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I want to do these two things (combined) with a time series T:

  1. forecast the seasonally adjusted component of T (STL used for the decomposition) and "add back" the seasonality (I assume that the seasonal component is unchanging, so I use naïve method for the seasonal component)
  2. fit a regression model with ARIMA errors (exogenous regressors included in the formula)

In other words, I want to obtain forecasts using the seasonally adjusted component of T integrating an external predictor and "adding back" the seasonality.

I can do these two operations separately, but I can't get them to work in combination

Here is some toy examples:

First, load libraries and data:

library(forecast)
library(tsibble)
library(tibble)
library(tidyverse)
library(fable)
library(feasts)
library(fabletools)


us_change <- readr::read_csv("https://otexts.com/fpp3/extrafiles/us_change.csv") %>%
  mutate(Time = yearquarter(Time)) %>%
  as_tsibble(index = Time)

Example of fit and forecast with seasonally adjusted component of T:

model_def = decomposition_model(STL,
                                Consumption  ~ season(window = 'periodic') + trend(window = 13),
                                ARIMA(season_adjust ~ PDQ(0,0,0)),
                                SNAIVE(season_year),
                                dcmp_args = list(robust=TRUE)) 

fit <- us_change %>% model(model_def)

report(fit)

forecast(fit, h=8) %>% autoplot(us_change)

Example of regression model with ARIMA errors (Income as predictor):

model_def = ARIMA(Consumption ~ Income + PDQ(0,0,0))

fit <- us_change %>% model(model_def)

report(fit)

us_change_future <- new_data(us_change, 8) %>% mutate(Income = mean(us_change$Income))

forecast(fit, new_data = us_change_future) %>% autoplot(us_change)

These examples work, but I would like to do something like this:

model_def = decomposition_model(STL,
                                Consumption  ~ season(window = 'periodic') + trend(window = 13),
                                ARIMA(season_adjust ~ Income + PDQ(0,0,0)),
                                SNAIVE(season_year),
                                dcmp_args = list(robust=TRUE))


fit <- us_change %>% model(model_def)

report(fit)

us_change_future <- new_data(us_change, 8) %>% mutate(Income = mean(us_change$Income))

forecast(fit, new_data = us_change_future) %>% autoplot(us_change)

I get this output in the console:

> fit <- us_change %>% model(model_def)
Warning message:
1 error encountered for model_def
[1] object 'Income' not found

> 
> report(fit)
Series: Consumption 
Model: NULL model 
NULL model> 

So I tried doing this in decomposition_model:

model_def = decomposition_model(STL,
                                Consumption  ~ season(window = 'periodic') + trend(window = 13),
                                ARIMA(season_adjust ~ us_change$Income + PDQ(0,0,0)),
                                SNAIVE(season_year),
                                dcmp_args = list(robust=TRUE))

No problem with the fit, but now I get an error in the forecast:

> forecast(fit, new_data = us_change_future) %>% autoplot(us_change)
Error in args_recycle(.l) : all(lengths == 1L | lengths == n) is not TRUE
In addition: Warning messages:
1: In cbind(xreg, intercept = intercept) :
  number of rows of result is not a multiple of vector length (arg 2)
2: In z[[1L]] + xm :
  longer object length is not a multiple of shorter object length

What am I doing wrong?

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