Heteroskedasticity

How to stabilize the variance of time series and improve forecasting performancePhoto by Samuel Ferrara on UnsplashThis article is a follow-up to my previous post. There, I describe how to detect heteroskedasticity in time series.We continue to study the issue of non-constant variance here. You’ll learn three approaches used to deal with this condition.Heteroskedasticity impacts the fitting of forecasting models.Time series with non-constant variance often have a long-tailed distribution. The data is left- or…

Detecting and dealing with non-constant variance in time seriesPhoto by Jannes Glas on UnsplashA time series is heteroskedastic if its variance changes over time. Otherwise, the data set is homoskedastic.Heteroskedasticity affects the modeling of time series. So, it is important to detect and deal with this condition.Let’s start with a visual example.Figure 1 below shows the popular airline passengers’ time series. You can see that the variation is different across the series. The variance is higher in the latter part of…

Photo by Philippe D on UnsplashHow to use the White’s heteroskedasticity consistent estimator using Python and statsmodelsIn this article, we shall learn how to employ the HC estimator to perform statistical inference that is robust to heteroskedasticity.This article is PART 2 of the following two part series:PART 1: Introducing White’s Heteroskedasticity Consistent EstimatorPART 2: A tutorial on White’s Heteroskedasticity Consistent Estimator using Python and StatsmodelsIn PART 1, we drilled into the theory of the…

An introduction to the HC estimator, and its importance in building regression models in the face of heteroskedasticityIn this article, we’ll bring together two fundamental topics in statistical modeling, namely the covariance matrix and heteroskedasticity.Covariance matrices are the work horses of statistical inference. They are used for determining if regression coefficients are statistically significant (i.e. different from zero), and for constructing confidence intervals for each coefficient. To do this work, they…

Understand OLS Linear Regression with a bit of mathImage by AuthorHeteroskedasticity and Autocorrelation are unavoidable issues we need to address when setting up a linear regression. In this article, let’s dive deeper into what are Heteroskedasticity and Autocorrelation, what are the Consequences, and remedies to handle issues.A typical linear regression takes the form as follows. The response variable (i.e., Y) is explained as a linear combination of explanatory variables (e.g., the intercept, X1, X2, X3, …) and ε is…