MSc in OR and MSc in Management Sciences



MATH6011 Forecasting


The Unit Profile gives a description of the unit, including aims and objects, summary of topics covered and assessment methods.


This unit uses Makridakis, S., Wheelwright, S.C. and Hyndman, R.J. 1998, Forecasting: Methods and Applications 3rd Ed., New York: Wiley as text book. In particular it uses the data sets provided in this book. Details of the data sets can be obtained by clicking on List of Data Files. You can download the complete set of data files in zipped form here:


The lectures are based on Working Notes which draw quite closely on the above book. You can access the working notes by clicking on the following links:


Working Notes: Chapter 1

1. Basic Forecasting Tools

1.1 Forecasting Methods and Examples

1.1.1 Examples

1.1.2 Quantitative and Qualitative Approach:

1.1.3 Explanatory Versus Black-Box Models:

1.2 Graphical Summaries

1.2.1 Time plot.

1.2.2 Seasonal plot.

1.2.3 Scatterplots.

1.3 Numerical Summaries

1.3.1 Statistics.

1.3.2 Univariate Statistics.

1.3.3 Bivariate.

1.3.4 Autocovariance; Autocorrelation.

1.4 Measures of Accuracy

1.4.1 Forecasting Errors

1.4.2 ACF of Forecast Error.

1.4.3 Prediction Interval.

1.5 Transformations

1.5.1 Mathematical Transforms

1.5.2 Calendar Adjustments.





Working Notes: Chapter 2

2. Time Series Decomposition

2.1 Additive and Multiplicative models

2.2 Smoothing

2.2.1 Moving Average

2.3 Decomposition

2.3.1 Additive Decomposition

2.3.2 Multiplicative Decomposition


Working Notes: Chapter 3

3. Basic Forecasting Methods

3.1 Averaging Methods

3.2 Single Exponential Smoothing

3.3 Holt's Linear Exponential Smoothing (LES)

3.4 Holt-Winter's Method

3.4.1 Holt-Winter's Method, Multiplicative Seasonality

3.4.2 Holt-Winter's Method, Additive Seasonality


Working Notes: Chapter 4

4. Regression

4.1 Linear Regression

4.1.1 The linear regression model

4.1.2 Least Squares Estimation, and Sums of Squares

4.1.3 Individual Coefficients

4.2 Multiple Linear Regression for Prediction

4.2.1 Additional Explanatory Variables

4.2.2 Time Related Explanatory Variables

4.2.3 Subset Selection

4.3 Local Polynomial Regression for Smoothing

4.4 Multiple Linear Regression for Forecasting


Working Notes: Chapter 5

5. Advanced Forecasting

5.1 Box-Jenkins Models

5.2 Judgemental Forecasting

5.3 Scenario Building



The Working Notes are precisely this. They are meant to be worked through.


They contain electronic Example-Exercises (eEE). The eEE's illustrate the topic or method being discussed. They are an essential part of the text and must be carefully studied.


Each eEE comes in two variations each with its own link. (i) One link is to a Web page giving the layout and results of an Excel spreadsheet. This allows you to get a quick picture of what has been calculated in the eEE. (ii) The other link is to an actual spreadsheet containing the data and the worked details using the data.


The idea is that you should try and do the example yourself. You can view the general layout of the worked example to see what is being calculated. BUT the aim is that you should open a separate worksheet and try to reproduce the calculations for yourself with minimum reference to the provided solution. Use the 'solution' only if you are really stuck and need a prompt.


In the spreadsheets, the following convention for cells is used:

Cells with a Yellow background - Headings, Incidental Information

Cells with a Green background - Input Information used in calculations on that Sheet

Cells with a Blue background - Calculations and Results that you should be producing.




Supporting Materials


Unit Profile

Working Notes: Chapter 1

Working Notes: Chapter 2

Working Notes: Chapter 3

Working Notes: Chapter 4

Working Notes: Chapter 5

List of Data Files


References mentioned in the Text


Wetherill, G.B. (1981). Intermediate Statistical Methods. London: Chapman and Hall.

Draper, N.R. and Smith, H. (1981). Applied Regression Analysis, 2nd Ed. New York: John Wiley.



Stop Press


Coursework Assignment 2002/3

Word File of the assignment: MA620cw03.doc


Coursework Assignment 2003/4

Word File of the assignment: Assignment04\MATH6011cw04.doc


Coursework Assignment 2004/5

Word File of the assignment: Assignment05\MATH6011cw05.doc


Coursework Assignment 2005/6

Web Version with Links to Datasets: Assignment06\MATH6011cw06.html


Typos and other Mistakes in the Hard Copy Handout

Please let me know if you find any mistakes. These will be corrected in the Web version:


Section 1.3.3:

The formula for the correlation should be:


Section 1.4.3:

ڤMSE should be