Search results for: LBP variance

Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

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Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: variance, lower semi-variance, range-based volatility, MPT

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Saba Riaz, Syed A. Hussain

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This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: V. Rao, A. Bedford

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As the efficient performance of national grid becomes increasingly important to maintain the electrical network stability, the balance between the generation and the demand must be effectively maintained. To do this, any losses that occur in the power network must be reduced by compensating for it. In this paper, one of the main cause for the losses in the network is identified as the variance, which hinders the grid’s power carrying capacity. The reason for the variance in the grid is investigated and identified as the rise in the integration of renewable energy sources (RES) such as wind and solar power. The intermittent nature of these RES along with fluctuating demands gives rise to variance in the electrical network. The losses that occur during this process is estimated by analyzing the network’s power profiles. Whilst researchers have identified different ways to tackle this problem, little consideration is given to energy storage. This paper seeks to redress this by considering the role of energy storage systems as potential solutions to reduce variance in the network. The implementation of suitable energy storage systems based on different applications is presented in this paper as part of variance reduction method and thus contribute towards maintaining a stable and efficient grid operation.

Keywords: energy storage, electrical losses, national grid, renewable energy, variance

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Authors: Rihab Belguith, Fathi Abid

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The paper develops a system-based approach to investigate the dynamic adjustment of debt structure and investment policies of the Dow-Jones index. This approach enables the assessment of relations among sales, debt, and investment opportunities by considering the simultaneous effect of the market environmental change and future growth opportunities. We integrate the firm-specific sales variance to capture the industries' conditions in the model. Empirical results were obtained through a panel data set of firms with different sectors. The analysis support that environmental change does not affect equally the different industry since operating leverage differs among industries and so the sensitivity to sales variance. Including adjusted-specific variance, we find that there is no monotonic relation between leverage, sales, and investment. The firm may choose a low debt level in response to high sales variance but high leverage to attenuate the negative relation between sales variance and the current level of investment. We further find that while the overall effect of debt maturity on leverage is unaffected by the level of growth opportunities, the shorter the maturity of debt is, the smaller the direct effect of sales variance on investment.

Keywords: dynamic panel, investment, leverage decision, sales uncertainty

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Authors: Raghunath Arnab

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The two-phase sampling which is also known as double sampling was introduced in 1938. In two-phase sampling, samples are selected in phases. In the first phase, a relatively large sample of size is selected by some suitable sampling design and only information on the auxiliary variable is collected. During the second phase, a sample of size is selected either from, the sample selected in the first phase or from the entire population by using a suitable sampling design and information regarding the study and auxiliary variable is collected. Evidently, two phase sampling is useful if the auxiliary information is relatively easy and cheaper to collect than the study variable as well as if the strength of the relationship between the variables and is high. If the sample is selected in more than two phases, the resulting sampling design is called a multi-phase sampling. In this article we will consider how one can use data collected at the first phase sampling at the stages of estimation of the parameter, stratification, selection of sample and their combinations in the second phase in a unified setup applicable to any sampling design and wider classes of estimators. The problem of the estimation of variance will also be considered. The variance of estimator is essential for estimating precision of the survey estimates, calculation of confidence intervals, determination of the optimal sample sizes and for testing of hypotheses amongst others. Although, the variance is a non-negative quantity but its estimators may not be non-negative. If the estimator of variance is negative, then it cannot be used for estimation of confidence intervals, testing of hypothesis or measure of sampling error. The non-negativity properties of the variance estimators will also be studied in details.

Keywords: auxiliary information, two-phase sampling, varying probability sampling, unbiased estimators

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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Performance of different filtering approaches depends on modeling of dynamical system and algorithm structure. For modeling and smoothing the data the evaluation of posterior distribution in different filtering approach should be chosen carefully. In this paper different filtering approaches like filter KALMAN, EKF, UKF, EKS and smoother RTS is simulated in some trajectory tracking of path and accuracy and limitation of these approaches are explained. Then probability of model with different filters is compered and finally the effect of the noise variance to estimation is described with simulations results.

Keywords: Gaussian approximation, Kalman smoother, parameter estimation, noise variance

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: evolutionary algorithms, portfolio optimization, skewness, stock selection

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: noise, signal-to-noise ratio, stochastic signals, variance estimation

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Authors: Jai Heui Kim, Sotheara Veng

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This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously.

