduction In the context of non-negative high-frequency financial time series, the multiplicative error model (MEM) is a generalized model. Maximum Likelihood Estimation (MLE) serves as the standard approach for parameter estimation when applying MEM to real-world modeling. This method relies on the assumption that the error term follows a specific known distribution with finite variance. However, directly imposing the assumption of a known distribution with bounded variance entails notable limitations. Methods In this model, a self-weighted M-estimation approach is used to estimate the model parameters. This estimation is performed considering the infinite variance of the model errors. Results On a theoretical level, this estimation proved to have strong consistency and asymptotic normality. The results of the numerical simulations show that self-weighted M-estimation is more robust than other estimation methods. Finally, the self-weighted M-estimation method is applied to the price range of polyethylene and polypropylene futures on the Dalian Commodity Exchange. Discussion The results demonstrate that the self-weighted M-estimation outperforms both maximum likelihood estimation and least absolute deviation estimation. This finding is particularly significant for financial applications, where extreme outliers and infinite-variance events are frequently observed.

In the geodetic data processing field, most methods for dealing with inequality constraints model are based on additive random error (ARE) models, and there have been few studies on mixed additive and multiplicative random error (MAAMRE) models with inequality constraints. To address this problem, a MAAMRE model with inequality constraints is first established based on the definition of inequality constraint equations, and then, a corresponding parameter estimation algorithm is proposed based on the idea of an exhaustive search method. In addition, considering a MAAMRE model for an ill-posed problem, an iterative regularization solution for an ill-posed MAAMRE model is first derived, and then, a specific parameter estimation algorithm for an ill-posed MAAMRE model with inequality constraints is further proposed by applying the exhaustive search approach. Finally, the feasibility and advantages of the proposed algorithms are verified by global positioning system (GPS) elevation fitting model and digital terrain model (DTM) examples.Graphical

This paper discusses the unsupervised learning problem for a mixture of gamma distributions. An important pan of the unsupervised problem is determining the number of components which best describes some data. We apply the minimum message length (MML) criterion to the unsupervised learning problem in the case of a mixture of gamma distributions. We give a comparison of criteria in the literature for estimating the number of components in a data set. The comparison concerns synthetic and RADARSAT SAR images.

Chasing volatility: A persistent multiplicative error model with jumps

A new variant of RealGARCH for volatility modeling

In this chapter, we present generalizations of the basic multiplicative error model as introduced in Chap. 5. Section 6.1 discusses a class of ACD models which can be presented in terms of a generalized polynomial random coefficient model according to Carrasco and Chen (2002). We illustrate various special cases, discuss the theoretical properties and show empirical illustrations. In Sect. 6.2, we consider regime-switching ACD models allowing for parameters which might change in dependence of observable or unobservable characteristics. We concentrate on threshold ACD models, smooth transition ACD models as well as Markov Switching ACD specifications. Section 6.3 focuses on ACD models accommodating long range dependence in the data. In this context, we discuss different possibilities to capture long memory.

Copula-Based Specification of Vector MEMs

This paper is concerned with the issues of modeling and projecting the dynamics of volatility when a group of potentially useful predetermined variables is available. We predict realized volatility and value at risk (VaR) with a nested set of multiplicative error models for realized volatility. We make use of recently proposed focused model selection/combination strategies as well as the classic AIC/BIC. Focused strategies consist of choosing the model that minimizes the estimated MSE of a given function of the parameters of interest to the forecaster. Results show that VaR forecasts can significantly be improved upon using focused prediction strategies. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

Enriched environment enhances left-right asymmetry of the hippocampus

Images segmentation is an important issue for many applications as pattern recognition and computer vision. Thresholding is an important and fast technique used in most applications. Gaussian Otsu's method is a thresholding technique based on between class variance. Gamma distribution models data more than Gaussian distribution. In this paper, we developed a new formula using Otsu's method for estimating the optimal threshold values based on Gamma distribution. Our method applied on bimodal and multimodal images. Also It uses an iteratively rather than sequentially to decrease the number of operations. Further, using Gamma distribution give satisfying thresholding results in low-high contrast images where modes are symmetric or non-symmetric. For our results, we compared it with the original Gaussian Otsu's method.

