Heteroscedasticity Effects Research Articles

Martian Case Study of Multivariate Correlation and Regression with Planetary Datasets

We synthesize multivariate correlation and regression methods to characterize unique relationships among compositional and physical properties of a planetary surface locally, regionally, and globally. Martian data including elemental mass fractions, areal fractions of mineral types, and thermal inertia constitute our case study. We incorporate techniques to address the effects of spatial autocorrelation and heteroscedasticity. We also utilize method and fit diagnostics. While the Mars Odyssey and Mars Global Surveyor missions provide the exploratory context in our discussion, our approach is applicable whenever the interrelationships of spatially binned data of continuous-valued planetary attributes are sought. For example, our regional-scale case study reinforces the strength of the spatial correlation among K, Th, and the dominant mineralogic type within northern low albedo regions (surface type 2) of Mars. Recent chemical and mineralogic data from the MESSENGER mission at Mercury and Dawn at Vesta may be analyzed effectively with these hierarchical regression methods to constrain geochemical processes. Likewise, our algorithm could be applied locally with the wide variety of compositional data expected from the MSL mission at Gale Crater in general, and the ChemCam sampling grids in particular.

Estimating herbaceous plant biomass in mountain grasslands: a comparative study using three different methods

It is a challenge to find effective methods to estimate biomass over a large range of biomass values in diverse plant communities, such as typically found in mountain grasslands. We compared the performance of three non-destructive methods for estimating plant biomass (3D quadrat: a point quadrat method, plate meter: a measure of physical volume, and visual estimation: a component of the BOTANAL method) in mountain grasslands. We tested whether: (1) all methods performed equally in terms of linearity of estimations over a large range of biomass and (2) under and over-estimations of biomass were related to specific plant compositions. We estimated plant biomass in 30 plots, for which real plant biomass was measured by destructive sampling. We accounted for the significant effect of heteroscedasticity (which was significant for all three methods) when testing for the linearity of the relationship between real biomass and biomass estimates. The plate meter displayed non-linearity, being insensitive to variation of biomass at low biomass values. BOTANAL and the 3D quadrat yielded linear relationships, with BOTANAL providing better estimates of real biomass (greater R²). Specific floristic compositions (e.g. presence of Deschampsia cespitosa, Chaerophyllum sp., and abundant small forbs) explained underestimation and overestimation of biomass estimates for the plate meter and 3D quadrat while BOTANAL was insensitive to floristic composition. In heterogeneous grasslands, BOTANAL appeared to be the most appropriate method, given its linear relationship with real biomass over the whole range of biomass and its low residual variation.

Evaluating Uses Of Information Technology In Health Care Administration

<span>This paper examines the distributional properties of stock returns in the Nigerian stock market. Because emerging stock markets present several institutional, political and economic barriers, we hypothesize that the structural adjustment program begun in 1986 resulted in a sustained increase in the variability of stock returns. Conventional variance homogeneity tests could not reject the hypothesis of changing volatility in the security returns process. However, the Lagrange multiplier test reveals the presence of autoregressive conditional heteroscedasticity (ARCH) effect in the stock returns.</span>

Stock Return Characteristics In A Thin Incipient Stock Market

<span>This paper examines the distributional properties of stock returns in the Nigerian stock market. Because emerging stock markets present several institutional, political and economic barriers, we hypothesize that the structural adjustment program begun in 1986 resulted in a sustained increase in the variability of stock returns. Conventional variance homogeneity tests could not reject the hypothesis of changing volatility in the security returns process. However, the Lagrange multiplier test reveals the presence of autoregressive conditional heteroscedasticity (ARCH) effect in the stock returns.</span>

A conditional CAPM: implications for systematic risk estimation

PurposeThe purpose of this paper is to examine, whether or not, the residuals of the market model (MM) are conditionally heteroscedastic; to examine, whether or not, there exists an intervalling effect in conditional heteroscedasticity in the residuals of the MM; to propose a simple data‐driven conditional capital asset pricing model (CAPM); and to examine the effect of conditional heteroscedasticity on the estimation of systematic risk.Design/methodology/approachSystematic risk coefficients (betas) are estimated at first using data of various frequencies from the Athens stock exchange without taking into account conditional heteroscedasticity. The same procedure is repeated, but this time taking into consideration conditional heteroscedasticity, which is found to exist. The results of the two approaches are compared.FindingsEmpirical evidence is provided for the existence of: conditional heteroscedasticity in MM residuals; a pronounced intervalling effect on autoregressive conditional heteroscedasticity (ARCH) in MM residuals; and generalized autoregressive conditional heteroscedasticity in mean type of conditional heteroscedasticity for the majority of cases where ARCH was present in MM residuals. These findings are conducive to a conditional CAPM, which takes into account the effect of conditional variance on expected returns, rather than the standard CAPM.Practical implicationsBetter estimates of financial risk.Originality/valueThe intervalling effect in ARCH in the residuals of the MM is examined for the first time.