Keywords: asymptotic analysis, constant elasticity of variance, portfolio optimization, stochastic optimal control, stochastic volatility

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Authors: Pei-Chen Wu

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Both preexisting cross-sectional and longitudinal studies of personality-depression relationship have suffered from one main limitation: they ignored the stability of the construct of interest (e.g., personality and depression) can be expected to influence the estimate of the association between personality and depression. To address this limitation, the Trait-State-Occasion (TSO) modeling was adopted to analyze the sources of variance of the focused constructs. A TSO modeling was operated by partitioning a state variance into time-invariant (trait) and time-variant (occasion) components. Within a TSO framework, it is possible to predict change on the part of construct that really changes (i.e., time-variant variance), when controlling the trait variances. 750 high school students were followed for 4 waves over six-month intervals. The baseline data (T1) were collected from the senior high schools (aged 14 to 15 years). Participants were given Beck Depression Inventory and Big Five Inventory at each assessment. TSO modeling revealed that 70~78% of the variance in personality (five constructs) was stable over follow-up period; however, 57~61% of the variance in depression was stable. For personality construct, there were 7.6% to 8.4% of the total variance from the autoregressive occasion factors; for depression construct there were 15.2% to 18.1% of the total variance from the autoregressive occasion factors. Additionally, results showed that when controlling initial symptom severity, the time-invariant components of all five dimensions of personality were predictive of change in depression (Extraversion: B= .32, Openness: B = -.21, Agreeableness: B = -.27, Conscientious: B = -.36, Neuroticism: B = .39). Because five dimensions of personality shared some variance, the models in which all five dimensions of personality were simultaneous to predict change in depression were investigated. The time-invariant components of five dimensions were still significant predictors for change in depression (Extraversion: B = .30, Openness: B = -.24, Agreeableness: B = -.28, Conscientious: B = -.35, Neuroticism: B = .42). In sum, the majority of the variability of personality was stable over 2 years. Individuals with the greater tendency of Extraversion and Neuroticism have higher degrees of depression; individuals with the greater tendency of Openness, Agreeableness and Conscientious have lower degrees of depression.

Keywords: assessment, depression, personality, trait-state-occasion model

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Authors: Bastien Batardière, Joon Kwon

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For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.

Keywords: convex optimization, variance reduction, adaptive algorithms, loopless

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: temporal differencing, video summarization, histogram differencing, sum conditional variance

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Authors: Byung Cheol Kim

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The Program Evaluation and Review Technique (PERT) is widely used for project management, but it struggles with subjective distributions, particularly due to its assumptions of constant variance and light tails. To overcome these limitations, we propose the Generalized PERT (G-PERT) model, which enhances PERT by incorporating variability in three-point subjective estimates. Our methodology extends the original PERT model to cover the full range of unimodal beta distributions, enabling the model to handle thick-tailed distributions and offering formulas for computing mean and variance. This maintains the simplicity of PERT while providing a more accurate depiction of uncertainty. Our empirical analysis demonstrates that the G-PERT model significantly improves performance, particularly when dealing with heavy-tail subjective distributions. In comparative assessments with alternative models such as triangular and lognormal distributions, G-PERT shows superior accuracy and flexibility. These results suggest that G-PERT offers a more robust solution for project estimation while still retaining the user-friendliness of the classic PERT approach.

Keywords: PERT, subjective distribution, project management, flexible variance

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Authors: David A. Swanson, Lucky M. Tedrow

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Taylor’s Law is a widely observed empirical pattern that relates variances to means in sets of non-negative measurements via an approximate power function, which has found application to human mortality. This study adds to this research by showing that Taylor’s Law leads to a model that reasonably describes the relationship between life expectancy at birth (e0, which also is equal to mean age at death in a life table) and variance at age of death in seven World Bank regional life tables measured at two points in time, 1970 and 2000. Using as a benchmark a non-random sample of four Japanese female life tables covering the period from 1950 to 2004, the study finds that the simple linear model provides reasonably accurate estimates of variance in age at death in a life table from e0, where the latter range from 60.9 to 85.59 years. Employing 2017 life tables from the Human Mortality Database, the simple linear model is used to provide estimates of variance at age in death for six countries, three of which have high e0 values and three of which have lower e0 values. The paper provides a substantive interpretation of Taylor’s Law relative to e0 and concludes by arguing that reasonably accurate estimates of variance in age at death in a period life table can be calculated using this approach, which also can be used where e0 itself is estimated rather than generated through the construction of a life table, a useful feature of the model.

