Regression with Intentional Time Gaps in Time Series Data - Collinearity Issue

[Guest]

Hi,
I am new to Stata and am having some issues with my analysis of safe haven asset performance during the 2008 GFC and COVID-19.
I am regressing safe haven asset returns (x) on stock market returns (y). I am using the following model:

I need to have five coefficients within the same regression so that there is one constant term for all.
Say I am looking at gold returns in the US, I need the following coefficients:

hedge (b1) - safe haven assets baseline hedge, i.e., normal times excluding crisis periods (GFC and COVID)
GFC (b2) - [COLOR=black !important]incremental safe haven asset beta i.e. [/COLOR]GFC crisis period which is 20 trading days (12/09/2008 - 09/10/2008)
total GFC beta (sum of b1 + b2) - total effect for the given crisis (normal times + GFC crisis period)
COVID (b3) - incremental asset beta i.e., COVID 20 day crisis period (20/02/2020 - 18/03/2020)
total COVID effect (sum of b1 + b3) - total effect for COVID crisis (normal times + COVID crisis period)

I end up with multiple gaps in the time series data which causes issues.
I know I need to create dummy variables and this works for GFC and COVID crisis periods. Next, I create dummies for the total GFC and total COVID then try to regress,
"regress GOLD USA hedge gfc total_gfc covid total_covid"
The total effects are ommitted due to collinearity.
I don't know if I should try something to do with sub samples, time periods etc. I have very little knowledge in this area.

(I also tried filling the gaps in the data with "." to show that they are intentional however then Stata does not read the variables at all.)

I am at a loss on how to fix this issue and if anyone has any advice, I would be so grateful if you could let me know.
Thank you very much in advance!

The results I am trying to mimic:

[Andrew Musau]

hedge (b1) - safe haven assets baseline hedge, i.e., normal times excluding crisis periods (GFC and COVID)
GFC (b2) - [COLOR=black !important]incremental safe haven asset beta i.e. [/COLOR]GFC crisis period which is 20 trading days (12/09/2008 - 09/10/2008)
total GFC beta (sum of b1 + b2) - total effect for the given crisis (normal times + GFC crisis period)
COVID (b3) - incremental asset beta i.e., COVID 20 day crisis period (20/02/2020 - 18/03/2020)
total COVID effect (sum of b1 + b3) - total effect for COVID crisis (normal times + COVID crisis period)

I end up with multiple gaps in the time series data which causes issues.
I know I need to create dummy variables and this works for GFC and COVID crisis periods. Next, I create dummies for the total GFC and total COVID then try to regress,
"regress GOLD USA hedge gfc total_gfc covid total_covid"
The total effects are ommitted due to collinearity.

The total effects are not estimated within the regression. "b1" refers to the coefficient on "hedge" and "b2" refers to the coefficient on "GFC". Then you'd use lincom to get the sum, e.g.,

sysuse auto, clear
regress price mpg weight disp turn, robust
lincom mpg+weight

Res.:

. regress price mpg weight disp turn, robust

Linear regression                               Number of obs     =         74
                                                F(4, 69)          =       8.06
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3869
                                                Root MSE          =     2375.5

------------------------------------------------------------------------------
             |               Robust
       price | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -75.61446   97.39065    -0.78   0.440    -269.9035    118.6746
      weight |   3.163333   1.368061     2.31   0.024     .4341258     5.89254
displacement |     3.3905    6.61112     0.51   0.610    -9.798323    16.57932
        turn |   -398.084   177.8671    -2.24   0.028    -752.9192   -43.24872
       _cons |   13338.64   6347.139     2.10   0.039     676.4428    26000.83
------------------------------------------------------------------------------

.
. lincom mpg+weight

 ( 1)  mpg + weight = 0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |  -72.45113   97.91878    -0.74   0.462    -267.7937    122.8915
------------------------------------------------------------------------------

.

[Guest]

Thank you so much for your response!
Since my post, I have realised that the model used is actually GJR-GARCH.
Do you have any experience with this by any chance?

[Andrew Musau]

I know of GARCH models, but I rarely engage in time-series analysis. My primary focus is on panel data models.