Contents
What is nonconstant variance?
Heteroskedasticity is when the variance of the error term, or the residual variance, is not constant across observations. Graphically, it means the spread of points around the regression line is variable.
What is variance in time series?
In some time series, the variance within a time series can have particularly increased amplitudes during the course of the time period observed. Transformations can be applied to the time series, in particular the log transformation, to coerce some form of stationarity.
What is the constant variance assumption?
Constant variance is the assumption of regression analysis that the standard deviation and variance of the residuals are constant for all values of the independent variable.
Why is variance constant?
It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant.
What is the error variance?
Residual Variance (also called unexplained variance or error variance) is the variance of any error (residual). The unexplained variance is simply what’s left over when you subtract the variance due to regression from the total variance of the dependent variable (Neal & Cardon, 2013).
When to worry about non-constant variance in a model?
If non-constant variance is a concern, look at a plot of residuals versus fits and/or a time series plot of the residuals. If something looks wrong, you’ll have to revise your guess at what the model might be.
What happens when nonconstant variance is too high?
For example, if the residual variance increases with the fitted values, then prediction intervals will tend to be wider than they should be at low fitted values and narrower than they should be at high fitted values. Some remedies for refining a model exhibiting excessive nonconstant variance includes the following:
Which is the best fit for non constant variance?
Since the purpose of the fit is to simply remove long term trend, a simple fit, such as a straight line, is typically used. For non-constant variance, taking the logarithm or square root of the series may stabilize the variance.
How to transform a time series to stationarity?
If the time series is not stationary, we can often transform it to stationarity with one of the following techniques. We can difference the data. That is, given the series \\(Z_t\\), we create the new series $$ Y_i = Z_i – Z_{i-1} \\, . $$ The differenced data will contain one less point than the original data.