代写代考 ETW3420: Principles of Forecasting and Applications

ETW3420: Principles of Forecasting and Applications

Principles of

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Forecasting and
Applications
Topic 1: Introduction

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

Forecasting is difficult

What can we forecast?

What can we forecast?

What can we forecast?

Which is easiest to forecast?

1 daily electricity demand in 3 days time
2 timing of next Halley’s comet appearance
3 time of sunrise this day next year
4 Google stock price tomorrow
5 Google stock price in 6 months time
6 maximum temperature tomorrow
7 exchange rate of $US/RM next week

how do we measure “easiest”?
what makes something easy/difficult to forecast?

Which is easiest to forecast?

1 daily electricity demand in 3 days time
2 timing of next Halley’s comet appearance
3 time of sunrise this day next year
4 Google stock price tomorrow
5 Google stock price in 6 months time
6 maximum temperature tomorrow
7 exchange rate of $US/RM next week

how do we measure “easiest”?
what makes something easy/difficult to forecast?

Factors affecting forecastability

Something is easier to forecast if:

we have a good understanding of the factors that contribute
there is lots of data available;
the forecasts cannot affect the thing we are trying to forecast.
there is relatively low natural/unexplainable random
variation.
the future is somewhat similar to the past

What can be forecast?

Many people wrongly assume that forecasts are not possible
in a changing environment.
Every environment is changing, and a good forecasting model
captures the way things are changing.
Forecasts rarely assume that the environment is unchanging.

What can be forecast?

What is normally assumed is that the way the environment is
changing will continue into the future – a highly volatile
environment will continue to be highly volatile; a business
with fluctuating sales will continue to have fluctuating sales;
an economy that has gone through booms and busts will
continue to go through booms and busts.
A forecasting model is intended to capture the way things
move, not just where things are.

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

Time series data

Definition
Time series data are observations on some variable over time,
usually at regular intervals.

Time series data – Example

International arrivals to Australia

1980 1990 2000 2010

Time series forecasting

Forecasting
Forecasting is estimating how the sequence of observations will
continue into the future.

Time series forecasting

ETS(A,N,A)

ETS(M,A,M)

ETS(A,N,A)

ETS(M,A,M)

1980 1990 2000 2010

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

The Forecasting Process

1 Define goal
2 Get data
3 Explore and visualize series
4 Pre-process data
5 Partition series – training/test sets
6 Apply forecasting method(s)/model(s)
7 Evaluate and compare forecasting performance
8 Implement forecasts/systems

Goal Definition

The first step in the forecasting process is to define the goal
of forecasting: Why are we producing forecasts for a
particular variable?
Must be able to motivate the need to forecast a variable of
There is a subtle difference as to why a variable of interest
might be important, and why forecasting that variable might
be important.

Goal Definition

Goals can be categorised as either descriptive or predictive.
Descriptive goal: impact assessment; causal arguments
Predictive goal: purely forecasting

Descriptive Goal Example

Descriptive Goal Example

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

Time Series Models

Definition
Time series models use only information on the variable to be

yt+1 = f(yt, yt−1, yt−2, …, error)
where t is time and y is the variable of interest.

e.g. ARIMA models and Exponential Smoothing models

useful when predictor variables not known or measured.
doesn’t lead to much understanding of system.

Cross-Sectional Models

Definition
Cross-sectional models assume that variable to be forecast is
affected by one or more predictor variables.

y = f(x1, x2, …, xk, error)

Electricity demand = f(….)

useful when predictor variables are known or measured.
regression models

Mixed Models

Definition
Mixed models combine features of both the time series and
cross-sectional models.

yt+1 = f(yt, yt−1, …, x1, x2, …, xk, error)

Dynamic regression models
Autoregressive distributed lag models
Panel data models

Time series models vs Cross-sectional models

Several reasons why a forecaster might select a time series model
rather than an explanatory model:

1 System may not be understood, and even if it was
understood, it may be extremely difficult to measure the
relationships that are assumed to govern its behaviour.

2 It is necessary to know or forecast the various predictors in
order to be able to forecast the variable of interest.

3 Main concern may be only to predict what will happen, not to
know why it happens.

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

CASE STUDY 1: Paperware company

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 to know what is wrong
and fix it.
Additional information

Program written in COBOL making
numerical calculations limited. It is not
possible to do any optimisation.
Their programmer has little experience
in numerical computing.
They employ no statisticians and want
the program to produce forecasts automatically.

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.

CASE STUDY 2: PBS

CASE STUDY 2: PBS

The Pharmaceutical Benefits Scheme (PBS) is the Australian
government drugs subsidy scheme.

Many drugs bought from pharmacies are subsidised to allow
more equitable access to modern drugs.
The cost to government is determined by the number and
types of drugs purchased. Currently nearly 1% of GDP.
The total cost is budgeted based on forecasts of drug usage.

CASE STUDY 2: PBS

CASE STUDY 2: PBS

In 2001: $4.5 billion budget, under-forecasted by $800
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 FORECAST function in

1 What can we forecast?

2 Time series data

3 The Forecasting Process

4 Forecasting Models

5 Some case studies

6 The statistical forecasting perspective

Basic Notation

t = 1, 2, …, T
An index denoting the time period of interest. t = 1 is the first
period in a series; t = T is the last period in the series.

y1, y2, …, yT
A series of T values measured over T periods, where yt denotes
the value of the series at time period t. Also used to denote the
random variable.

ŷt+h|1:t, Ft+h|1:t
The h-step-ahead forecast at time t, conditional on observing
y1, y2, …, yt. In other words, it is the forecast value of yt+h obtained
at time t, given that we observe y1, y2, …, yt. 35

Basic Forecasting Concepts

A point forecast for yT+h is a statement that yT+h will assume a
particular value.
A forecast interval is a statement that yT+h will lie in a
specified interval with a specified probability.
Forecast intervals are generally much more useful than point
forecasts since they incoporate a statement about how
confident we are about the accuracy of our forecast.

Basic Forecasting Concepts

To distinguish between a point prediction and a point
forecast, assume we have a sample of T observations,
(y1, y2, …, yT)
When the predicted value of y is generated for t = 2, 3, …, T,
using a model, these predictions pertain to within-sample
observations.
A forecast of yT+j for j >= 1 is a statement about the value of
the time series in period T + j. These forecasts pertain to
out-of-sample observations.

Basic Forecasting Concepts

The forecasting rule that minimizes the mean squared error
of the forecast

E(FE(h)2) = E[(yT+h − FT+h)2]

is by setting
FT+h = E(yT+h|y1, y2, …, yT)

However, we don’t observe E(yT+h|y1, y2, …, yT), therefore in

FT+h = Ê(yT+h|y1, y2, …, yT)
where the latter denotes the estimated value of
E(yT+h|y1, y2, …, yT).

Sample futures

1980 1990 2000 2010 2020

Total international visitors to Australia

Forecast intervals

1980 1990 2000 2010 2020

Forecasts of total international visitors to Australia

What can we forecast?
Time series data
The Forecasting Process
Forecasting Models
Some case studies
The statistical forecasting perspective

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