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# Topic: Homoskedasticity

###### In the News (Wed 17 Jul 19)

 Heteroskedasticity - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-21) This will be true if the observations of the error term are assumed to be drawn from identical distributions. Heteroskedasticity (aka skewedness, opposite: homoskedasticity) is a violation of this assumption. For example, the error term could vary or increase with each observation, something that is often the case with cross sectional or time series measurements. encyclopedia.worldsearch.com /heteroskedasticity.htm   (438 words)

 Introduction to Econometrics by James H. Stock , Mark W. Watson / Sun Sep 4 2:48:44 CEST 2005   (Site not responding. Last check: 2007-10-21) The book is clear, and it skips a lot of useless, obsolete stuff that most undergraduates have typically to go over just because everyone else has gone over it before. Everything is based on large-sample theory, the regressors are never assumed to be "nonstochastic", and homoskedasticity is treated as an exception (which is what happens in practice), not as a rule. There are nice, long empirical applications in each chapter, and some examples are dealt with in more chapters, so that you can see how new concepts are applied to the same problem, and how our understanding of the problem changes and improves with more refined tools. www.it-literature-portal.com /itl_content.php/ASIN/0201715953/Content.html   (343 words)

 [No title] Ramsey's test for homoskedasticity B. Explain how you would fit a piecewise linear regression function with two "knots" (at Xm and Xn) for a simple regression model: Y = f(X). Goldfeld and Quandt's test for homoskedasticity B. Assume you have micro data on a number of individuals, giving: Yi = annual expenditure on clothing, Xi = annual income; and you know which individuals are female, and which individuals are college graduates. Breusch and Pagan's test for homoskedasticity B. Nerlove used cross-sectional data for 1955 on 145 privately owned utilities in the U.S. to regress the logarithm of total cost on the logarithms of output, wage rate, price of capital and price of fuel. www.sfu.ca /~maki/e435/e83595.fex   (536 words)

 Tobacco Control -- eLetters for Mandel et al., 14 (1) 10-12 Using the corrected data, White's test for heteroskedasticity rejected homoskedasticity (p = 0.016) in the case of total revenues. We corrected for the heteroskedasticity in total revenues by using a weighted least squares analysis using the inverse of the number of video lottery machines as the weight. Average revenues were homoskedastic (p=0.13) so we continued to use an unweighted regression, as in the original paper. tc.bmjjournals.com /cgi/eletters/14/1/10   (222 words)

 Homoskedasticity and Heteroskedasticity A univariate stochastic process X is said to be homoskedastic if standard deviations of terms If a process is not unconditionally heteroskedastic or not conditionally heteroskedastic, it is said to be unconditionally homoskedastic or conditionally homoskedastic, respectively All these notions extend to higher dimensions, A multivariate stochastic process X is said to be homoskedastic if its covariance matrix is constant for all times t, etc. www.riskglossary.com /articles/heteroskedasticity.htm   (280 words)

 [No title]   (Site not responding. Last check: 2007-10-21) The most likely deviation from homoskedastic errors in the context of pooled cross-section time-series data (or panel data) is likely to be error variances specific to the cross-sectional unit. The resulting test statistic is distributed Chi-squared(N_g) under the null hypothesis of homoskedasticity. Greene's discussion of Lagrange multiplier, likelihood ratio and standard Wald test statistics points out that these statistics are sensitive to the assumption of normality of the errors. www.stata-journal.com /software/sj1-1/st0004/xttest3.hlp   (343 words)

 Title page for ETD etd-01062004-023244   (Site not responding. Last check: 2007-10-21) This study applied Monte Carlo simulations to investigate the robustness of parameter estimates for a two-level Hierarchical Linear Model (HLM) to the violations of the second-level residual homoskedasticity and independence assumptions. The first factor represented three homoskedasticity levels of the residuals at the second level of the model: no assumption violation, moderate violation, and an extreme violation. The second factor represented three independence levels for the residuals at the second level of the model: no assumption violation, a violation by misspecifing a second-level predictor having a medium-positive effect size, and a violation by misspecifing a second-level predictor having a small-negative effect size. etd.lib.fsu.edu /theses/available/etd-01062004-023244   (601 words)

 Value-at-Risk   (Site not responding. Last check: 2007-10-21) A stochastic process is covariance stationary if every segment of a given length has the same unconditional means, standard deviations and correlations (including autocorrelations and cross correlations) as every other segment of the same length. It is homoskedastic if the unconditional covariance matrix is the same for all terms of the stochastic process. Covariance stationarity implies homoskedasticity—just consider segments of length one and apply the definition of covariance stationarity. www.value-at-risk.net /exercises/exercise04_09.htm   (93 words)

 RePEc   (Site not responding. Last check: 2007-10-21) Abstract: Asymptotic variance of estimated parameters in models of conditional expectations are calculated analytically assuming a GARCH process for conditional volatility. In estimating models of long- horizon expectations, the VAR approach provides an efficiency advantage over long-horizon regressions under homoskedasticity, but that ordering can reverse under heteroskedasticity, especially when the conditional mean and variance are both persistent. In such cases, the VAR approach maintains a slight efficiency advantage if the OLS estimator is replaced by an alternative GMM estimator. www.inomics.com /cgi/repec?handle=RePEc:nbr:nberte:0140   (142 words)