Bootstrap methods for comparing independent regression slopes

In this study, we explore the effects of non-normality and heteroscedasticity when testing the hypothesis that the regression lines associated with multiple independent groups have the same slopes. The conventional approach involving the F-test and the t-test (F/t approach) is examined. In addition, we introduce two robust methods which allow simultaneous testing of regression slopes. Our results suggest that the F/t approach is extremely sensitive to violations of assumptions and tends to yield misleading conclusions. The new robust alternatives are recommended for general use.

A conditional CAPM: implications for the estimation of systematic risk

The purpose of this paper is to examine: (i) whether or not, the residuals of the Market Model are conditionally heteroscedastic; (ii) whether or not, there exists an intervalling effect in conditional heteroscedasticity in the residuals of the Market Model; (iii) the effect of conditional heteroscedasticity on the estimation of systematic risk.; as well as to propose a simple data driven conditional CAPM. To this end daily closing price of stocks traded at the Athens Stock Exchange are used. Empirical evidence is provided for the existence of: (a) conditional heteroscedasticity in MM residuals; (b) a pronounced intervalling effect on ARCH in MM residuals; (c) GARCH in mean type of conditional heteroscedasticity for the majority of cases where ARCH was present in MM residuals. These findings in terms of theory are conducive to a conditional CAPM, which takes into account the effect of conditional variance on expected returns, rather than the standard CAPM. Furthermore, in terms of practical implications these findings may lead to better estimates of systematic risk.

Behaviour of stock markets’ memories

In this article, we show that the memory of markets has nonchaotic behaviour. Its time trend is neutral and nonlinearity tests such as Brock, Dechert, Sheinkman (BDS) rejects nonlinearity in stock markets’ memories. The estimation of fractional differencing parameters is carried out by various methods such as Maximum Likelihood Estimation (MLE), Nonlinear Least Squares (NLS), Hurst exponents, Gewek, Porter- Hudak (GPH), wavelet transformation, and Whittle. Also Lyapunov exponents are estimated by two methods of Rosenstein and Jacobian. Results of Lyapunov exponent estimation shows memory of markets are not chaotic. Furthermore, there are no any Autoregressive Conditional Heteroscedasticity (ARCH) effects in memory of markets. ARCH test is more specific than the BDS test and it may powerful test for detecting possible ARCH effects. All of tests show memory of markets has random behaviour.

A study of REITs in the Asia-Pacific area: volatility characters and their long-term relationship with stock indices

This study examines some important characters of Real Estate Investment Trusts (REITs) in six Asia-Pacific areas including Australia, Japan, Singapore, Taiwan, Korea and Hong Kong. The results show that volatility behaviours of REITs have Generalized Autoregressive Conditional Heteroscedastic (GARCH) effects; in addition, REITs and stocks have a long term relationship in all markets.

Conventional and advanced time series estimation: application to the Australian and New Zealand Intensive Care Society (ANZICS) adult patient database, 1993–2006

Time series analysis has seen limited application in the biomedical Literature. The utility of conventional and advanced time series estimators was explored for intensive care unit (ICU) outcome series. Monthly mean time series, 1993-2006, for hospital mortality, severity-of-illness score (APACHE III), ventilation fraction and patient type (medical and surgical), were generated from the Australia and New Zealand Intensive Care Society adult patient database. Analyses encompassed geographical seasonal mortality patterns, series structural time changes, mortality series volatility using autoregressive moving average and Generalized Autoregressive Conditional Heteroscedasticity models in which predicted variances are updated adaptively, and bivariate and multivariate (vector error correction models) cointegrating relationships between series. The mortality series exhibited marked seasonality, declining mortality trend and substantial autocorrelation beyond 24 lags. Mortality increased in winter months (July-August); the medical series featured annual cycling, whereas the surgical demonstrated long and short (3-4 months) cycling. Series structural breaks were apparent in January 1995 and December 2002. The covariance stationary first-differenced mortality series was consistent with a seasonal autoregressive moving average process; the observed conditional-variance volatility (1993-1995) and residual Autoregressive Conditional Heteroscedasticity effects entailed a Generalized Autoregressive Conditional Heteroscedasticity model, preferred by information criterion and mean model forecast performance. Bivariate cointegration, indicating long-term equilibrium relationships, was established between mortality and severity-of-illness scores at the database level and for categories of ICUs. Multivariate cointegration was demonstrated for {log APACHE III score, log ICU length of stay, ICU mortality and ventilation fraction}. A system approach to understanding series time-dependence may be established using conventional and advanced econometric time series estimators.

