Residual Heteroscedasticity Research Articles

MULTIVARIATE REGRESSION APPLIED TO THE PERFORMANCE OTIMIZATION OF A COUNTERCURRENT ULTRACENTRIFUGE - A PRELIMINARY STUDY

In this work, the least-squares methodology with covariance matrix is applied to determine a data curve fitting in order to obtain a performance function for the separative power U of an ultracentrifuge as a function of variables that are experimentally controlled. The experimental data refer to 173 experiments on the ultracentrifugation process for uranium isotope separation. The experimental uncertainties related to the independent variables measurements are considered in the calculation of the experimental separative power values, determining an experimental data input covariance matrix. The process control variables, which significantly influence the U values, are chosen in order to give information on the ultracentrifuge behaviour when submitted to several levels of feed flow F and cut . After the model goodness-of-fit validation, a residual analysis is carried out to verify the assumed basis concerning its randomness and independence and mainly the existence of residual heteroscedasticity with any regression model variable. The response curves are made relating the separative power with the control variables F and , to compare the fitted model with the experimental data and finally to calculate their optimized values.

The consequences of seasonal adjustment for periodic autoregressive processes

Summary This paper examines the effect of X-11 seasonal adjustment on periodicautoregressive processes, using both analytic techniques and simulation. Analytical resultsshow that adjustment reduces (but does not eliminate) periodicity in the coefficients ofa stationary PAR(1) process, and it generally moves the coefficients towards unity. Anonstationary periodically integrated process is converted into a process with a conventionalunit root and induced periodic heteroscedasticity. Simulations confirm that, for finite samples,evidence of periodicity in the coefficients and in residual heteroscedasticity may remain afteradjustment,butperiodicvariationinlong-runcoefficientsisannihilated.Theoverallconclusionis that adjustment alters, but does not destroy, periodic properties. Keywords: Seasonal adjustment , X-11 , Periodic processes , Unit root tests . 1. INTRODUCTION Seasonality is an important feature of macroeconomic time series, but it is typically of littleinterest to economists. Consequently, empirical analysis of macroeconomic time series is almostalways undertaken using seasonally adjusted values, frequently based on the US Bureau of theCensus X-11 Method (see, for example, Dagum 1988) or its recent development X-12 (Findley

Disequilibrium institutional factors in aggregate money demand: evidence from three economies

This paper investigates the disequilibrium effects of a number of institutional factors on the aggregate money demand behaviour of three Asian economies: Japan, Korea and Singapore. It identifies these institutional factors with strong government interventions through monetary or fiscal policies. The investigation is carried out through progressive model search following the equilibrium-correction modelling (ECM) approach. The findings confirm to the arguments that undesirable empirical results from the ECM procedure, such as residual (unconditional or conditional) heteroscedasticity or coefficient non-constancy, are most probably symptoms of the missing variable problem in the underlying theoretical model, and that extension of the theoretical model accordingly to include certain institutional factors pertaining to the particular economies under investigation can enhance the significance of the empirical studies in a substantial way.

Relative Cohort Size and Fertility: The Socio-Political Context of the Easterlin Effect

The conclusion of this study is that structures of collective social protection and changes in rates of female labor force participation influence cohort relative economic status and thus specify the effect of relative cohort on swings in fertility. Both income potential (affected by entering cohort size) and expected standard of living (affected by previous cohort size) are determined by cohort size. A large youth cohort relative to the parental cohort results in low income and low fertility. The Easterlin thesis that relative cohort size (the ratio of persons aged 30-64 years to persons aged 15-29 years) corresponds to shifts in fertility is supported for the period 1950-80 in the US. Replications of this thesis in Europe were unsuccessful. This study indicates that relative cohort size affects fertility depending on the country and the time period. This study examines 18 high-income countries during 1951-86. Measures of stable institutional characteristics of welfare states which may affect the relationship between relative cohort size and fertility include female labor force participation social security spending consensus democracy (Lijpharts five component scale) corporatism (Pampel Williamson and Stryker) total years of leftist rule commitment to egalitarian social policies (Esping-Andersons index of decommodification) and governability (Schmitter). Principal components factor analysis ordinary least squares (fixed-effects and generalized) models and multivariate analysis are constructed or performed. All mediating influences on fertility are not accounted for. Heterogeneity autocorrelation heteroscedasticity and contemporaneous correlation of residuals are controlled for. Relative cohort size which is lagged two years to allow for the gap between fertility desires and births modestly affects average fertility among 18 countries and at 38 time points. Relative cohort size has weak effects in Europe and in countries with high collectivism scores. High female labor force participation depresses the effect of relative cohort size. Relative cohort size has the strongest effects in the US Canada Ireland and the Netherlands. Effects in Germany Switzerland and Sweden are negligible or negative. The generalized least squares pooled model provides more accurate estimates. Social and institutional characteristics of nations affect the influence of relative cohort size on fertility.

International comparisons of health care expenditure — conversion factor instability, heteroscedasticity, outliers and robust estimators

In his comment on our [Gerdtham and Jiinsson (1991)] results concerning conversion factor instability in regressions of per capita health care expenditure on per capita GDP based on cross-sectionals of 22 OECD countries,’ Murthy (1992) makes two points. First, he questions the assumption of residual homoscedasticity across countries that we, and Parkin et al. (1987), made in regressions (1)+3). Second, he questions the appropriateness of the Least Square estimator (LS) that we (and Parkin et al.) used to estimate the regression coefficients of the simple two-variable model. Murthy argues that the sample of countries is such that one could expect problems with both residual heteroscedasticity and outliers. Consequently, he uses White’s heteroscedastic consistent covariance matrix estimator to re-estimate the standard errors of the regression coefficients using our data [White (1980)]. Murthy has also calculated various measures to check for the presence of outliers (pp. 3-4). This exercise led to the detection of three observations which might influence the regression coefftcients. Since LS is based on squared deviations from the regression line c (yi-a-pxi)‘, there will be a

A test for heteroscedasticity and non-normality of regression residuals: A practical approach

This paper discusses alternative and relatively easier tests for heteroscedasticity and non-normality of regression residuals. The estimates of the test statistics are obtained along with the estimates of other regression coefficients and involve no additional calculations. The advantage is that there is no need for a priori information on sources of heteroscedasticity and non-normality.

Heteroscedasticity of residuals: a non-parametric alternative to the goldfeld-quandt peak test

This paper discusses the problem of heteroscedasticity of residuals in a regression model. Tests that detect a monotonie relationship between mean and variance are presented. The theo-retical shortcomings of these tests are discussed and the tests are compared by an empirical sampling computation of their powers.