Forecasting Random Walk

[Jules89]

Hello,

I have a variable S_t and I would like to "estimate" a "random walk" of the following type:
S_t = S_t-x + error_t, where x is an arbitrary number bigger than 1. Then I want to do one step ahead out of sample forecasting.

Afterwards I would like to estimate the following model: S_t-S_(t-x) = \alpha*Z_t-1 + error_t and also want to do one step ahead out of sample forecasting.
Afterwards I want to compare the forecasts and test for equal MSEs and encompassing by using the clarkforetest.src procedure, because the models are nested.

So basicly I want to test a random walk, with a larger difference than 1, against an alternative model with an explainatory varriable and then apply Clark and McCrakens procedure. Is there any suggestion how I can do that? I dont know to "estimate" a model S_t = S_t-x + error_t, I know that the coefficient is one, but how can I put that into the clarkforetest.src procedure?

Thank you for your help

Best Jules

[Jules89]

So my idea was the following:

let S be my variable to be forecasted and X be my variable for which I want to test the forecasting accuracy:
I want to test S_t-S_(t-10)= error_t against S_t-S_(t-10)= a*X_t + error_t:

@forecastproc(scheme=3) S "last date of Insample period" "start" "end"
# S{10}
# X

Is that correct? Or would it be like estimating a random walk as:
linreg S
# S{10}?????

Thanks a lot

Jules

[IRJ]

For a random walk without a drift (i.e. without a constant), there are no parameters to estimate so you need not estimate any model. You simply generate the forecast in RATS with a something like:

Code: Select all

 set s = s{1}

For a random walk with drift (i.e. with a constant), you need to estimate a model with only a constant (i.e. intercept). In RATS,

Code: Select all

 linreg s
#constant 

Note that with a rolling window, this is equivalent to a moving window historical average of the series itself.

You can't use the procedure clarkforetest.src when one of the models does not contain estimated parameters. Usually, the random walk with or without a drift are usually a benchmark against which to compare other models so I'm not sure that you'd benefit much from comparing two random walks.