Comparing the regression slopes of independent groups

In this study, we explore the effects of non-normality and heteroscedasticity when testing the hypothesis that regression lines associated with two independent groups have the same slopes. Our results indicate that some recently proposed methods that allow heteroscedasticity and perform well in extant simulation studies do not perform well for the situation at hand. Two of the methods studied here are recommended for general use.

Time-varying predictability in crude-oil markets: the case of GCC countries

This paper uses a time-varying parameter model with generalized autoregressive conditional heteroscedasticity effects to examine the dynamic behavior of crude-oil prices for the period February 7, 1997–January 8, 2010. Using data from four countries of the Gulf Cooperation Council, we find evidence of short-term predictability in oil-price changes over time, except for several short sub-periods. However, the hypothesis of convergence towards weak-form informational efficiency is rejected for all markets. In addition, we explore the possibility of structural breaks in the time-paths of the estimated predictability indices and detect only one breakpoint, for the oil markets in Qatar and the United Arab Emirates. Our empirical results therefore call for new empirical research to further gauge the predictability characteristics and the determinants of oil-price changes.

Nonlinear Time Series Modeling and Forecasting for Periodic and ARCH Effects

Abstract Generalized autoregressive conditional heteroscedastic (GARCH) nonlinear time series model may be employed to describe data sets depicting volatility. This model along with its estimation procedure is thoroughly studied. Lagrange multiplier (LM) test for testing presence of Autoregressive conditional heteroscedastic (ARCH) effects is also discussed. As an illustration, modeling and forecasting of monthly rainfall data of Sub-Himalayan West Bengal meteorological subdivision, India is carried out. As the data exhibits presence of seasonal component, Hylleberg, Engle, Granger and Yoo (1990) [HEGY] seasonal unit root test is applied to the data with a view to make the series stationary through “differencing filter”. Subsequently, GARCH model is employed on the residuals obtained after carrying out Periodic autoregressive (PAR) modeling of the seasonal variation. Further, Mixture periodic ARCH (MPARCH) model, which is an extension of GARCH model, is also applied on zero conditional mean residual serie...

Fetal echocardiography: z‐score reference ranges for a large patient population

The main goal was to develop new z-score reference ranges for common fetal echocardiographic measurements from a large referral population. A retrospective cross-sectional study of 2735 fetuses was performed for standard biometry (biparietal diameter (BPD) and femoral diaphysis length (FDL)) and an assessment of menstrual age (MA). Standardized fetal echocardiographic measurements included aortic valve annulus and pulmonary valve annulus diameters at end-systole, right and left ventricular diameters at end-diastole, and cardiac circumference from a four-chamber view of the heart during end-diastole. Normal z-score ranges were developed for these echocardiographic measurements using MA, BPD and FDL as independent variables. This was accomplished by using first standard regression analysis and then weighted regression of absolute residual values for each parameter in order to adjust for inconstant variance. A simple, linear regression model was the best description of the data in each case and correlations between fetal cardiac measurements and the independent variables were excellent. There was significant heteroscedasticity of standard deviation with increasing gestational age, which also could be modeled with simple linear regression. After this adjustment, the residuals conformed to a normal distribution, validating the calculation and interpretation of z-scores. Development of reliable z-scores is possible for common fetal echocardiographic parameters by applying statistical methods that are based on a large sample size and weighted regression of absolute residuals in order to minimize the effect of heteroscedasticity. These normative ranges should be especially useful for the detection and monitoring of suspected fetal cardiac size and growth abnormalities.

Comparison of three weighting schemes in weighted regression analysis for use in a chemistry laboratory

Background To minimize the effect of heteroscedasticity in chemical and other data, weighted regression analysis is the preferred regression technique. In this work a regression weight that maximizes accuracy and precision was sought. Method Using real and simulated data from a serum cotinine assay, performance of 3 weighting schemes, namely, 1/ X, 1/ X 2, and 1/ s 2( Y) to calibrate chemical data was evaluated. Two performance measures were used to evaluate the accuracy and precision of each scheme to estimate concentrations in unknown specimens. Results The weight, 1/ X—particularly for low concentrations—was not acceptable. The performance of both, 1/ X 2 and 1/ s 2( Y) was close, 1/ X 2 being slightly better in many cases. Overall, however, when the variance of instrument signal increased beyond certain limits, none of the weighting schemes performed acceptably. Conclusion Because of its simplicity and ease of use, 1/ X 2 is recommended for general application. If, however, instrument signal variance is too high to be managed by statistical techniques, the only solution is to control such variance through laboratory-based solutions.

