a) The objective of smoothing methods is to smoothen out the random variations due to irregular components of the time series and thereby provides an overall impression of the pattern of movement in the data over time.
Required:
Explain the following smoothing methods:
i) Moving averages                                                                                                                                                             (2 marks)

ii) Exponential Smoothing                                                                                                                                                  (2 marks)

b) The number of enquiries being made to a mail order business during Monday to Friday working week is given as:

Required:                                                                                                                          (16 marks)
i) Plot the data on a graph.

ii) Compute a 5 period moving average values for the data.

iii) Compute a ‘weighted’ moving average values for the data if the smoothing Constant
is

iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.

v) Comment on the suitability of the two smoothing methods above.

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method.                  (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations.                                             (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data.                                                          (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model.                                                                                                                                                           (6 marks)