Forecasting
Time Series Analysis
Introduction
• Planning depends on forecasts of demand.
• Forecasting demand is an essential part of an
efficient organisation.
• Short term – couple of months.
• Medium term – up to a year.
• Long term – over a year.
• Paradoxical – have to make forecasts but they will
be in error.
• Time consuming and costly.
• Continuous process.
2
Time series
• Set of historical data in chronological order.
e.g. Hourly, daily, weekly, monthly, quarterly or
annual sales.
• Data broken down into components.
• Trend component (T) – long term movement of the
data – its general upward or downward direction.
• Seasonal variation (S) – predictable variation that
occurs at particular times.
• Graph has a zig zag pattern.
• Seasonal variation not necessarily seasons.
• Random or residual variation (R) – due to random
isolated events that are not predictable.
3
Trend
•
•
•
•
Represented by a line – the trend line.
Plot data.
Use moving averages to calculate trend values.
Position each moving average at centre of time
period to which it refers.
• Plot trend values on the graph of the data.
• Trend line (average line) runs roughly through centre
of the data.
• Number of time points to average = number of time
periods before the cycle repeats.
4
Example 1
Yr
1
Period
1
Period
2
Period
3
Jan Apr
May Aug
Sep Dec
8
13
10
Graph of Sales
Sales
18
16
14
12
2
9
15
11
3
9
16
13
10
8
6
1
2
3
1
2
3
1
2
3
Period
5
Year
Period
Sales
1
1
8
2
13
3
10
1
9
2
15
3
11
1
9
2
16
3
13
11
111
3
Trend
6
Year
Period
Sales
1
1
8
2
13
3
10
1
9
2
15
3
11
1
9
2
16
3
13
11
111
3
Trend
31
7
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
2
15
3
11
1
9
2
16
3
13
11
111
Trend
8
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
34
2
15
3
11
1
9
2
16
3
13
11
111
Trend
9
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
34
2
15
35
3
11
1
9
2
16
3
13
11
111
Trend
10
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
34
2
15
35
3
11
35
1
9
2
16
3
13
11
111
Trend
11
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
34
2
15
35
3
11
35
1
9
36
2
16
3
13
11
111
Trend
12
3
Year
Period
Sales
1
1
8
2
13
31
3
10
32
1
9
34
2
15
35
3
11
35
1
9
36
2
16
38
3
13
11
111
Trend
13
3
Trend
13
31
10.3
3
10
32
1
9
34
2
15
35
3
11
35
1
9
36
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
14
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
2
15
35
3
11
35
1
9
36
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
15
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
11.3
2
15
35
3
11
35
1
9
36
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
16
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
11.3
2
15
35
11.7
3
11
35
1
9
36
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
17
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
11.3
2
15
35
11.7
3
11
35
11.7
1
9
36
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
18
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
11.3
2
15
35
11.7
3
11
35
11.7
1
9
36
12.0
2
16
38
3
13
Year
Period
Sales
1
1
8
2
11
111
19
3
Trend
13
31
10.3
3
10
32
10.7
1
9
34
11.3
2
15
35
11.7
3
11
35
11.7
1
9
36
12.0
2
16
38
12.7
3
13
Year
Period
Sales
1
1
8
2
11
111
20
Graph of Sales
Sales
18
16
14
12
10
8
6
1
2
3
1
2
3
1
2
3
Period
21
Example 2
Year
Q1
Q2
Q3
Q4
I
10
26
20
7
II
14
31
22
11
III
20
37
26
17
22
Graph of Sales
Sales
40
35
30
25
20
15
10
5
0
1
2
3
4
1
2
3
4
1
2
3
4
Quarter
23
Year
Qtr
Sales
1
1
10
2
26
3
20
4
7
1
14
2
31
3
22
4
11
2
4
8
Trend
24
Year
Qtr
Sales
3
1
20
2
37
3
26
4
17
4
8
Trend
25
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
2
3
20
4
7
1
14
2
31
3
22
4
11
26
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
67
2
4
7
1
14
2
31
3
22
4
11
27
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
67
4
7
72
2
1
14
2
31
3
22
4
11
28
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
67
4
7
72
2
1
14
74
2
31
3
22
4
11
29
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
67
4
7
72
2
1
14
74
2
31
78
3
22
4
11
30
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
67
4
7
72
2
1
14
74
2
31
78
3
22
84
4
11
31
Year
Qtr
Sales
4
8
Trend
90
3
1
20
2
37
3
26
4
17
32
Year
Qtr
Sales
4
8
Trend
90
3
1
20
94
2
37
3
26
4
17
33
Year
Qtr
Sales
4
8
Trend
90
3
1
20
94
2
37
100
3
26
4
17
34
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
130
67
4
7
72
2
1
14
74
2
31
78
3
22
84
4
11
35
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
130
67
4
7
139
72
2
1
14
74
2
31
78
3
22
84
4
11
36
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
63
3
20
130
67
4
7
139
72
2
1
14
146
74
2
31
152
78
3
22
162
84
4
11
174
37
Year
Qtr
Sales
4
8
Trend
90
3
1
20
184
94
2
37
194
100
3
26
4
17
38
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
130
16.25
63
3
20
67
4
7
139
72
2
1
14
146
74
2
31
152
78
3
22
162
84
4
11
174
39
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
130
16.25
139
17.40
146
18.25
152
19.00
162
20.25
174
21.75
63
3
20
67
4
7
72
2
1
14
74
2
31
78
3
22
84
4
11
40
Year
Qtr
Sales
1
1
10
2
26
4
8
Trend
130
16.25
139
17.40
146
18.25
152
19.00
162
20.25
174
21.75
63
3
20
67
4
7
72
2
1
14
74
2
31
78
3
22
84
4
11
41
Year
Qtr
Sales
4
8
Trend
184
23.00
194
24.25
90
3
1
20
94
2
37
100
3
26
4
17
42
Graph of Sales & Trend
Sales
40
35
30
25
20
15
10
5
0
1
2
3
4
1
2
3
4
1
2
3
4
Quarter
43