Negative coefficient of leverage effect in TGARCH model

[TomDoan]

Note that those are all (economically) tiny. They're only "statistically significant" because you have 2800 data points. Since all GARCH models are at best approximations, with enough (real-world) data, you will always reject the model, if you stick to a conventional .05 significance level. The fact that those correlations change when you change the sample range means that they're just artifacts of a particular subsample, and not actually something that should be included in the model.

See Leamer, Specification Searches, Chapter 4 (particularly Section 4.1) for a discussion of the absurdity of sticking with .05 significance levels as the sample size gets large.

[jack]

I greatly appreciate your help and comments.

I have a dataset for Mexico Peso from 1990 to 2000. In 2005, Mexico introduced Peso-Dollar futures contract. I want to see if this event has increase the volatility of spot market.

But Mexico on December 20, 1994 officially undervalued Peso 20 percent and therefor led to huge volatility in the market. So, there are large outlires for this period.

I don't know how to deal with this event. Can I delete this period from analysis? Can I delete the outlires of this period?

I have attached the data.

As always, I would be grateful if you could possibly guide me about this problem.

mexico.xlsx

(202 KiB) Downloaded 710 times

[TomDoan]

This is an example where someone basically just deleted several extreme outliers in a price series, thus making a return connecting the before and after prices:

https://estima.com/forum/viewtopic.php? ... =75#p14714

(you can work back through the thread to find the reference to the paper). If it's just one or two entries, you can also just put in a single entry dummy for each.

[jack]

Dear Tom,

I am studying ARCH-GARCH e-course. And I am reviewing your excelent comments here in this thread.

But I have a question about using normal distribution, QMLE, and t distribution.

You said that:

4 is a really small degrees of freedom for the t

and You said:

You seem to have rather dirty data, so you probably need the t.

What NUMBER is good for using t distribution? What do you mean exactly by "dirty"?

What about normal distribution and QMLE? DATA are most of times non-normal. SO,it seems one should always QMLE when data is not normally distribute (if the choice is between normal and QMLE NOT t distribution).
I ask this question because my policy variable is often insignificant by QLME but it is significant by normal distribution. So the results is very different.
And I don't konw why results about policy variable's p-valuse is so different when I use different distributions.

[TomDoan]

Dear Tom,

I am studying ARCH-GARCH e-course. And I am reviewing your excelent comments here in this thread.

But I have a question about using normal distribution, QMLE, and t distribution.

You said that:

4 is a really small degrees of freedom for the t

and You said:

You seem to have rather dirty data, so you probably need the t.

What NUMBER is good for using t distribution? What do you mean exactly by "dirty"?

You already described why the data are "dirty" above. A GARCH model assumes that the same process works (at least approximately) across the range that you use. Exchange rates that have been manipulated by one of the two countries aren't going to satisfy that assumption. Look at your data. Does the period before the devaluation look anything at all like the period after? Given that that period is ten years before the intervention in which you're interested, just start your analysis after things have settled down after the devaluation.

What about normal distribution and QMLE? DATA are most of times non-normal. SO,it seems one should always QMLE when data is not normally distribute (if the choice is between normal and QMLE NOT t distribution).
I ask this question because my policy variable is often insignificant by QLME but it is significant by normal distribution. So the results is very different.
And I don't konw why results about policy variable's p-valuse is so different when I use different distributions.

A t-distribution (particularly with a low degrees of freedom) means that really extreme outliers (like 10 standard deviations) aren't all that unlikely. By contrast, they are very unlikely with a Normal. If you have a dummy variable for the volatility which catches a range with several of the big outliers, those outliers can be "explained" by giving a big number to that dummy to increase the variance, and thus decrease how extreme those outliers are. That will most likely reduce the log likelihood at all the more standard types of points somewhat, but the improvement in the extreme values will outweigh those.

[jack]

Tom wrote:
Given that that period is ten years before the intervention in which you're interested, just start your analysis after things have settled down after the devaluation.

Dear Tom,

The period isn't ten years before the intervention in which I'm interested.

The ten years period is actually two sub-period: Five years before the introduction of futures contract and five years after the introduction of futures contract.
I want to examine the effects of the introduction of futures contract on spot market volatility. So, I use a dummy variable in a GARCH model for evaluating its effect.
Therefore I couldn't omit the first period. But as you said, first period is really different from second period because we have government intervention in the market in the latter days of the first period.

This is the problem I face in this exercise.

[TomDoan]

I have a dataset for Mexico Peso from 1990 to 2000. In 2005, Mexico introduced Peso-Dollar futures contract. I want to see if this event has increase the volatility of spot market.

But Mexico on December 20, 1994 officially undervalued Peso 20 percent and therefor led to huge volatility in the market. So, there are large outlires for this period.

I can only go by what you write. Obviously, you don't mean 2005 in the first paragraph which is where I got the 10 years. If you meant 1995, then you have basically two interventions at roughly the same time (devaluation and the addition of futures contracts), so it will probably be hard to separate the effects of the two.

You could skip perhaps a two year period around the interventions and do separate estimates before and after and compare them. Those can be treated as independent so the inference isn't difficult.

[jack]

I'm sorry it was my mistake. The correct date is 1995 as you said.

You could skip perhaps a two year period around the interventions and do separate estimates before and after and compare them. Those can be treated as independent so the inference isn't difficult.

Thank you for your suggestion. You mean comparing the A and B coefficients of the two GARCH models? Can we make inference about the effects of the introduction of futures contract on spot market volatility by compering those estimates?

[TomDoan]

A or B or C or any function of those. In effect, that's like putting dummies on all coefficients in the GARCH model.

[jack]

Dear Tom,

These are the results:

C1>C2 (1=first period, 2=second period)
A1>A2
B1<B2

Has the volatility of spot market increased after the introduction of futures contract?

[TomDoan]

The steady-state variance from a GARCH model is c/(1-a-b).