Nuffield Free-Standing Mathematics Activity

House price moving averages

© Nuffield Foundation 2012 © Rudolf Stricker

How have house prices in the UK changed since 2000? Do the house prices change more in some quarters of the year than in others? © Nuffield Foundation 2010 How could fluctuations due to seasonal factors be smoothed out?

House price moving averages

Moving averages can be used to smooth out fluctuations due to seasonal factors.

Moving averages

For data points

p

1

, p

2 , … the simple moving average at interval

m

with

n

data points is:

x m



p m



p m

 1 

p m

 2  .....

p m

 (

n

 1 )

n

It is often quicker to calculate successive values using

x m

 1 

x m



p m

 (

n

 1 )

n

© Nuffield Foundation 2010 

p m

 1

n

.

Weighted moving averages

The problem of lag can be addressed by using weighting.

The linear weighted moving average is:

x m



np m

 

n



n

1 

p



m

 1 

n

  

n

 1  

n

2   2

p



m

  ...

2   .....

2  1 

p m

 (

n

 1 ) where the denominator is the triangular number with sum

n



n

 1  2 © Nuffield Foundation 2010

Reflect on your work

• What is a moving average? Why are they used?

• Describe two methods of calculating a moving average. • Describe how to find a weighted moving average. • Why does a weighted moving average help to overcome the problem of lag? © Nuffield Foundation 2012