ACCA MA · Guided practice (Show me how)
Chapter 19: Time Series Analysis
Time series - the trend, and the seasonal variation around it
Set out below are the sales per quarter, in thousands of units, of a company over the last three years.
| Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | |
|---|---|---|---|---|
| 2000 | 80 | 87 | 82 | 90 |
| 2001 | 90 | 95 | 93 | 102 |
| 2002 | 105 | 112 | 103 | 116 |
Identify the trend and calculate the average seasonal variation for each quarter, using the additive model.
Because there are four quarters in a year, a four-quarter average falls BETWEEN two quarters rather than on one. Averaging two of those in turn puts the trend back on a quarter - that is what "centred" means. Work to two decimal places throughout.
(a) The trend
Calculate the four-quarter moving averages and the centred trend at 2000 Q3, 2000 Q4 and 2001 Q1.
(b) Seasonal variation
Calculate the seasonal variations at 2000 Q3, 2000 Q4, 2001 Q1 and 2001 Q2, and the average seasonal variation for each quarter, using the additive model.
Opening this exercise…