Having trouble understanding sources of hetroscedasticity

  • Thread starter Rabolisk
  • Start date
  • Tags
    Sources
In summary, the conversation is about understanding how the specification of an equation can lead to heteroscedasticity in a time series model. The person is trying to understand the variance part of the equation and is questioning why the constant γ is not squared when outside the variance operator. It is suggested that one way to introduce heteroscedasticity in the model is by increasing γt over time, assuming that ϖ is a random variable with the same behavior over time.
  • #1
Rabolisk
6
0
Hey. Iam trying to understand how specification of the equation can lead to hetroscedasticity. This is stright out of my notes.

Yt=B1+B2x2t+B3x3t+...+BkXkt+[itex]\gamma[/itex][itex]\varpi+[/itex]ε[itex]^{}_{t}[/itex]


Yt=B1+B2x2t+B3x3t+...+Bkxkt+ε[itex]^{*}_{t}[/itex]

where
ε[itex]^{*}_{t}[/itex] = εt + [itex]\gamma[/itex][itex]\varpi[/itex]t

Since Var(εt) = [itex]\sigma[/itex][itex]^{2}_{ε}+[/itex][itex]\gamma[/itex][itex]^{}_{t}[/itex]var([itex]\varpi[/itex]t)

I don't understand the variance part. I know that the variance of any epsilon is [itex]\sigma[/itex]2, but why does the γt go outside the variance operator? I know it's a constant so why isn't it γ2?
 
Physics news on Phys.org
  • #2
Rabolisk said:
Hey. Iam trying to understand how specification of the equation can lead to hetroscedasticity. This is stright out of my notes.

Yt=B1+B2x2t+B3x3t+...+BkXkt+[itex]\gamma[/itex][itex]\varpi+[/itex]ε[itex]^{}_{t}[/itex]


Yt=B1+B2x2t+B3x3t+...+Bkxkt+ε[itex]^{*}_{t}[/itex]

where
ε[itex]^{*}_{t}[/itex] = εt + [itex]\gamma[/itex][itex]\varpi[/itex]t

Since Var(εt) = [itex]\sigma[/itex][itex]^{2}_{ε}+[/itex][itex]\gamma[/itex][itex]^{}_{t}[/itex]var([itex]\varpi[/itex]t)

I don't understand the variance part. I know that the variance of any epsilon is [itex]\sigma[/itex]2, but why does the γt go outside the variance operator? I know it's a constant so why isn't it γ2?

If γ is a constant the it's a typo and γ should be squared when outside the variance.

This seems a time series, so one to way to introduce heterocedasticity in this model is by increasing γt over time, I am assuming ϖ is a random variable with the same behavior over time (it's not clear in your formulation since sometimes they both have the t subscript at the end but not in the beginning).
 

1. What is hetroscedasticity?

Hetroscedasticity is a statistical term that refers to the unequal distribution of variance in a dataset. In other words, it means that the variability of data points is not consistent across the range of values.

2. What causes hetroscedasticity?

There can be several factors that cause hetroscedasticity, such as outliers, measurement errors, and omitted variables. It can also occur due to the nature of the data, such as in time series data where the variance may increase over time.

3. How does hetroscedasticity affect statistical analysis?

Hetroscedasticity can lead to biased and unreliable results in statistical analysis. It can affect the accuracy of regression models, significance tests, and confidence intervals, making it difficult to draw valid conclusions from the data.

4. How can hetroscedasticity be detected?

There are several ways to detect hetroscedasticity, such as visual inspection of scatter plots, statistical tests like the Breusch-Pagan test, and residual plots in regression analysis.

5. What can be done to address hetroscedasticity?

If hetroscedasticity is detected, there are a few methods that can be used to address it, such as transforming the data, using weighted regression, or using robust regression techniques. It is also important to identify and address the underlying causes of hetroscedasticity.

Similar threads

  • Atomic and Condensed Matter
Replies
1
Views
2K
Replies
11
Views
3K
Back
Top