1. BUSINESS MATHEMATICS
&
STATISTICS

2. Exponential Smoothing
LECTURE 33
Review Lecture 32
Time Series and
Exponential Smoothing
Part 2

3. TREND

5. EXTRACTING RANDOM VARIATIONS
DAY 1
Afternoon trend = 180
Afternoon seasonal variation = 36
Trend – variation = 180 – 36 = 144
Actual value = 140
Random variation = 140 – 144 = -4
Conclusion
Expected = Trend + Seasonal
Random = Actual - expected

7. FORECAST Forecast for day 4 = Trend for afternoon of day 4 +
Seasonal adjustment for afternoon period
Trend = 180 to 195 ( 6 intervals)
= 15/6 = 2.5 per period
Figure for evening of day 3 = = 197.5
Morning of day 4 = = 200
Afternoon of day 4 = = 202.5
After adjustment of seasonal variation = -36
= – 36 = or 166

8. SEASONABLE VARIATIONS
Seasonal Variations
Regarded as constant amount added to or subtracted from the trends
Reasonable Assumption
As seasonal peaks and troughs are roughly of constant size
In Practice
Seasonal variations will not be constant
Will themselves vary as trend increases or decreases
Peaks and troughs can become less prounced

10. FORECASTING APPLE PIE SALES

14. FORECAST Sale steadily declined from 139.0 to 130.5
Over 4 quarters decline = – = 8.5
Trend in Spring 1995 = 133.5
Annual decrease = 8.5
Trend in 1996 = – 8.5 = 125
Seasonal variation = -8
Final forecast = 125 – 8 = 117

15. FORECASTING IN UNPREDICTABLE SITUATIONS
Two methods studied indicate certain features
Steady increase in data
Repeated seasonal variations
Many cases do not conform to these patterns
There may not be a trend
No short term pattern
Figures may hover around an average mark
How to forecast under these conditions?

17. FORECAST Week no. Actual sales Forecast 1 4500 - 2 4000 4500
Forecast in week 2 is the same as week 1
Actual sale = 4000
Forecast 500 too high
Another approach would be toincorporate the proportion of error in the estimate
new forecast = old forecast + proportion of error  Or
new forecast = old forecast +  x (old actual – old forecast)

18. BUSINESS MATHEMATICS
&
STATISTICS