BUSINESS MATHEMATICS & STATISTICS.

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Presentation transcript:

BUSINESS MATHEMATICS & STATISTICS

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

TREND

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

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 = 195 + 2.5 = 197.5 Morning of day 4 = 197.5+ 2.5 = 200 Afternoon of day 4 = 200 + 2.5 = 202.5 After adjustment of seasonal variation = -36 = 202.5 – 36 = 166.5 or 166

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

FORECASTING APPLE PIE SALES

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

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?

FORECAST Week no. Actual sales Forecast 1 4500 - 2 4000 4500 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)

BUSINESS MATHEMATICS & STATISTICS