4
$\begingroup$

I wish to predict variable $y$, and so I am tempted to estimate

$$ y_t = \beta_0 + \beta_1 x_t+ u_t $$

Looking at a plot of $y$, the series does not seem stationary. Instead I regress like so:

$$ y_t - y_{t-1} = \gamma ( x_t - x_{t-1} ) + u_t $$

Now the purpose of this time series transformation is to make the series stationary - lets assume that the series is stationary in the changes.

How do then back track, and calculate the actual level predictions?

Bonus points for R code.

$\endgroup$

1 Answer 1

5
$\begingroup$

If you have

  1. a starting point $y_t$ at levels,
  2. predictions of the increments $\Delta \hat y_{t+1},\dotsc,\Delta \hat y_{t+h}$,

then to obtain the prediction $\hat y_{t+h}$ you need to sum $y_t$ and all the predicted increments $\Delta \hat y_{t+i}$ for $i=1,\dotsc,h$:

$$ \hat y_{t+h} = y_t + \Delta \hat y_{t+1} + \dotsc + \Delta \hat y_{t+h} $$

In R this can be done as follows: sum(c(y[t],dy_hat[1:h])) where y is the original data vector and dy_hat is a vector composed of the predicted increments $\Delta \hat y_{t+1},\dotsc,\Delta \hat y_{t+h}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.