How to deal with overlapping problem

[atbui]

Hi
I am running Uncovered interest rate parity (UIP) regression. The model is said to be faced ovelapping obeservation. Could anybody explain me the problem of overlapping observation and how to eliminate this in the model

Thank you very much

[TomDoan]

A good description of this is in Hayashi(2000), Econometrics, (Princeton University Press) pp 418-427; RATS example file hayp438.prg. The summary is that the residuals are serial correlated due to overlapping "forecasts", but you can't apply GLS to correct for that because the RHS variables aren't exogenous---if you run an AR(1) correction on y(t)=x(t)b+u(t), you are actually running

y(t)-rho y(t-1)=(x(t)-rho x(t-1))b + u(t)-rho u(t-1)

Because of the construction of the variables, x(t-1) is likely to be correlated with u(t), making OLS on the transformed data inconsistent.

One way to handle this is to estimate the regression by OLS, then correct the covariance matrix for the serial correlation. Hayashi describes using what are known as Hodrick-Hansen standard errors, which is done in RATS with the options LWINDOW=FLAT and LAGS=# of lags. You can also use Newey-West (LWINDOW=NEWEY and LAGS=#...) or any of the other options for the lag window. There is also a specialized covariance matrix calculation which is described in the forum at http://www.estima.com/forum/viewtopic.php?f=5&t=608. These Hodrick standard errors use a calculation which is valid only for multi-step predictability regressions.

[IRJ]

Can we generalize this by saying that the Hodrick-Hansen standard errors and Newey-West standard errors could in general both be appropriate for an overlapping observations case?
And do Hansen-Hodrick standard errors refer to standard errors discussed in Hansen and Hodrick (1980) "Forward exchange rates as optimal predictors of future spot rates: An econometric analysis", Journal of Political Economy, 88, 829-853?
Thanks.

[TomDoan]

Correct and correct.

[comac]

Dear Tom,

I saw this post is pretty old but I'd have a quick question on this. Again on the UIP

The question is: does this Newey Window correction also generalize to the multivariate case (i.e. in a VAR) ?

For instance, assume that in I am estimating the UIP in a VAR (Delta exchange rate: DS and interest rate spread: (i-i*)). I first select the number of lags as to be equal to N, based on the information criteria.
What if I then estimate....

Code: Select all

SYSTEM(model=varmodel)
VARIABLES DS (i - i*)
LAGS 1 to N
DET CONSTANT
END(SYSTEM)
SUR(MODEL=varmodel,....,LWINDOW=NEWEY,LAGS=maturity-1)


Or better, what's the interpretation of correcting for MA terms in this case? Does it make sense? If no, what's the option lwindow used for?

Many thanks in advance

[TomDoan]

Dear Tom,

I saw this post is pretty old but I'd have a quick question on this. Again on the UIP

The question is: does this Newey Window correction also generalize to the multivariate case (i.e. in a VAR) ?

For instance, assume that in I am estimating the UIP in a VAR (Delta exchange rate: DS and interest rate spread: (i-i*)). I first select the number of lags as to be equal to N, based on the information criteria.
What if I then estimate....

Code: Select all

SYSTEM(model=varmodel)
VARIABLES DS (i - i*)
LAGS 1 to N
DET CONSTANT
END(SYSTEM)
SUR(MODEL=varmodel,....,LWINDOW=NEWEY,LAGS=maturity-1)


Or better, what's the interpretation of correcting for MA terms in this case? Does it make sense? If no, what's the option lwindow used for?

Many thanks in advance

The combination of lagged dependent variables with serially correlated errors produces inconsistent estimates for the same reason cited above, so if your VAR is leaving serial correlation in the residuals, you have a problem. (Of course, the whole point of choosing optimal lags on the VAR is to effectively get rid of the serial correlation).