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An alternative to explicitly modelling the heteroskedasticity is using a resampling method such as the wild bootstrap. Given that the studentized bootstrap, which standardizes the resampled statistic by its standard error, yields an asymptotic refinement, [13] heteroskedasticity-robust standard errors remain nevertheless useful.
Heteroscedasticity often occurs when there is a large difference among the sizes of the observations. A classic example of heteroscedasticity is that of income versus expenditure on meals. A wealthy person may eat inexpensive food sometimes and expensive food at other times. A poor person will almost always eat inexpensive food.
Conversely, a “large" R 2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a ...
where T is the sample size, is the residual and is the row of the design matrix, and is the Bartlett kernel [8] and can be thought of as a weight that decreases with increasing separation between samples. Disturbances that are farther apart from each other are given lower weight, while those with equal subscripts are given a weight of 1.
Step 3: Select the equation with the highest R 2 and lowest standard errors to represent heteroscedasticity. Step 4: Perform a t-test on the equation selected from step 3 on γ 1 . If γ 1 is statistically significant, reject the null hypothesis of homoscedasticity.
In a sample of T residuals under the null hypothesis of no ARCH errors, the test statistic T'R² follows distribution with q degrees of freedom, where ′ is the number of equations in the model which fits the residuals vs the lags (i.e. ′ =).
Consider the model ^ = {} =. The Ramsey test then tests whether (), (), …, has any power in explaining y.This is executed by estimating the following linear regression = + ^ + + ^ +,
The most basic identity in accounting is that the balance sheet must balance, that is, that assets must equal the sum of liabilities (debts) and equity (the value of the firm to the owner). In its most common formulation it is known as the accounting equation: Assets = Liabilities + Equity. where debt includes non-financial liabilities.