FORECASTING - FTMS€¦ · Step 2 Calculate the moving average (the trend) for the period....
Transcript of FORECASTING - FTMS€¦ · Step 2 Calculate the moving average (the trend) for the period....
FORECASTINGBusiness Decision Techniques
BUSS 0204
The components of time series
A time series is a series of figures or values recorded over time.
Any pattern found in the data is then assumed to continue into the future and an extrapolative forecast is produced.
There are four components of a time series: ◦ trend,
◦ seasonal variations,
◦ cyclical variations and
◦ random variations.
Standard time series models
1. The time series additive model: y = t + c + s + I
2. The time series multiplicative model: y = t × c × s × I
Where y is a given time series valuet is the trend componentc is the cyclic components is the seasonal componenti is the irregular component
Description of time series components
1. TrendThis is a long term movement
2. Cyclical variationRepeating up and down movements due to interactions of factors influencing economy.
3. Seasonal variationThe effect of seasons – spring, summer. Autumn and winter – on the series.
4. Irregular or random variationThese are disturbances due to ‘everyday’ unpredictable influences, such as weather conditions, illness and so on.
Based on the data, plot the time series.
Numbers of car sell in XYZ Company
Qtr 1 Qtr 2 Qtr 3 Qtr 4
Year 1 73 90 121 98
Year 2 69 92 145 107
Year 3 86 111 157 122
Year 4 88 109 159 131
0
20
40
60
80
100
120
140
160
180
Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4
Year 1 Year 2 Year 3 Year 4
Freq
uen
cy
Year
Numbers of car sell in XYZ Company
A
B
C
Finding the Trend (T) Moving Average (MA) eliminates S and I,
leaving T and C. In practice C rarely exists (Keynesian intervention), leaving T
12 months/ 4 quarter centred MA
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Year Sales value 4 quarter
moving total
4 quarter moving
average
2009
2010
2011
2012
2013
2014
52
23
84
55
36
67
Finding the Trend (T) – odd
Year Quarter Sales
value
4 quarter
moving
total
4 quarter
moving
average
Centered
4 quarter
moving
average
2013
2014
1
2
3
4
1
2
3
4
75
32
48
85
93
60
92
47
10
Finding the Trend (T) – even
Moving Average (Centred)
12 month centred moving average or 4 quarter moving average eliminates S
Averaging process eliminates I
C is often absent from data
So left with T (Trend)
11
Finding Trend
Centred moving average gives us the trend (T)
These points can be plotted on a scatter diagram
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Finding the seasonal component using the additive model
Step 1 : The additive model for time series analysis is Y = T + S + R
Step 2 : If we deduct the trend from the additive model, we get Y - T = S + R .
Step 3 : If we assume that R, the random, component of the time series is relatively small and therefore negligible, then S = Y - T
Therefore, the seasonal component, S = Y - T (the de-trended series).
Example: The trend and seasonal variationsAbsence and sickness records of HJA Corp.
Required Find the seasonal variation for each of the
10 days, and the average seasonal variation for each day of the week using the moving averages method.
Week Monday Tuesday Wednesday Thursday Friday
1 4 7 8 11 18
2 3 8 10 13 21
Finding the seasonal component using the multiplicative model
Step 1 Calculate the moving total for an appropriate period.
Step 2 Calculate the moving average (the trend) for the period. (Calculate the mid-point of two moving averages if there are an even number of periods.)
Step 3 Calculate the seasonal variation. For a multiplicative model, this is Y/T.
Step 4 Calculate an average of the seasonal variations.
Step 5 Adjust the average seasonal variations so that they add up to an average of 1.
Therefore, the seasonal component, S = Y/T (the de-trended series)
ForecastingStep 1 Plot a trend line: use the line of best
fit method, linear regression analysis or the moving averages method.
Step 2 Extrapolate the trend line. This means extending the trend line outside the range of known data and forecasting future results from historical data.
Step 3 Adjust forecast trends by the applicable average seasonal variation to obtain the actual forecast.
(a) Additive model – add positive variations to and subtract negative variations from the forecast trends.
(b) Multiplicative model – multiply the forecast trends by the seasonal variation.