How to estimate integrated Mean Reversion-Momentum Model?

[johnsirius]

Dear Eviews users and experts,

I've been trying to work this out this whole afternoon, basically its a model that combines stock price mean reversion process and momentum component together in a same process. It looks just like a multiple regression (Please see the attachment) only the coefficient is a function instead of a single number.

Descriptions of the Model: μ is a constant, δ is an autoregressive coefficient, ρ is the momentum coefficients, and the η is the mean-zero normal random term (serially and cross-sectionally uncorrelated with variance (σ sub_η)^2 )

I'm using Eviews 6, coding abilities are quite limited. I don't know if this is even doable in Eviews without much of codings. WIll be really appreciated if some of you experts can lend a hand. Thanks heaps in advance!

Regards,
John

[johnsirius]

I've figured out most of the parts with only one left now, it looks very simple：

X= (1-δ)μ + δ Xt-1 + e
(μ is a constant, Xt-1 is the lagged X, δ is the autoregressive coefficient)

I know for X= μ + δ Xt-1 + e , the command is simply x c x(-1)

In View>Representation, it looks like this:

Estimation Command:
=========================
LS X C X(-1)

Estimation Equation:
=========================
X = C(1) + C(2)*X(-1)

I've tried modifying the estimation equation to X = (1-C(2))*C(1) + C(2)*X(-1), but makes no change at all. It seems Evews doesn't recognise the modifications, am I doing the right thing here? If not what is the correct estimation command for X= (1-δ)μ + δ Xt-1 + e ?

Cheers,
John

[trubador]

This looks more like a Panel regression. I think you should formulate your model in Panel framework.

[johnsirius]

This looks more like a Panel regression. I think you should formulate your model in Panel framework.

Thanks a lot for your reply trubador, I have always been a fan of yours. But can you please be a bit more specific?

As far as I know, panel regression requires the data to be structured based on multiple cross-sectional datasets, whereas in my case, the only two time-series input are 1) a specific country price index; 2) a world price index. Perhaps I mis-specified the model?

Cheers,
John

[trubador]

I am not a Panel expert, so I cannot give any advice on this type of modeling. The multiplication of two constants leads to identification problem, since you are trying to estimate the model with a single equation. In other words, (1-c(2))*c(1) is indistinguishable from a single constant, c(3), and therefore you need additional information to accomplish that. However, if you are certain about your model, then you can first estimate X = c(3) + c(2)*X(-1), and then obtain c(1) = c(3)/(1-c(2)) as a residual. Yet, this is not an actual/correct solution to your problem...

[startz]

I've figured out most of the parts with only one left now, it looks very simple：

X= (1-δ)μ + δ Xt-1 + e
(μ is a constant, Xt-1 is the lagged X, δ is the autoregressive coefficient)

I know for X= μ + δ Xt-1 + e , the command is simply x c x(-1)

In View>Representation, it looks like this:

Estimation Command:
=========================
LS X C X(-1)

Estimation Equation:
=========================
X = C(1) + C(2)*X(-1)

I've tried modifying the estimation equation to X = (1-C(2))*C(1) + C(2)*X(-1), but makes no change at all. It seems Evews doesn't recognise the modifications, am I doing the right thing here? If not what is the correct estimation command for X= (1-δ)μ + δ Xt-1 + e ?

Cheers,
John

You should get the same value for c(2) and the same R-square, but you should be getting a different value for c(1).

[johnsirius]

You should get the same value for c(2) and the same R-square, but you should be getting a different value for c(1).

Thanks for your reply startz, what I've done is I entered XIT=(1-C(2))*C(1)+C(2)*XIT(-1) in the command section, and the representation shows:

Estimation Command:
=========================
LS(DERIV=AA) XIT=(1-C(2))*C(1)+C(2)*XIT(-1)

Estimation Equation:
=========================
XIT=(1-C(2))*C(1)+C(2)*XIT(-1)

Substituted Coefficients:
=========================
XIT=(1-0.990903074124)*-2.01110543959+0.990903074124*XIT(-1)

Does this mean I have successfully estimated X= (1-δ)μ + δ Xt-1 + e？ To me it looks correct, however, my only concern is when I looked at the estimation output:

Variable Coefficient Std. Error t-Statistic Prob.

C(2) 0.990903 0.009130 108.5269 0.0000
C(1) -2.011105 3.475028 -0.578731 0.5634

The variable has now changed to C(1) and C(2), instead of C and XIT(-1). Therefore, does this still mean Xt-1 (or XIT-1) is the explanatory variable?

[startz]

Yes, looks like you've done everything right.