Keywords: empirical pattern, mean age at death in a life table, mean age of a stationary population, stationary population

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Authors: Zheming Cao

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Control loops are the most important components in the wind turbine system. Product quality, operation safety, and the economic performance are directly or indirectly connected to the performance of control systems. This paper proposed a performance evaluation method based on minimum-variance for wind turbine control system. This method can be applied on PID controller for pitch control system in the wind turbine. The good performance result demonstrated in the paper was achieved by retuning and optimizing the controller settings based on the evaluation result. The concepts presented in this paper are illustrated with the actual data of the industrial wind farm.

Keywords: control performance, evaluation, minimum-variance, wind turbine

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Authors: Seyed Mohammad Nasir Mousavi, Amir Mashayekh, Pasha Hejazi, Sanaz Kanani Zadeh Khalkhali

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To determine the stability of the oil percent canola varieties, an experiment was done in a randomized complete block design with four replications in four research stations of the country Shahrood, Esfahan, Kermanshah, Varamin. Analysis of variance showed that there is cultivars considerable variability in the percentage of oil. The results showed that the coefficient of variation of oil Hyola 401 and Hyola308 stability and flexibility are high. Cultivars Cooper and Likord are minimum variance Shukla that stable for the percentage of oil Based on the chart AMMI 1, cultivars Zarfam and Hyola 401 are of oil percentage than other varieties had higher stability. On the chart AMMI2, cultivars Karun and Hyola 308 are identified as stable, also location Isfahan is stable

Keywords: canola, stability, AMMI, variance Shukla

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Authors: Murad A. Bein

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This paper empirically examines the time-varying relationship and spillover effects between the international crude oil price and ten emerging equity markets, namely three oil-exporting countries (Brazil, Mexico, and Russia) and seven Central and Eastern European (CEE) countries (Bulgaria, Croatia, Czech Republic, Hungary, Poland, Romania, and Slovakia). The results revealed that there are spillover effects from oil markets into almost all emerging equity markets save Slovakia. Besides, the oil supply glut had a homogenous effect on the emerging markets, both net oil-exporting, and oil-importing countries (CEE). Further, the time variance drastically increased during financial turmoil. Indeed, the time variance remained high from 2009 to 2012 in response to aggregate demand shocks (global financial crisis and Eurozone debt crisis) and quantitative easing measures. Interestingly, the time variance was slightly higher for the oil-exporting countries than for some of the CEE countries. Decision-makers in emerging economies should therefore seek policy coordination when dealing with financial turmoil.

Keywords: crude oil, spillover effects, emerging equity, time-varying, aggregate demand shock

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Authors: Sukovatov K.Yu., Bezuglova N.N.

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Winter precipitation variability over the Altai Krai was investigated by retrieving temporal patterns. The spectral singular analysis was used to describe the variance distribution and to reduce the precipitation data into a few components (modes). The associated time series were related to large-scale atmospheric and oceanic circulation indices by using lag cross-correlation and wavelet-coherence analysis. GPCC monthly precipitation data for rectangular field limited by 50-550N, 77-880E and monthly climatological circulation index data for the cold season were used to perform SSA decomposition and retrieve statistics for analyzed parameters on the time period 1951-2017. Interannual variability of winter precipitation over the Altai Krai are mostly caused by three natural factors: intensity variations of momentum exchange between mid and polar latitudes over the North Atlantic (explained variance 11.4%); wind speed variations in equatorial stratosphere (quasi-biennial oscillation, explained variance 15.3%); and surface temperature variations for equatorial Pacific sea (ENSO, explained variance 2.8%). It is concluded that under the current climate conditions (Arctic amplification and increasing frequency of meridional processes in mid-latitudes) the second and the third factors are giving more significant contribution into explained variance of interannual variability for cold season atmospheric precipitation over the Altai Krai than the first factor.

