Dueker JBES 1997 MS-GARCH models

[TomDoan]

These are replication files for Dueker(1997), "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," J of Business & Economic Statistics, vol. 15, no 1, 26-34. Dueker fits several different models with different types of switching. All of models allow the mean to switch, but several have "variances" switching, and two have the degrees of freedom in the conditional t density switching in different ways.

Switching GARCH (as opposed to ARCH) models require "collapsing" the history of the regimes in some fashion. Dueker waits one period longer for this than Gray(1996) does. This actually makes it easier to adapt the technique to different models than Gray's.

Switching ARCH/GARCH models is one of the topics in the 2nd Edition of the Structural Breaks and Switching Models course materials. In particular, it applies the Dueker filter to the model and data from Gray, as Dueker's data set really doesn't seem to find any sign of a regime break.

Zip with programs and data

Detailed description

[lumengobobo46]

Dear Tom

I am trying to display the conditional variance according to the different regimes for the first programme (DUEKER-SWARCH). I use the followings:
set momo = gv(1)*h(i)
graph
# momo

i have an answer: missing operator or adjacent operator.

please can you help. I will also like to display the series momo.

Regards

[TomDoan]

1. Where are you putting this?
2. The "ARCH" factors are dependent upon the expanded states (8 of them with two regimes and two lags + current) and the GV scaling depends upon the contemporaneous regimes, so you wouldn't be using gv(1). Are you looking for eight time series, or did you want something else?

[lumengobobo46]

Hi tom

Thank you for your prompt response
1. I write the code at the end of the programme.
2. I want to obtain all the time series for conditional volatility (ARCH) related to the different regimes. they are more than 2000 observations.

Regards

[TomDoan]

Hi tom

Thank you for your prompt response
1. I write the code at the end of the programme.
2. I want to obtain all the time series for conditional volatility (ARCH) related to the different regimes. they are more than 2000 observations.

Regards

What I'm saying is that at each point in time, there are eight numbers, one for each combination of regimes for t, t-1 and t-2. At any given time period, many of those will have virtually zero probability, so the conditional volatility could be almost complete nonsense. I don't think those time series are especially useful---so the question is, what do you really want?

[lumengobobo46]

Hi Tom
I am currently trying to replicate a paper: "Rodrigues, J.C. (2007). Measuring financial contagion: A copula approach, journal of emepirical economics,14, 401-423." by using my own data. The main idea of the paper is to find dependence of conditional volatilities in high and low regime (states) of volatilities. i thought that if i can have time-series data of volatilities in the different regimes, after estimating a SWARCH model, then i could model a copula to find dependence between them. I am expecting the dependence to be different in the different regimes(represented by those time series i would like to derive from the estimated SWARCH model).

REgards

[sr64420]

Dear Tom,
I have another questions on these programs. Is it possible to retrieve the GARCH series in the different programs swgarch-df, swgarch-k etc. ?

Thank you
Serge

[TomDoan]

Dear Tom,
I have another questions on these programs. Is it possible to retrieve the GARCH series in the different programs swgarch-df, swgarch-k etc. ?

Thank you
Serge

The VECTOR[SERIES] HS has the collapsed filtered estimates of the variances. How useful they will be is unclear since a variance associated with an improbable regime could be almost anything.

[jack]

Tom,
can I compute the smoothed probabilities and the ex ante probabilities for SW-GARCH-DF model (with switching degrees of freedom and means with
conditionally t distributed errors) just as Gray has done in his paper?

[TomDoan]

Yes. It's exactly the same with all those models.

[jack]

Tom,
1.When I run the W-GARCH-DF model ( with switching degrees of freedom and means with
conditionally t distributed errors) with the uploaded data you provided (s&p500), I get this error:

NO CONVERGENCE IN 67 ITERATIONS
LAST CRITERION WAS 0.0000000
SUBITERATIONS LIMIT EXCEEDED.
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Usable Observations

2. How can I compute the smoothed probabilities and the ex ante probabilities for SW-GARCH-DF model?

[TomDoan]

Tom,
1.When I run the W-GARCH-DF model ( with switching degrees of freedom and means with
conditionally t distributed errors) with the uploaded data you provided (s&p500), I get this error:

NO CONVERGENCE IN 67 ITERATIONS
LAST CRITERION WAS 0.0000000
SUBITERATIONS LIMIT EXCEEDED.
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK
Usable Observations

The original program seems to work fine. However, the switching degrees of freedom seems like a throwaway idea that isn't worth pursuing---there just isn't much of a difference in what observations will look like based upon changing the d of f. (Note that the variances will be the same in the two regimes).

2. How can I compute the smoothed probabilities and the ex ante probabilities for SW-GARCH-DF model?

It's the same for all these models. You already asked about that:

https://estima.com/forum/viewtopic.php?p=13658#p13658

[jack]

The original program seems to work fine. However, the switching degrees of freedom seems like a throwaway idea that isn't worth pursuing---there just isn't much of a difference in what observations will look like based upon changing the d of f. (Note that the variances will be the same in the two regimes).

There are 5 models in Dueker paper. Which one do you think is worth pursuing?

[TomDoan]

Based upon the results in the paper, probably none. At least with that data set, none of them show a clear advantage over a single regime model. However, switching degrees of freedom seems almost pointless---the difference between two different values for the degrees of freedom given a common variance is too minor to be useful in separating data into regimes. (Smaller d.f. means that both larger absolute values and values close to zero are more common).

[jack]

Thanks a lot for your reply.
So which one do you recommend for modeling two regime volatility: Gray' model? Dueker? or Hamilton-Susmel model?

I ask this question because I am somehow baffled by these models and I do not know which one is better than others in practice.