Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

ARMA Representation of Integrated and Realized Variances

This paper derives the ARMA representation of integrated and realized variances when the spot variance depends linearly on two autoregressive factors, i.e., SR SARV(2) models. This class of processes includes affine, GARCH diffusion, CEV models, as well as the eigenfunction stochastic volatility and the positive Ornstein-Uhlenbeck models. We also study the leverage effect case, the relationship between weak GARCH representation of returns and the ARMA representation of realized variances. Finally, various empirical implications of these ARMA representations are considered. We find that it is possible that some parameters of the ARMA representation are negative. Hence, the positiveness of the expected values of integrated or realized variances is not guaranteed. We also find that for some frequencies of observations, the continuous time model parameters may be weakly or not identified through the ARMA representation of realized variances.

Effects of the heterogeneity of the variances on reliability generalization : An example with the beck depression inventory

Resumen tomado de la publicaci??n

The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Demand side management for the European Supergrid: occupancy variances of European single-person households

The prospect of a European Supergrid calls for research on aggregate electricity peak demand and Europe-wide Demand Side Management. No attempt has been made as yet to represent a time-related demand curve of residential electricity consumption at the European level. This article assesses how active occupancy levels of single-person households vary in single-person household in 15 European countries. It makes use of occupancy time-series data from the Harmonised European Time Use Survey database to build European occupancy curves; identify peak occupancy periods; construct time-related electricity demand curves for TV and video watching activities and assess occupancy variances of single-person households.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Quantifying heteroskedasticity using slope of local variances index

In econometrics, heteroskedasticity refers to the case when the variances of the error terms of the data in hand are not equal. Heteroskedastic time series are challenging to different forecasting models. However, all available solutions adopt the strategy of accommodating heteroskedasticity in the time series and consider it as a type of noise. Some statistical tests were developed over the past three decades to determine whether a time series features heteroskedastic behaviour. This paper presents a novel strategy to handle this problem by deriving a quantifying measure for heteroskedasticity. The proposed measure relies on the definition of heteroskedasticity as a time-variant variance in the time series. In this work, heteroskedasticity is measured by calculating local variances using linear filters, estimating variance trends, calculating changes in variance slopes, and finally obtaining the average slope angle. The results confirm that the proposed index complies with the widely popular heteroskedasticity tests.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The double sampling and the EWMA charts based on the sample variances

We propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is its faster detection of process changes and its better diagnostic feature; that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the double sampling (DS) and the exponentially weighted moving average (EWMA) charts based on the VMAX statistic. (C) 2008 Elsevier B.V. All rights reserved.

Variances of direct genetic effects, maternal genetic effects, and cytoplasmic inheritance effects for milk yield, fat yield, and fat percentage

Milk yield, fat yield, and fat percentage during the first three lactations were studied using New York Holsteins that were milked twice daily over a 305-d, mature equivalent lactation. Those data were used to estimate variances from direct and maternal genetic effects, cytoplasmic effects, sire by herd interaction, and cow permanent environmental effects. Cytoplasmic line was traced to the last female ancestor using DHI records from 1950 through 1991. Records were 138,869 lactations of 68,063 cows calving from 1980 through 1991. Ten random samples were based on herd code. Samples averaged 4926 dams and 2026 cytoplasmic lines. Model also included herd-year-seasons as fixed effects and genetic covariance for direct-maternal effects. Mean estimates of the effects of maternal genetic variances and direct-maternal covariances, as fractions of phenotypic variances, were 0.008 and 0.007 for milk yield, 0.010 and 0.010 for fat yield, and 0.006 and 0.025 for fat percentage, respectively. Average fractions of variance from cytoplasmic line were 0.011, 0.008, and 0.009 for milk yield, fat yield, and fat percentage. Removal of maternal genetic effects and covariance for maternal direct effects from the model increased the fraction of direct genetic variance by 0.014, 0.021, and 0.046 for milk yield, fat yield, and fat percentage; little change in the fraction was due to cytoplasmic line. Exclusion of cytoplasmic effects from the model increased the ratio of additive direct genetic variance to phenotypic variance by less than 2%. Similarly, when sire by herd interaction was excluded, the ratio of direct genetic variance to phenotypic variance increased 1% or less.

Estimation of variances of the effects of incomplete diallels using a matrix approach

A matrix approach is described for assessing the variance of effects in incomplete diallels designs. The method is illustrated by reference to simulated complete and incomplete diallels using different combinations of constraints, average degree of dominance and, for the incomplete diallel, number of hybrids. Our results showed that caution should be taken in working with incomplete diallels under conditions of overdominance because there were changes in the rank of the genotypes when the excluded hybrid had parents with a low frequency of the favorable allele (i.e. the allele which increases expression of a character). The expression described in this paper is a rapid and safe approach to estimate variances and covariances of the effects of contrasts of incomplete diallels. Copyright by the Brazilian Society of Genetics.