 CIRANO : Knowledge into action A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literatures. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. www.cirano.qc.ca /en/publication_detail.php?id=2001s-25&print_page=1   (304 words)

 Testing for Homoskedasticity: Why use predicted values? Hi, I have been reading a lot of articles on empirical studies using multiple regreession. Many scientists use a scatterplot of the standardized residuals and standardized PREDICTED values to test for homoskedasticity. If there was no pattern they concluded that the variance of the residuals was costant across all level of the INDEPENDENT variables (homoskedasticity). www.mail-archive.com /edstat@lists.ncsu.edu/msg04697.html   (132 words)

 A New Test of the Martingale Difference Hypothesis Comparing with many commonly used autocorrelation- and spectrum-based tests, it has better power against a larger class of alternatives that may be serially correlated or uncorrelated. Moreover, this test does not rely on the assumption of conditional homoskedasticity and requires a weaker moment condition. Our simulations confirm that the proposed test is powerful against various linear and nonlinear alternatives and is quite robust to the failure of higher-order moments. www.bepress.com /snde/vol8/iss4/art1   (216 words)

 [No title] Homoskedasticity in a picture:  E(uX=x) = 0 (u satisfies Least Squares Assumption #1) The variance of u does not change with (depend on) x Heteroskedasticity in a picture:  E(uX=x) = 0 (u satisfies Least Squares Assumption #1) The variance of u depends on x — so u is heteroskedastic. What if the errors are in fact homoskedastic?: You can prove some theorems about OLS (in particular, the Gauss-Markov theorem, which says that OLS is the estimator with the lowest variance among all estimators that are linear functions of (Y1,,Yn); see Section 15.5). The two formulas coincide (when n is large) in the special case of homoskedasticity The bottom line: you should always use the heteroskedasticity-based formulas — these are conventionally called the heteroskedasticity-robust standard errors. www.econ.iastate.edu /classes/econ472/Falk/notes_the_ols_estimator_inference.doc   (1754 words)

 Matteo Richiardi: Generalizing Gibrat As expected, the homoskedastic system (mean and variance of the growth rate independent of size) with no entry and exit exhibits very fast diverging dynamics, as soon as we move away from the line of figure 1. Note that the asymmetry due to the threshold at 0 induce per se – a negative correlation between the mean of the observed growth rate and size, the stronger the bigger the growth rate. However, in the case of mean homoskedasticity as defined above, this is not enough to preserve the system from implosion. jasss.soc.surrey.ac.uk /7/1/2.html   (7760 words)

 [No title] We reject the null hypothesis of homoskedasticity, and conclude that there is heteroskedasticity. We (strongly) reject the null hypothesis of homoskedasticity, in favor of the alternative hypothesis that there is heteroskedasticity proportional to EMBED Equation.3. This fails to reject the null hypothesis of homoskedasticity — the GQ test doesn’t detect the problem. 18.318: Introduction to Econometrics Lab Exercise # 4 Sisir Sarma PAGE  PAGE 1 Thursday 2:30 p.m. www.umanitoba.ca /faculties/arts/economics/Sisir/2004/summer/Exercise4.doc   (1379 words)

 [No title] Homoskedasticity This assumption means that we do not expect to get larger errors in some cases than in others. But homoskedasticity is violated only when this happens in a predictable manner. Homoskedasticity (cont.) Example: income and spending on certain goods. www.columbia.edu /itc/sipa/U4320y-003/overheads/lecture09.ppt   (858 words)

 [No title] For the fixed value, the b’s were set to a value of.5 For the generated data sets with differing leverage amounts, the b’s were.5, 1, 1.5, and 2. EGR assumed homoskedasticity and therefore data sets were generated with a fixed value of 2. Heteroskedasticity was created by letting the values of s be 5, 10, 15, and 20 with one-fourth of the observations using each value. www.turtletrader.com /mfa-articles/perfpers.doc   (5683 words)

 [No title] Example Length of sentence (Y) as a function of age (X) Homoskedastic pattern Up through age 30, the variability in sentences over the various age levels is about comparable. Testing for Multivariate Homoskedasticity The variability in the dependent variable (Y) over multiple independent variables can not be illustrated graphically. Instead, the statistical model is first estimated  Predictions (Y') made from the model And the residuals (Y' - Y) are then plotted against the predictions (Y') Example Time served in prison as a function of gender, prior convictions, and education. www.shsu.edu /~icc_cmf/cj_742/stats4.doc   (1836 words)

 Notes By the end of today's class, you should be able to answer these questions for the problem of heteroskedasticity. The first burning issue today is a matter of spelling: Heteroskedasticity is the preferred spelling of those conscious of the Greek origins of the word -- "differing skips" in contrast to "same skips" (homoskedasticity) -- while heteroscedasticity is the spelling that appears most commonly in print. If the null hypothesis is true, that is the errors are homoskedastic, then the test statistic is www.brynmawr.edu /Acads/Econ/econ304/class18_txt.html   (1065 words)

