1
$\begingroup$

I would like to assess a single time-series for a changing variance structure that might be leading to spurious variance estimates when that time-series is used in regression.

In my head two terms come to mind: (1) Heteroscedasticity and (2) Volatility Clustering

Here are my related questions on this:

  1. (True/False) Heteroscedasticity is related to non-constant variance of the errors while Volatility Clustering is related to non-constant variance of the levels of the time-series. As such Heteroscedasticity can only be tested for using residuals from a regression. Variance Clustering on the other hand could be tested for on the levels themselves without the need for regression.
  2. How could I test an individual time-series for Volatility Clustering?
  3. Can Volatility Clustering lead to spurious regressions? If so is this effect enacted through inducing Heteroscedasticity in the regression?
$\endgroup$
2
$\begingroup$

1. I would say, heteroskedasticity can characterize original series, too. Suppose the variance of the original series was $\sigma_1^2$ from time $t_1$ to $t_k$ and turned to $\sigma_2^2$ since $t_{k+1}$. I would call that heteroskedasticity. Conversely, volatility clustering can characterize model residuals as well as the original series.

2. A popular specific type of volatility clustering is autoregressive conditional heteroskedasticity (ARCH). There is a Lagrange multiplier test known as ARCH-LM test.

3. The question is quite broad; let us consider the base case. Recall that OLS estimates are consistent (even) under heteroskedasticity. Consider two variables $x$ and $y$ that are linearly independent and mean-stationary but one or both of them have volatility clustering. The OLS estimate of the slope coefficient from a regression of $y$ on $x$ should (still) converge to zero as sample size increases. Aside from the base case, I cannot quickly come up with a situation where volatility clustering alone would yield spurious correlation between two linearly independent series (I do not claim it is impossible, but I do not see how it could work).

$\endgroup$
0
$\begingroup$

1) Heteroscedasticity is related to non-constant variance of the errors GIVEN that Volatility Clustering does not exist or has been remedied via Level Shift Detection Procedures ( Intervention Detection Procedures ) and model parameters are found to be inavariant over time and that other error mean-adjustment procedures have been used as necessary.

2) Given that you have accounted for autoregressive structure AND anomnaly detection such as Pulses , Seasonal Pulses , Time Trend changes , parameter changes over time and either Box-cox transformations of deterministic error variance cjanges THEN if it can be proven that there is one pr more level/step changes then you can conclude about Level Changes

3) Lots of things can lead to spurious regression.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.