revision.Rmd

---
title: "ETC3550: Applied forecasting for business and economics"
author: "Revision"
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 = FALSE, cache=TRUE, warning=FALSE, message=FALSE)
library(fpp2)
options(digits=4)
```

# Some case studies

## CASE STUDY 1: Paperware company

\fontsize{11}{13}\sf

\begin{textblock}{7.6}(0.2,1.5)
\textbf{Problem:} Want forecasts of each of hundreds of
items. Series can be stationary, trended or seasonal. They currently
have a large forecasting program written in-house but it doesn't seem
to produce sensible forecasts. They want me to tell them what is
wrong and fix it.

\textbf{Additional information}
\begin{itemize}\itemsep=0cm\parskip=0cm
  \item  Program  written in COBOL making numerical calculations limited. It is not possible to do any optimisation.
  \item Their programmer has little experience in numerical computing.
  \item They employ no statisticians and want the program to produce forecasts automatically.
\end{itemize}
\end{textblock}

\placefig{8}{1.}{width=4.8cm}{tableware2}


## CASE STUDY 1: Paperware company

### Methods currently used
A
: 12 month average

C
: 6 month average

E
: straight line regression over last 12 months

G
: straight line regression over last 6 months

H
: average slope between last year's and this year's values.
  (Equivalent to differencing at lag 12 and taking mean.)

I
: Same as H except over 6 months.

K
: I couldn't understand the explanation.


## CASE STUDY 2: PBS

\fontsize{13.5}{15.5}\sf

  * In 2001: \$4.5 billion budget, under-forecasted by \$800 million.
  * Thousands of products. Seasonal demand.
  * Subject to covert marketing, volatile products, uncontrollable expenditure.
  * Although monthly data available for 10 years, data are aggregated to annual values, and only the first three years are used in estimating the forecasts.
  * All forecasts being done with the \texttt{FORECAST} function in MS-Excel!


\begin{alertblock}<2>{}
\textbf{Problem:} How to do the forecasting better?
\end{alertblock}
\vspace{5cm}


## CASE STUDY 3: Car fleet company

**Client:** One of Australia's largest car fleet companies

**Problem:** how to forecast resale value of vehicles? How
should this affect leasing and sales policies?

\pause

### Additional information
 - They can provide a large amount of data on previous vehicles and their eventual resale values.
 - The resale values are currently estimated by a group of specialists. They see me as a threat and do not cooperate.

## CASE STUDY 4: Airline

\fontsize{12}{14}\sf

```{r, fig.height=3.5}
autoplot(melsyd[,"Economy.Class"],
  main="Economy class passengers: Melbourne-Sydney",
  xlab="Year",ylab="Thousands")
```

## CASE STUDY 4: Airline

**Problem:** how to forecast passenger traffic on major routes?

### Additional information

  * They can provide a large amount of data on previous routes.
  * Traffic is affected by school holidays, special events such as
the Grand Prix, advertising campaigns, competition behaviour, etc.
  * They have a highly capable team of people who are able to do
most of the computing.


# Review of topics covered

## 1. Introduction to forecasting and R

 - `ts` objects
 - seasonal periods
 - frequency, start, end
 - You don't have to write R code for the exam, but you do have to read and understand R code.

## 2. Time series graphics

 - time plot
 - season plot
 - subseries plot
 - lag plot
 - ACF

## 3. The forecasters' toolbox

  - Measures of forecast accuracy: MAE, MSE, RMSE, MAPE, MASE
  - Training/test sets. Out-of-sample accuracy
  - Problem of over-fitting.
  - Time series cross-validation
  - Box-Cox transformations to stabilize changing variance. Back-transformations after forecasting.
  - Residual diagnostics: ACF, white noise, LB test.
  - Simple methods: naive, seasonal naive, drift, \rlap{mean.}
  - One-step prediction intervals based on RMSE

## 6: Time series decomposition

  - Describing a time series: seasonality, trend, cycles, changing variance, unusual features.
  - Difference between seasonality and cyclicity
  - Moving averages
  - Classical decomposition, X-12-ARIMA, STL: 
      should know how to interpret.
  - Seasonal adjustment
  - Advantages/disadvantages of each method
  - Forecasting and decomposition

## 7: Exponential smoothing

  - Simple exponential smoothing.
  - Holt's local trend method
  - Damped trend methods
  - Holt-Winters seasonal method (additive and multiplicative versions)
  - ETS state space formulation
  - Interpretation of `ets()` output in R.
  - Computing forecasts by setting future $\varepsilon_t$ to 0.
  - Assumptions for prediction intervals
  - Formula sheet provided

## 8: ARIMA models
\fontsize{14}{16}\sf

  - Stationarity.
  - Differencing: first-differences and seasonal-differences. What to use when.
  - White noise, random walk, AR($p$), MA($q$), ARMA($p$,$q$),
        ARIMA($p,d,q$), ARIMA($p,d,q$)($P,D,Q$)$_s$.
  - Backshift operator notation
  - ACF, PACF.  Model identification.
  - ARIMA models, Seasonal ARIMA models
  - Order selection and goodness of fit (AICc)
  - Interpretation of `Arima()` and `auto.arima()` output in R.

## 8: ARIMA models (cont'd)

  - Expanding out an ARIMA model for forecasting
  - Finding point forecasts for given ARIMA process
  - Assumptions for prediction intervals
  - One-step prediction intervals based on RMSE
  - Effect of differencing on forecasts.
  - Effect of a constant on forecasts.
  - ARIMA vs ETS


## 5: Multiple regression

  - Interpretation of coefficients as marginal effects
  - Residual diagnostics: scatterplots of residuals vs predictors and residuals vs fitted values.
  - Dummy variables, seasonal dummies, piecewise linear trends, interventions
  - Splines
  - Harmonic regression
  - AIC, AICc, BIC, $R^2$, adjusted $R^2$
  - Matrix formulation
  - Multicollinearity
  - Interpretation of R output.

## 9: Dynamic regression models
\fontsize{14}{16}\sf

  - Regression with ARMA errors
  - Using lagged predictors
  - Difference between regression residuals and ARIMA residuals.
  - When estimating, need to difference all variables if errors non-stationary
  - Problems with OLS and autocorrelated errors
  - Forecasting for regression models with ARMA errors
  - Stochastic vs deterministic trends
  - Dynamic harmonic regression 
  - Multiple seasonal series

# Exam

## Exam

  - Five questions, all to be attempted.

  - Q1: Short answers/explanations. Write about 1/4 page on four topics (out of six possible topics). Nuanced answers required.
  - Q2: Describing a time series, choosing a forecasting method
  - Q3: ETS models
  - Q4: ARIMA model
  - Q5: Dynamic regression.

  - Formula page as for ETC3550 2017.

## Exam: 6 June am

**Preparing for the exam**

  - 2015, 2016 \& 2017 exams from ETC2450/ ETC3550 to go on Moodle with solutions.
  - Exercises.  Make sure you have done them all!
  - Identify your weak points and practice them.
  - Write your own summary of the material covered.
  - Practice explaining the material to a class-mate.

\pause

### Help available
See Puwasala in first instance.

See me at 11am-1pm on Wednesday 30th.


## Useful resources for forecasters

**Organization:**

 * International Institute of Forecasters.

**Annual Conference:**

 * International Symposium on Forecasting, Boulder.
   June 2018.

**Journals:**

 * International Journal of Forecasting
 * Foresight

###
Links to all of the above at **forecasters.org**



## Happy forecasting

###
Good forecasters are not smarter than everyone else, they merely have their ignorance better organised.