1. Smoothing a time series using moving means
12 Further mathematics
Smoothing a time series using moving means

2. Smoothing a time series using moving means

3. Smoothing a time series using moving means

4. Smoothing a time series using moving means

5. Smoothing a time series using moving means

6. Smoothing a time series using moving means
Two observations can be made from this plot:
1 five-mean smoothing is more effective in reducing the irregular fluctuations than three-mean smoothing
2 the five-mean smoothed plot shows that there is no clear trend although the raw data suggest that there might be an increasing trend.

7. Smoothing a time series using moving means
There are many ways of smoothing a time series. Moving means of group size other than three and five are common and often very useful.
However, if we smooth over an even number of points, we run into a problem. The centre of the set of points is not at a time point belonging to the original series. Usually, we solve this problem by using a process called centring.
Centring involves taking a two-moving mean of the already smoothed values so that they line up with the original time values. It is a two-step process.

8. Smoothing a time series using moving means

9. Smoothing a time series using moving means

10. Smoothing a time series using moving means

11. Exercise 6B All Questions
WORK TO BE COMPLETED
Exercise 6B All Questions