12-practical.Rmd

---
title: "ETC3550: Applied forecasting for business and economics"
author: "Ch12. Some practical forecasting issues"
date: "OTexts.org/fpp2/"
fontsize: 14pt
output:
  beamer_presentation:
    fig_width: 7
    fig_height: 3.5
    highlight: tango
    theme: metropolis
    includes:
      in_header: header.tex
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, cache=TRUE, warning=FALSE, message=FALSE)
library(fpp2)
options(digits=3,width=50)
```

# Models for different frequencies

## Models for different frequencies

\vspace*{-0.2cm}

### Models for annual data

 * ETS, ARIMA, Dynamic regression
\pause

### Models for quarterly data

 * ETS, ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA
\pause

### Models for monthly data

 * ETS, ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA

## Models for different frequencies

### Models for weekly data

 * ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA, TBATS
\pause

### Models for daily, hourly and other sub-daily data

 * ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA, TBATS


# Ensuring forecasts stay within limits

## Positive forecasts
\fontsize{12}{12}\sf

```{r}
eggs %>%
  ets(model="AAN", damped=FALSE, lambda=0) %>%
  forecast(h=50, biasadj=TRUE) %>%
  autoplot()
```


# Forecast combinations

## Forecast combinations

### Clemen (1989)
"The results have been virtually unanimous: combining multiple forecasts leads to increased forecast accuracy. \dots In many cases one can make dramatic performance improvements by simply averaging the forecasts."

## Forecast combinations
\fontsize{10}{10}\sf\vspace*{-0.2cm}
```r
train <- window(auscafe, end=c(2012,9))
h <- length(auscafe) - length(train)
ETS <- forecast(ets(train), h=h)
ARIMA <- forecast(auto.arima(train, lambda=0, biasadj=TRUE),
  h=h)
STL <- stlf(train, lambda=0, h=h, biasadj=TRUE)
NNAR <- forecast(nnetar(train), h=h)
TBATS <- forecast(tbats(train, biasadj=TRUE), h=h)
Combination <- (ETS[["mean"]] + ARIMA[["mean"]] +
  STL[["mean"]] + NNAR[["mean"]] + TBATS[["mean"]])/5

autoplot(auscafe) +
  autolayer(ETS, series="ETS", PI=FALSE) +
  autolayer(ARIMA, series="ARIMA", PI=FALSE) +
  autolayer(STL, series="STL", PI=FALSE) +
  autolayer(NNAR, series="NNAR", PI=FALSE) +
  autolayer(TBATS, series="TBATS", PI=FALSE) +
  autolayer(Combination, series="Combination") +
  xlab("Year") + ylab("$ billion") +
  ggtitle("Australian monthly expenditure on eating out")
```

## Forecast combinations
\fontsize{10}{10}\sf\vspace*{-0.2cm}
```{r combine1, message=FALSE, warning=FALSE, echo=FALSE}
train <- window(auscafe, end=c(2012,9))
h <- length(auscafe) - length(train)
ETS <- forecast(ets(train), h=h)
ARIMA <- forecast(auto.arima(train, lambda=0, biasadj=TRUE),
  h=h)
STL <- stlf(train, lambda=0, h=h, biasadj=TRUE)
NNAR <- forecast(nnetar(train), h=h)
TBATS <- forecast(tbats(train, biasadj=TRUE), h=h)
Combination <- (ETS[["mean"]] + ARIMA[["mean"]] +
  STL[["mean"]] + NNAR[["mean"]] + TBATS[["mean"]])/5
```

```{r combineplot, dependson="combine1", echo=FALSE, fig.height=4.8}
autoplot(auscafe) +
  autolayer(ETS, series="ETS", PI=FALSE) +
  autolayer(ARIMA, series="ARIMA", PI=FALSE) +
  autolayer(STL, series="STL", PI=FALSE) +
  autolayer(NNAR, series="NNAR", PI=FALSE) +
  autolayer(TBATS, series="TBATS", PI=FALSE) +
  autolayer(Combination, series="Combination") +
  xlab("Year") + ylab("$ billion") +
  ggtitle("Australian monthly expenditure on eating out")
```

## Forecast combinations
\fontsize{11}{15}\sf
```{r combineaccuracy, dependson="combine1"}
c(ETS = accuracy(ETS, auscafe)["Test set","RMSE"],
  ARIMA = accuracy(ARIMA, auscafe)["Test set","RMSE"],
  `STL-ETS` = accuracy(STL, auscafe)["Test set","RMSE"],
  NNAR = accuracy(NNAR, auscafe)["Test set","RMSE"],
  TBATS = accuracy(TBATS, auscafe)["Test set","RMSE"],
  Combination =
    accuracy(Combination, auscafe)["Test set","RMSE"])
```

# Missing values

## Missing values
\fontsize{14}{15}\sf

**Functions which can handle missing values**

 * `auto.arima()`, `Arima()`
 * `tslm()`
 * `nnetar()`

**Models which cannot handle missing values**

 * `ets()`
 * `stl()`
 * `stlf()`
 * `tbats()`

\pause

### What to do?
 1. Model section of data after last missing value.
 2. Estimate missing values with `na.interp()`.

## Missing values
\fontsize{12}{12}\sf
```{r}
autoplot(gold)
```

## Missing values
\fontsize{12}{12}\sf
```{r, fig.height=3}
gold %>% na.interp() %>%
  autoplot(series="Interpolated") +
    autolayer(gold, series="Original") +
    scale_color_manual(
      values=c(`Interpolated`="red",`Original`="gray"))
```

# Outliers

## Outliers

```{r, fig.height=3.4}
autoplot(gold)
```

## Outliers

```{r, fig.height=3.4}
tsoutliers(gold)
```

## Outliers

```{r, fig.height=3.4}
gold %>% tsclean() %>% autoplot()
```