The technique of image histogram modification can be applied to the problem of image enhancement. Global and local histogram equalisation and local area histogram equalisation are two well-known techniques for the same purpose. In this research work, a new method is proposed to enhance the contrast of bimodal SAR images using histogram specification with Gamma distribution. The method is aimed to read the original image and calculate its original histogram. Then apply the maximum likelihood with Gamma distribution (ML) technique on the original histogram to get accurate statistical parameters as the means and prior probabilities of the two modes. The two estimated modes are thus separated by shifting the first mode to the left or shifting the second mode to the right or performing both shifts. After shifting, a new histogram called 'desired histogram' is generated from a mixture of Gamma distributions using updated data. By applying a histogram specification method, a high contrast SAR image will be produced. The new method of contrast enhancement of SAR image has been applied on bimodal SAR images and showed good results.

A new [formula omitted]-deformed parametric model for the size distribution of wealth

In this paper, the impact of non-Markovian distributed primary radio (PR) on/off activities on the opportunity time for secondary radio (SR) transmission is studied. The licensed spectrum is partitioned into N frequency bins (FBs) and each primary user is assumed to require only one FB for transmission. The PR activity in each FB is modeled as an independent on/off process. The sojourn time for PR activity in the ‘on’ state and in the ‘off’ state is described by the Pareto distribution and the hyper-Erlang distribution, respectively. Numerous cases are examined in this paper. In the first case, we assume the PR activity factors statistically identical in all the FBs. For this case, we examine the scenarios in which the PR traffic is light and also when it is heavy. In the second case, we assume that the PR activity factors between any two FBs are statistically different. Through the performance of extensive simulations, the probability density function (PDF) of the opportunity time is modeled and studied for different number of FBs, which is varied from N=2 to N=10. The goodness-of-fit of the statistical model to the simulated opportunity time is verified by the Kolmogorov-Smirnov test at 5% level of significance. The results show that when the PR activities are statistically identical, the PDF of the opportunity time can be described by a Gamma distribution. However, when the PR activities are statistically different, a hyper-Gamma distribution (mixture of Gamma distributions) provides a very good fit to the PDF of the opportunity time. We highlight the inadequacy of the Exponential and hyper-Exponential distribution fits for the PDF of the opportunity time in these cases. From these modeling results, the opportunity time can be reproduced with relative ease, and its statistics can be exploited for future SR performance studies.

BackgroundDespite sustained economic growth and reduction in money metric poverty in last two decades, prevalence of malnutrition remained high in India. During 1992–2016, the prevalence of underweight among children had declined from 53% to 36%, stunting had declined from 52% to 38% while that of wasting had increased from 17% to 21% in India. The national average in the level of malnutrition conceals large variation across districts of India. Using data from the recent round of National Family Health Survey (NFHS), 2015–16 this paper examined the spatial heterogeneity and meso-scale correlates of child malnutrition across 640 districts of India.MethodsMoran’s I statistics and bivariate LISA maps were used to understand spatial dependence and clustering of child malnutrition. Multiple regression, spatial lag and error models were used to examine the correlates of malnutrition. Poverty, body mass index (BMI) of mother, breastfeeding practices, full immunization, institutional births, improved sanitation and electrification in the household were used as meso scale correlates of malnutrition.ResultsThe univariate Moran’s I statistics was 0.65, 0.51 and 0.74 for stunting, wasting and underweight respectively suggesting spatial heterogeneity of malnutrition in India. Bivariate Moran’s I statistics of stunting with BMI of mother was 0.52, 0.46 with poverty and − 0.52 with sanitation. The pattern was similar with respect to wasting and underweight suggesting spatial clustering of malnutrition against the meso scale correlates in the geographical hotspots of India. Results of spatial error model suggested that the coefficient of BMI of mother and poverty of household were strong and significant predictors of stunting, wasting and underweight. The coefficient of BMI in spatial error model was largest found for underweight (β = 0.38, 95% CI: 0.29–0.48) followed by stunting (β = 0.23, 95% CI: 0.14–0.33) and wasting (β = 0.11, 95% CI: 0.01–0.22). Women’s educational attainment and breastfeeding practices were also found significant for stunting and underweight.ConclusionMalnutrition across the districts of India is spatially clustered. Reduction of poverty, improving women’s education and health, sanitation and child feeding knowledge can reduce the prevalence of malnutrition across India. Multisectoral and targeted intervention in the geographical hotspots of malnutrition can reduce malnutrition in India.