# Time Series

Time Series, Sampling and Index Numbers
Worksheet
Activity 1.
The volume of sales by month in a department store for the year 20X4 were as follows:
£
670,000
680,000
685,000
683,000
690,000
710,000
712,000
710,000
690,000
680,000
685,000
660,000

Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec

(a) Plot these sales on a graph.
(b) Isolate the trend by using a scattergraph
Activity 2
The following time series shows a set of sales figures for eight quarters, which are clearly
increasing.
Year
20X4

20X5

Quarter Sales
£000
1
3
2
5
3
5
4
5
1
7
2
9
3
9
4
9

Identify the trend using a 4 quarter moving average.

1

Activity 3
The following data represents the sales for TS limited for the eight quarters shown:

Year 1
Year 2

Q1
74
84

Q2
100
106

Q3
94
120

Q4
127
141

(a) Plot the above data.
(b) Calculate the trend using moving averages.
(c) Plot the trend.
Activity 4
X Ltd is forecasting its sales for the four quarters of 20XS. It has carried out a linear
regression exercise on its past sales data and established the following:
a=20
b=0.7
The equation of the regression line is therefore:
y = 20 + 0.7x
When x is number of the quarter and y is the sales value in £000s.
Calculate the sales for each of the quarters in 20X5.
Activity 5
A regression line has been calculated as y = 192 + 2.40x, where
x is the output and
y is the total cost.
You are required to:
(a) Explain this formula.
(b) Use it to predict the total cost for (i) 500 units and (ij) 1,500 units.
Activity 6
Given below are the estimated trend figures for a company's sales for the next four quarters:
20X3
£
Quarter 1
560,000
Quarter 2
580,000
Quarter 3
605,000
Quarter 4
632,000
The seasonal variations using the multiplicative model have been calculated as:
Quarter 1 + 15%
Quarter 2 + 10%
Quarter 3 -5%
Quarter 4 -20%
Calculate the forecast sales figures for each of the next four quarters....