Keywords: interannual variability, winter precipitation, Altai Krai, wavelet-coherence

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Authors: Autcha Araveeporn

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This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov chain Monte Carlo method, maximum likelihood method, normal distribution

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to the low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effect of these random errors, they must be accurately modeled. Where the key is the successful implementation that depends on how well the noise statistics of the inertial sensors is selected. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors

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Authors: Wael M. Bazzi, Amir Rastegarnia, Azam Khalili

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In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation method based on incremental distributed least mean-square (IDLMS) algorithm. The proposed method contains two phases: I) Estimation of each sensors observation noise variance, and II) Estimation of the desired parameter using the estimated observation variances. To deal with the reliability of measurements, in the second phase of the proposed algorithm, the step-size parameter is adjusted for each sensor according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the IDLMS algorithm in the same condition.

Keywords: adaptive filter, distributed estimation, sensor network, IDLMS algorithm

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Authors: Jodie Stevenson, Lisa-Marie Emerson, Abigail Millings

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Mindfulness has been conceptualized as a dispositional trait, which is different across individuals. Previous research has independently identified both adult attachment orientations and emotion regulation abilities as correlates of dispositional mindfulness. Research has also presented a two-factor model of the relationship between these three constructs. The present study aimed to further develop this model and investigated theses relationships in a sample of 186 participants. Participants completed the Five Factor Mindfulness Questionnaire Short Form (FFMQ-SF), the Experiences in Close Relationships Scale for global attachment (ECR), the Emotion Regulation Questionnaire (ERC), and the Adult Disorganized Attachment scale (ADA). Exploratory factor analysis revealed a 3-factor solution accounting for 59% of the variance across scores on these measures. The first factor accounted for 32% of the variance and loaded highly on attachment and mindfulness subscales. The second factor accounted for 15% of the variance with strong loadings on emotion regulation subscales. The third factor accounted for 12% of the variance with strong loadings on disorganized attachment, and the mindfulness observes subscale. The results further confirm the relationship between attachment, mindfulness, and emotion regulation along with the unique addition of disorganized attachment. The extracted factors will then be used to predict well-being outcomes for an undergraduate student population.

Keywords: adult attachment, emotion regulation, mindfulness, well-being

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Authors: Abiodun Musbau Lawal, Sunday Samson Babalola, Uzor Friday Ordu

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Issue of employees counterproductive work behavior in government owned organization in emerging economies has continued to be a major concern. This study investigated the factors of pay satisfaction, intent to leave and age as predictors of counterproductive work behavior among non-academic employee in a Nigerian federal government owned university. A sample of 200 non-academic employees completed questionnaires. Hierarchical multiple regression was conducted to determine the contribution of each of the predictor variables on the criterion variable on counterproductive work behavior. Results indicate that age of participants (β = -.18; p < .05) significantly independently predicted CWB by accounting for 3% of the explained variance. Addition of pay satisfaction (β = -.14; p < .05) significantly accounted for 5% of the explained variance, while intent to leave (β = -.17; p < .05) further resulted in 8% of the explained variance in counterproductive work behavior. The importance of these findings with regards to reduction in counterproductive work behavior is highlighted.

Keywords: counterproductive, work behaviour, pay satisfaction, intent to leave

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Authors: Jayanta Pokharel, Gokarna Aryal, Netra Kanaal, Chris Tsokos

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Investment in stocks and shares aims to seek potential gains while weighing the risk of future needs, such as retirement, children's education etc. Analysis of the behavior of the stock market returns and making prediction is important for investors to mitigate risk on investment. Historically, the normal variance models have been used to describe the behavior of stock market returns. However, the returns of the financial assets are actually skewed with higher kurtosis, heavier tails, and a higher center than the normal distribution. The Laplace distribution and its family are natural candidates for modeling stock returns. The Variance-Gamma (VG) distribution is the most sought-after distributions for modeling asset returns and has been extensively discussed in financial literatures. In this paper, it explore the other Laplace family, such as Asymmetric Laplace, Skewed Laplace, Kumaraswamy Laplace (KS) together with Variance-Gamma to model the weekly returns of the S&P 500 Index and it's eleven business sector indices. The method of maximum likelihood is employed to estimate the parameters of the distributions and our empirical inquiry shows that the Kumaraswamy Laplace distribution performs much better for stock returns modeling among the choice of distributions used in this study and in practice, KS can be used as a strong alternative to VG distribution.

