VAR and back-transformation: Principles of forecasting

[nickcox896]

Most of the time, when conducting empirical VAR analysis we need to take

a) the log of the variables,
b) the first difference of the variables
c) the second difference of the variables,
d) the difference of logs of the variables

due to non-stationarity of the variables.

Within ARIMA we can easily handle these 4 cases. I am not sure how to handle them within VAR.

My attempt (with data from the online textbook)

library(fpp3)

 google_stock <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) >= 2015) |>
  mutate(day = row_number()) |>
  update_tsibble(index = day, regular = TRUE)

google_2015 <- google_stock |> filter(year(Date) == 2015)

Case 1:the log of variables
case_1<- google_2015 |> model(VAR(vars(log(Open), log(High)))) |> forecast(h = 3, bootstrap = TRUE, times=100)

This case seems to be working OK. I hope the code I run is correct

Case 2:the first difference of variables

case_2<- google_2015  |>  model(VAR(vars(difference(Open), difference(High)))) |> forecast(h = 3,  bootstrap = TRUE, times=100)
 
Error in `inverse_table$get()`:
! No supported inverse for the `difference` transformation.
Run `rlang::last_trace()` to see where the error occurred.

Case 3:the second difference of variables

case_3<- google_2015  |>  model(VAR(vars(difference(Open,2), difference(High,2)))) |> forecast(h = 3,  bootstrap = TRUE, times=100)
 
Error in `inverse_table$get()`:
! No supported inverse for the `difference` transformation.
Run `rlang::last_trace()` to see where the error occurred.

case 4: the difference of logs of the variables

case_4<- google_2015  |>  model(VAR(vars(difference(log(Open)), difference(log(High))))) |> forecast(h = 3,  bootstrap = TRUE, times=100)
 
Error in `inverse_table$get()`:
! No supported inverse for the `difference` transformation.
Run `rlang::last_trace()` to see where the error occurred.

So the main problem is how to run cases 2 up to 4, which hold almost always in empirical analysis. I did some search and I think that we have to write some additional functions before running the VAR models based on this site (https://cran.r-project.org/web/packages/fable/vignettes/transformations.html) but I am not sure how to do it with the fable package.

[robjhyndman]

You need the VARIMA() function if you want more than a stationary VAR model. e.g.,

case_4 <- google_2015 |>
  model(VARIMA(vars(log(Open), log(High)) ~ pdq(d = 1, q = 0))) |>
  forecast(h = 3, bootstrap = TRUE, times = 100)

[nickcox896]

Thank you! Very good idea.

[nickcox896]

I noticed that the following code

google_2015 |>
  model(VARIMA(vars(log(Open), log(High)) ~ pdq(d = 1, q = 0))) 
# A mable: 1 x 2
# Key:     Symbol [1]
  Symbol `VARIMA(vars(log(Open), log(High)) ~ pdq(d = 1, q = 0))`
  <chr>                                                   <model>
1 GOOG                                    <VARIMA(1,1,1) w/ mean>

does not produce a VAR(p)=VARMA(p,0) in differences of logs but a VARMA(p,1) in differences of logs, although we set q=0.

With ARIMA that I checked I did not notice this issue

[robjhyndman]

Please report as a new bug at https://github.com/tidyverts/fable/issues