  Heteroskedasticity is a statistical anomaly that describes differing
variances of error terms in a time series dataset. The presence of
heteroskedasticity in data imposes serious challenges for forecasting models
and many statistical tests are not valid in the presence of heteroskedasticity.
Heteroskedasticity of the data affects the relation between the predictor
variable and the outcome, which leads to false positive and false negative
decisions in the hypothesis testing. Available approaches to study
heteroskedasticity thus far adopt the strategy of accommodating
heteroskedasticity in the time series and consider it an inevitable source of
noise. In these existing approaches, two forecasting models are prepared for
normal and heteroskedastic scenarios and a statistical test is to determine
whether or not the data is heteroskedastic.
  This work-in-progress research introduces a quantifying measurement for
heteroskedasticity. The idea behind the proposed metric is the fact that a
heteroskedastic time series features a uniformly distributed local variances.
The proposed measurement is obtained by calculating the local variances using
linear time invariant filters. A probability density function of the calculated
local variances is then derived and compared to a uniform distribution of
theoretical ultimate heteroskedasticity using statistical divergence
measurements. The results demonstrated on synthetic datasets shows a strong
correlation between the proposed metric and number of variances locally
estimated in a heteroskedastic time series.