Keywords: stock returns, variance-gamma, kumaraswamy laplace, maximum likelihood

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Authors: Khalid Mujaljal, Hassan Alhajhoj

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This paper empirically investigates the influence of oil price fluctuations on the key macroeconomic variables of the Kingdom of Saudi Arabia using unrestricted VAR methodology. Two analytical tools- Granger-causality and variance decomposition are used. The Granger-causality test reveals that almost all specifications of oil price shocks significantly Granger-cause GDP and demonstrates evidence of causality between oil price changes and money supply (M3) and consumer price index percent (CPIPC) in the case of positive oil price shocks. Surprisingly, almost all specifications of oil price shocks do not Granger-cause government expenditure. The outcomes from variance decomposition analysis suggest that positive oil shocks contribute about 25 percent in causing inflation in the country. Also, contribution of symmetric linear oil price shocks and asymmetric positive oil price shocks is significant and persistent with 25 percent explaining variation in world consumer price index till end of the period.

Keywords: Granger causality, oil prices changes, Saudi Arabian economy, variance decomposition

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Authors: Usoro Anthony E., Udoh Emediong

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Diagonal Vector Autoregressive Models are special classes of the general vector autoregressive models identified under certain conditions, where parameters are restricted to the diagonal elements in the coefficient matrices. Variance, autocovariance, and autocorrelation properties of the upper and lower diagonal VAR models are derived. The new set of VAR models is verified with empirical data and is found to perform favourably with the general VAR models. The advantage of the diagonal models over the existing models is that the new models are parsimonious, given the reduction in the interactive coefficients of the general VAR models.

Keywords: VAR models, diagonal VAR models, variance, autocovariance, autocorrelations

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Authors: Alan Wan

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In recent years, the body of literature on frequentist model averaging in statistics has grown significantly. Most of this work focuses on models with different mean structures but leaves out the variance consideration. In this paper, we consider a regression model with multiplicative heteroscedasticity and develop a model averaging method that combines maximum likelihood estimators of unknown parameters in both the mean and variance functions of the model. Our weight choice criterion is based on a minimisation of a plug-in estimator of the model average estimator's squared prediction risk. We prove that the new estimator possesses an asymptotic optimality property. Our investigation of finite-sample performance by simulations demonstrates that the new estimator frequently exhibits very favourable properties compared to some existing heteroscedasticity-robust model average estimators. The model averaging method hedges against the selection of very bad models and serves as a remedy to variance function misspecification, which often discourages practitioners from modeling heteroscedasticity altogether. The proposed model average estimator is applied to the analysis of two real data sets.

Keywords: heteroscedasticity-robust, model averaging, multiplicative heteroscedasticity, plug-in, squared prediction risk

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Authors: Mai A. Ibrahim, Mohammed El-Beltagy, Motaz Khorshid

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Emerging Markets return distributions have shown significance departure from normality were they are characterized by fatter tails relative to the normal distribution and exhibit levels of skewness and kurtosis that constitute a significant departure from normality. Therefore, the classical Markowitz Mean-Variance is not applicable for emerging markets since it assumes normally-distributed returns (with zero skewness and kurtosis) and a quadratic utility function. Moreover, the Markowitz mean-variance analysis can be used in cases of moderate non-normality and it still provides a good approximation of the expected utility, but it may be ineffective under large departure from normality. Higher moments models and median models have been suggested in the literature for asset allocation in this case. Higher moments models have been introduced to account for the insufficiency of the description of a portfolio by only its first two moments while the median model has been introduced as a robust statistic which is less affected by outliers than the mean. Tail risk measures such as Value-at Risk (VaR) and Conditional Value-at-Risk (CVaR) have been introduced instead of Variance to capture the effect of risk. In this research, higher moment models including the Mean-Variance-Skewness (MVS) and Mean-Variance-Skewness-Kurtosis (MVSK) are formulated as single-objective non-linear programming problems (NLP) and median models including the Median-Value at Risk (MedVaR) and Median-Mean Absolute Deviation (MedMAD) are formulated as a single-objective mixed-integer linear programming (MILP) problems. The higher moment models and median models are compared to some benchmark portfolios and tested on real financial data in the Egyptian main Index EGX30. The results show that all the median models outperform the higher moment models were they provide higher final wealth for the investor over the entire period of study. In addition, the results have confirmed the inapplicability of the classical Markowitz Mean-Variance to the Egyptian stock market as it resulted in very low realized profits.

Keywords: Egyptian stock exchange, emerging markets, higher moment models, median models, mixed-integer linear programming, non-linear programming

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Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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