## RWWD, RWD, Drift, Mean

Econometrics questions and discussions

### RWWD, RWD, Drift, Mean

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 dataOPEN 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 formlog USXJPN / lUSXJPN** compute log returnsset dlUSXJPN = 100.0*( lUSXJPN - lUSXJPN{1} )** view basic statisticstable / USXJPN lUSXJPN dlUSXJPN***===============================* Choose returns seriesset y = dlUSXJPN*** (1) RWWD (RW without Drift) or naive modelset RWWD = y{1}* Orboxjenk(diffs=1,define=foreeq_RWWD_y) y 2 6236uforecast(equation=foreeq_RWWD_y,from=(6236+1),steps=1) yhat_RWWD_y* Orequation(coeffs=1.0) eqn1_naive y# y{1}uforecast(equation=eqn1_naive,static,steps=1) eqn1_naive_foreprin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore* (2) RWD (RW with Drift) modelboxjenk(diffs=1,constant,define=foreeq_RWD) y 2 6236uforecast(equation=foreeq_RWD,from=(6236+1),steps=1) yhat_RWD_yprin 6230 6237 y RWWD yhat_RWWD_y eqn1_naive_fore yhat_RWD_y* Drift or mean/constant term for RWDdiff y / dylinreg(define=foreeq_DRIFT) dy 3 6236# constantuforecast(equation=foreeq_DRIFT,from=(6236+1),steps=1) yhat_DRIFT_y* ORboxjenk(diffs=0,constant,define=foreeq_DRIFTBJ) dy 2 6236uforecast(equation=foreeq_DRIFTBJ,from=(6236+1),steps=1) yhat_DRIFTBJ_yprin 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 handset RESULTSBH_DRIFT = RWWD + yhat_DRIFT_yset RESULTSBH_DRIFTBJ = RWWD + yhat_DRIFTBJ_yprin 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 modelboxjenk(diffs=0,constant,define=foreeq_MEAN) y 2 6236uforecast(equation=foreeq_MEAN,from=(6236+1),steps=1) yhat_MEAN_yprin 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

Posts: 201
Joined: Thu Apr 15, 2010 6:30 am
Location: London, UK

### Re: RWWD, RWD, Drift, Mean

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

Posts: 7240
Joined: Wed Nov 01, 2006 5:36 pm

### Re: RWWD, RWD, Drift, Mean

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

Posts: 201
Joined: Thu Apr 15, 2010 6:30 am
Location: London, UK

### Re: RWWD, RWD, Drift, Mean

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

Posts: 7240
Joined: Wed Nov 01, 2006 5:36 pm 