RWWD, RWD, Drift, Mean

Econometrics questions and discussions

RWWD, RWD, Drift, Mean

Unread postby ac_1 » Tue Dec 29, 2020 6:45 am

Hi Tom,

I am modelling fx-rates, I would like to know if the the following 3 benchmark models are correctly specified (with forecasts) in RATS for the fx-rates RETURNS series, or are they only true for the fx-rates LOG-LEVELS series, or true for either RETURNS and LOG-LEVELS fx-rates series?:

(1) RWWD (RW without Drift) or naive model.
(2) RWD (RW with Drift) model,
including calculation of the Drift term for RWD model.
(3) MEAN/CONSTANT model.

Here's a reproducible example using the RATS dataset g10xrate.xls:
Code: Select all
*===============================
* read in data
OPEN DATA "/Users/Shared/RATS/Examples/g10xrate.xls"
DATA(FORMAT=XLS,NOLABELS,ORG=COLUMNS,TOP=2) 1 6237 USXJPN USXFRA USXSUI USXNLD USXUK $
USXBEL USXGER USXSWE USXCAN USXITA
*
* transform data into log form
log USXJPN / lUSXJPN
*
* compute log returns
set dlUSXJPN = 100.0*( lUSXJPN - lUSXJPN{1} )
*
* view basic statistics
table / USXJPN lUSXJPN dlUSXJPN
*
*
*===============================
* Choose returns series
set y = dlUSXJPN
*
*
* (1) RWWD (RW without Drift) or naive model
set RWWD = y{1}
* Or
boxjenk(diffs=1,define=foreeq_RWWD_y) y 2 6236
uforecast(equation=foreeq_RWWD_y,from=(6236+1),steps=1) yhat_RWWD_y
* Or
equation(coeffs=1.0) eqn1_naive y
# y{1}
uforecast(equation=eqn1_naive,static,steps=1) eqn1_naive_fore
prin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore


* (2) RWD (RW with Drift) model
boxjenk(diffs=1,constant,define=foreeq_RWD) y 2 6236
uforecast(equation=foreeq_RWD,from=(6236+1),steps=1) yhat_RWD_y
prin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore yhat_RWD_y


* Drift or mean/constant term for RWD
diff y / dy
linreg(define=foreeq_DRIFT) dy 3 6236
# constant
uforecast(equation=foreeq_DRIFT,from=(6236+1),steps=1) yhat_DRIFT_y
* OR
boxjenk(diffs=0,constant,define=foreeq_DRIFTBJ) dy 2 6236
uforecast(equation=foreeq_DRIFTBJ,from=(6236+1),steps=1) yhat_DRIFTBJ_y
prin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore yhat_RWD_y yhat_DRIFT_y yhat_DRIFTBJ_y

* Check Equivalence RWD (RW with Drift) and results by hand
set RESULTSBH_DRIFT = RWWD + yhat_DRIFT_y
set RESULTSBH_DRIFTBJ = RWWD + yhat_DRIFTBJ_y
prin 6230 6237 y RWWD yhat_RWWD_y yhat_RWD_y eqn1_naive_fore yhat_RWD_y yhat_DRIFT_y RESULTSBH_DRIFT RESULTSBH_DRIFTBJ


* (3) MEAN/CONSTANT model
boxjenk(diffs=0,constant,define=foreeq_MEAN) y 2 6236
uforecast(equation=foreeq_MEAN,from=(6236+1),steps=1) yhat_MEAN_y
prin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore yhat_RWD_y yhat_DRIFT_y RESULTSBH_DRIFT RESULTSBH_DRIFTBJ yhat_MEAN_y


many thanks,
Amarjit
ac_1
 
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Re: RWWD, RWD, Drift, Mean

Unread postby TomDoan » Wed Dec 30, 2020 1:09 pm

I'm not really sure what you're asking. That's the correct way to forecast any series using those simple models. They just don't make sense as forecasting models for returns.
TomDoan
 
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Re: RWWD, RWD, Drift, Mean

Unread postby ac_1 » Thu Dec 31, 2020 6:01 am

TomDoan wrote:They just don't make sense as forecasting models for returns.


Why?

The aim is to compare the 3 models with each other, plus additional models - then the obvious question is what are good models for forecasting returns?
ac_1
 
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Location: London, UK

Re: RWWD, RWD, Drift, Mean

Unread postby TomDoan » Thu Dec 31, 2020 4:24 pm

ac_1 wrote:
TomDoan wrote:They just don't make sense as forecasting models for returns.


Why?

The aim is to compare the 3 models with each other, plus additional models - then the obvious question is what are good models for forecasting returns?


There are entire textbooks written to answer that question. And there's a great deal of literature devoted to how returns (of traded financial assets) are expected to behave. They are, at best, very weakly correlated, which means that random walk models are unreasonable.
TomDoan
 
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