Reduction of Heteroscedasticity in Time Series

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SUMMARY

The discussion focuses on methods for reducing heteroscedasticity in time series data, specifically addressing the derivation of variance functions in relation to the mean. The user inquires about handling variance modeled as a high-order polynomial, such as ##𝑎𝑢_𝑡^5+𝑏𝑢_𝑡^4+𝑐𝑢_𝑡^3##, which is less commonly discussed than lower-order functions. Key techniques for addressing this issue include identifying optimal power transformations and other transformation methods to stabilize variance. The conversation highlights the need for clarity in statistical inquiries to facilitate better responses.

PREREQUISITES
  • Understanding of heteroscedasticity in time series analysis
  • Familiarity with polynomial regression models
  • Knowledge of variance functions and their derivation
  • Experience with power transformations in statistical modeling
NEXT STEPS
  • Research methods for deriving variance functions in time series data
  • Explore polynomial regression techniques for high-order variance modeling
  • Learn about optimal power transformation methods for stabilizing variance
  • Investigate statistical software tools for implementing variance stabilization techniques
USEFUL FOR

Statisticians, data analysts, and researchers working with time series data who need to address issues of heteroscedasticity and improve model accuracy.

mertcan
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Hi, I have some crucial questions belong to statistics:

First, How can we derive the variance function with respect to mean for a given data?

Secondly, I would like to ask: what method should we employ if the variance in time series behaves like a high order (such as ##𝑎𝑢_𝑡^5+𝑏𝑢_𝑡^4+𝑐𝑢_𝑡^3## polynomial function with respect to mean? On internet, I have always encountered the case where variance is a function of ##𝑢_𝑡^2 or 𝑢_𝑡^4## like in this link I have not seen a case that variance is a function such as ##𝑎𝑢_𝑡^5+𝑏𝑢_𝑡^4+𝑐𝑢_𝑡^3## . What should we do for the last case? How do we find the optimal power transformation or optimal other transformation methods to reduce heteroscedasticity?
 
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Why can not I get any response? If you think my question is not explicit could you make me aware of it?
 

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