The Development of Rating Curve Considering Variance Function Using Pseudo-likelihood Estimation Method

This paper employs a new estimation method for estimating stage–discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of heteroscedasticity of residuals. Therefore, the model with pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation (P-LE) method. Also simulated annealing, a sort of global optimization techniques, is adapted to minimize the log likelihood of the weighted residuals. At first, the developed P-LE model was applied to a hypothetical site where stage–discharge data were generated by incorporating various errors for statistical test. Also, the limit of stages for segmentation is estimated in the process of P-LE using the Heaviside function. For the validation of effects of the developed P-LE model, the results of the conventional log-transformed linear regression (LT-LR) model and the P-LE model are estimated and compared. After statistical simulation, the developed P-LE model is then applied to the real data sets from six gauge stations in the Geum River basin. It can be suggested that this new estimation method is applied to real river sites to successfully determine the weights taking into account error distributions from observed discharge data.

Optimal Sequential Design in a Controlled Non‐parametric Regression

Abstract. In a non‐parametric regression, the heteroscedasticity (dependence of the variance of the regression error on the predictor) can be a serious complication in estimation or visualization of an underlying regression function. If a controlled sampling is permitted, then the statistician can choose the design of predictors which attenuates the effect of heteroscedasticity. It is proposed to use a design which minimizes the mean integrated squared error of the regression function estimation. Then the corresponding optimal design density is proportional to the standard deviation of the regression error (the so‐called scale function). Because in general the statistician does not know an underlying scale function, the natural question is as follows: is it possible to suggest a sequential design which performs as well as an oracle that knows the underlying scale function? The answer is ‘yes’, and a corresponding sequential procedure is developed. It is proved, for the first time in the literature, that a data‐driven sequential design, together with an adaptive regression estimator, can mimic the oracle and be sharp minimax. Further, it is shown that the suggested method is feasible for small samples.

Volatility Clustering in U.S. Home Prices

Generalized autoregressive conditional heteroscedasticity (GARCH) effects imply the probability of large losses is greater than standard mean-variance analysis suggests. Accurately capturing GARCH for housing markets is vital for portfolio management. Previous investigations of GARCH in housing have focused on narrow regions or aggregated effects of GARCH across markets, imposing one nationwide effect. This paper tests fifty state housing markets for GARCH, and develops individual GARCH models for those states, allowing for different effects in each. Results indicate there are GARCH effects in over half the states, and the signs and magnitudes vary widely, highlighting the importance of estimating separate GARCH models for each market.

A comparison of photographic analyses used to quantify zooxanthella density and pigment concentrations in Cnidarians

Many cnidarians exist in an obligatory mutualism with dinoflagellates commonly called zooxanthellae. When these symbioses are stressed, zooxanthella densities often decrease (i.e., bleaching), resulting in reduced host fitness or mortality. Because zooxanthellae play a prominent role in the coloration of hosts, several analyses of reflected spectra from photographic images have been developed to quantify zooxanthella densities and serve as a proxy for invasive sampling methods. To date these techniques have not been compared. In this study, global information system (GIS) tools, commonly used with aerial and satellite images, and photographs of healthy and bleached sea anemones, Aiptasia pallida (Verrill), were used to compare these image analysis methods. Zooxanthella densities and chlorophyll- a concentrations were correlated with image brightness (i.e., digital number) in: the red, green, and blue bands (RGB); the average of the three RGB bands (RGB/3); intensity and saturation bands (IHS); and using a principal components analysis (PCA) of the RGB bands. RGB brightness correlations with zooxanthella densities and chlorophyll- a concentrations were highest using the blue band, followed by green, then red. Using any one band within RGB, however, restricts comparisons to similar color morphs. RGB/3, IHS or PCA transformations enable intra and inter-specific comparisons where colors may vary. Among these transformations, PCA and intensity had higher correlations, followed by RGB/3, then saturation. RGB/3 and IHS, unlike PCA, ignore the correlations between the three RGB bands, treating each pixel independently. PCA uses these correlations, and in doing so lessens the effects of heteroscedasticity in the data. In addition, the observed reciprocal relationship of intensity and saturation may serve as a standardized criterion for bleaching. Finally, this study demonstrates that GIS has broad interdisciplinary applications for spatial and spectral analyses from the individual colony to reef scale assessments.

Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.