 [No title] Triplett (2004: Chapter 4) noted he reconsidered the empirical effects of this adjustment in his previous 1989 study of PCs and found little difference, as did Silver and Heravi (2002) for washing machines. Now there is a sense in which if the constraints on the error structure were less restrictive, we would have more faith in the index. Indeed the homoskedasticity would lead to less bias in the standard errors and more reliable test results. But these constraints do not lead to bias in the estimated dummy variable coefficient. www.ipeer.ca /papers/SilveronvanDalen%20Bode,June%2004comments.doc   (2248 words)

 ECON 413 – Assignment #6 Use the Park test to test the null hypothesis of homoskedasticity, using SQFT as the proportionality factor. Use the White test to test the null hypothesis of homoskedasticity. What is the underlying functional form of the variance of the error term assumed for the Goldfeld-Quandt and Park tests? econ413.wustl.edu /fa03/HW6.htm   (400 words)

 Re: Testing for Homoskedasticity: Why use predicted values? Jennifer Bo writes: > I have been reading a lot of articles on empirical studies > using multiple regreession. Many scientists use a scatterplot > of the standardized residuals and standardized PREDICTED > values to test for homoskedasticity. If there was no pattern they > concluded that the variance of the residuals was constant across all > level of the INDEPENDENT variables (homoskedasticity). www.usenet.com /newsgroups/sci.stat.edu/msg00762.html   (307 words)

 Stock-Watson: Q&A You can teach the Gauss-Markov theorem any time after introducing the sampling distribution of the OLS estimator and the concept of homoskedasticity.  With these two concepts in hand, it is possible to pose the question:  if we want to have the smallest possible sampling variance of our estimator of β In contrast to the sandwich estimator, this estimator is consistent only if the likelihood is correctly specified, that is, only if Equation (9) holds. In the special case of the linear model (where the likelihood is specified with errors that are homoskedastic and normally distributed), the sandwich estimator in Equation ksghome.harvard.edu /~JStock/tb/q&a_2.htm   (1288 words)

 Glossary and Essays for letter H These issues can serve as the underlying securities for various derivative products. Homoskedasticity or Homoscedasticity - Is the condition of constant residual variance. Horizontal Spread - Is a spread which is composed of two puts or two calls on the same underlying instrument. www.oasismanagement.com /glossary/h.html   (870 words)

 Glossary of research economics It is a statistic for testing whether dependent variable y is heteroskedastic as a function of regressors X. If it is, that suggests use of GLS or SUR estimation in place of OLS. Large values of test statistic reject the hypothesis that y is homoskedastic in X. The meaning of 'large' varies with the number of variables in X. Quoting almost directly from the Stata manual: The Breusch and Pagan (1980) chi-squared statistic -- a Lagrange multiplier statistic -- is given by Homoskedasticity of errors is assumed although this can be dubious since we are open to the possibility that the parameter vector ( econterms.com /econtent.html   (14743 words)

 The Chow Test The derivation of the Chow test assumes that the errors have the same variance (homoskedasticity) in the 2 groups and the errors are independently distributed (that is, no autocorrelation). However, the homoskedasticity assumption appears reasonable for the log-linear model. For both models the Durbin-Watson test statistic rejects the null hypothesis of no autocorrelation in the errors. shazam.econ.ubc.ca /intro/chowtest.htm   (980 words)

 Econometrics Review for Midterm   (Site not responding. Last check: 2007-10-21) Linear regression model: OLS assumptions, properties of OLS estimators, multicollinearity, hypothesis tests and confidence intervals for coefficients, interpretation of R , standard error of the regression (SER), dummy (or binary) variables, homoskedasticity, heteroskedasticity, omitted variable bias. You should be familiar with and be able to interpret the regression results reported by EViews. www.ac.aup.fr /kdunz/Courses/Econometrics/MidtermReview.htm   (291 words)

 Midterm Estimate the population model using ordinary least squares (ols) and assuming that the stochastic errors are homoskedastic. Estimate the population model using ols and assuming that the stochastic errors are heteroskedastic. Which set of results (the results that assume homoskedasticity or the results that allow for heteroskedasticity) do you believe provide better estimates of www.wellesley.edu /Economics/econ203-Witte/Exam1_2003.html   (320 words)

 Estimating Conditional Expectations When Volatility Fluctuates Asymptotic variances of estimated parameters in models of conditional expectations are calculated analytically assuming a GARCH process for conditional volatility. Under such heteroskedasticity, OLS estimators of parameters in single-period models can possess substantially larger asymptotic variances than GMM estimators employing additional multiperiod moment conditions - an approach yielding no efficiency gain under homoskedasticity. In estimating models of long-horizon expectations the VAR approach provides an efficiency advantage over long-horizon regressions under homoskedasticity, but that ordering can reverse under heteroskedasticity, especially when the conditional mean and variance are both persistent. ideas.repec.org /p/fth/pennfi/17-93.html   (258 words)

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