7-6-forecasting-regression.Rmd

---
title: "7. Time series regression models"
author: "7.6 Forecasting with regression"
date: "OTexts.org/fpp3/"
classoption: aspectratio=169
titlepage: fpp3title.png
titlecolor: fpp3red
toc: false
output:
  binb::monash:
    colortheme: monashwhite
    fig_width: 7.5
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    keep_tex: no
    includes:
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---


```{r setup, include=FALSE}
source("setup.R")
```


## Ex-ante versus ex-post forecasts

 * \orange{Ex ante forecasts} are made using only information available in advance.
    - require forecasts of predictors
 * \orange{Ex post forecasts} are made using later information on the predictors.
    - useful for studying behaviour of forecasting models.

 * trend, seasonal and calendar variables are all known in advance, so these don't need to be forecast.

## Beer production
\fontsize{7}{7}\sf

```{r beeryetagain, echo=TRUE}
recent_production <- aus_production |> filter(year(Quarter) >= 1992)
recent_production |> model(TSLM(Beer ~ trend() + season())) |> 
   forecast() |> autoplot(recent_production)
```

## Scenario based forecasting

 * Assumes possible scenarios for the predictor variables
 * Prediction intervals for scenario based forecasts do not include the uncertainty associated with the future values of the predictor variables.


## US Consumption

```{r usconsumptionf, echo=TRUE}
fit_consBest <- us_change |>
  model(
    TSLM(Consumption ~ Income + Savings + Unemployment)
  )

future_scenarios <- scenarios(
  Increase = new_data(us_change, 4) |>
    mutate(Income = 1, Savings = 0.5, Unemployment = 0),
  Decrease = new_data(us_change, 4) |>
    mutate(Income = -1, Savings = -0.5, Unemployment = 0),
  names_to = "Scenario"
)

fc <- forecast(fit_consBest, new_data = future_scenarios)
```

## US Consumption

```{r usconsumptionf2, echo=TRUE}
us_change |> autoplot(Consumption) +
  labs(y = "% change in US consumption") +
  autolayer(fc) +
  labs(title = "US consumption", y = "% change")
```

## Building a predictive regression model {-}

 * If getting forecasts of predictors is difficult, you can use lagged predictors instead.
$$y_{t+h}=\beta_0+\beta_1x_{1,t}+\dots+\beta_kx_{k,t}+\varepsilon_{t+h}$$

 * A different model for each forecast horizon $h$.