a) State the TWO (2) main models of time series analysis.                                                                                                (2 marks)

b) Membership of Pro Amalion, a network of professional volunteers, has grown over the years but in the months of the second quarter there was always a decline. The table below shows membership records for a period of four years:

Required:
i) Calculate the centred four-quarterly moving average of membership.                                                                            (4 marks)

ii) Using a least squares trend equation base on (i) above, calculate the trend values.                                                       (5 marks)

iii) Using (ii) above, calculate the percentage seasonal variation and the average seasonal variation of membership.         (5 marks)

iv) Determine the seasonally adjusted forecast of membership for each of the four quarters of Year 5.                            (4 marks)

The quarterly unit sales of electronic items of a retail company for the last three years are as follows:

Required:
i) Calculate a centred three moving average of the unit sales.                                                                                           (3 marks)

ii) Calculate the trend using a centred four-quarterly moving average.                                                                             (4 marks)

iii) Calculate the four seasonal variations using (ii) and the multiplicative model.                                                           (7 marks)

iv) Forecast the number of unit sales for the year 2016 using the multiplicative model.                                                   (4 marks)

v) Comment on your answer in (iv).                                                                                                                                   (2 marks)

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. There is a general feeling that the underlying trend has been rising, but nobody has yet analysed the figures. The total number of shops employees has remained virtually unchanged over the few years.
The mean number of absentees per day for each quarter of the years 1999 to 2001 and quarter 1 in 2002 is given in the table below:

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures.                                                                        (3 marks)

b) Using the method of 2 quarterly centered moving,
i) determine the trend in the series and superimpose this on your graph in (a) above.                                                       (4 marks)

ii) determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i) above.                                                                                                                                                                (3 marks)

c) Using an appropriate decomposition model to determine the seasonal variations in the data. Give reasons for your choice of model.                                                                                                                                                                                  (5 marks)

d) Use your analysis above to produce roughly forecasts of the mean number of absentees there will be in the remaining quarters of 2002. Comment on your forecast.                                                                                                                                   (5 marks)

(a) State the Four (4) factors which may be  present in a Time Series Data.                                                      (4 Marks)

(b) Quarterly Sales of a Golden Tree Chocolate Bar at a Popular Mall in KoKoLand City are given as follows:

Required:
(i) Calculate the trend in the series using a 4-point centered moving average method.                                                    ( 4 Marks)

(ii) Using (i) calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis.               ( 4 Marks)

(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data.                  ( 4 Marks)

(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model.                                                                ( 4 Marks)