Reduction of Heteroscedasticity in Time Series

In summary, the conversation discusses two main questions related to statistics. The first question is about deriving the variance function with respect to the mean for a given dataset. The second question is about determining the appropriate method to use when the variance in a time series follows a high order polynomial function with respect to the mean, specifically in the case where the variance is a function of ##𝑎𝑢_𝑡^5+𝑏𝑢_𝑡^4+𝑐𝑢_𝑡^3##. The speaker also asks for advice on how to find optimal power transformations or other transformation methods to reduce heteroscedasticity. The conversation ends with the speaker expressing frustration at not receiving
  • #1
mertcan
340
6
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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  • #2
Why can not I get any response? If you think my question is not explicit could you make me aware of it?
 

1. What is heteroscedasticity in time series data?

Heteroscedasticity in time series data refers to the phenomenon where the variance of the data changes over time. This means that the data points are not equally spread out and the variability of the data increases or decreases over time.

2. Why is it important to reduce heteroscedasticity in time series data?

Reducing heteroscedasticity in time series data is important because it can lead to biased and unreliable statistical analyses. Heteroscedasticity violates the assumption of equal variance in statistical models, which can result in incorrect conclusions and predictions.

3. What are some common methods for reducing heteroscedasticity in time series data?

Some common methods for reducing heteroscedasticity in time series data include transforming the data, using weighted least squares regression, and applying autoregressive conditional heteroscedasticity (ARCH) models. Other techniques such as detrending and deseasonalizing the data can also help reduce heteroscedasticity.

4. How can we detect heteroscedasticity in time series data?

One way to detect heteroscedasticity in time series data is by visually inspecting the data for any patterns or trends in the variability. Another method is to use statistical tests such as the Breusch-Pagan test or the White test to determine if there is significant heteroscedasticity present in the data.

5. Can we completely eliminate heteroscedasticity in time series data?

It is not always possible to completely eliminate heteroscedasticity in time series data. However, by using appropriate methods and techniques, we can reduce its impact and improve the accuracy of our analyses and predictions. It is important to carefully select and apply the appropriate method based on the specific characteristics of the data and the goals of the analysis.

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