Actual Naïve Forecast error

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Jemima Douglas
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1 Naïve, & Moving verage Simple Slope Ted Mitchell Simplest possible forecast Tomorrow will be like today Naïve is the basis for comparison of all methods. Ignores any historical data previous to today Year 0 ctual 0 Year ctual Year ctual Year ctual N = N = SE = ME =.

2 Momentum Total Historical verage 0 orecast using average of the total history Get the forecast for the next If things have momentum they are easier to predict. verages are a measure of momentum Various averages are used for prediction Total historical average Moving averages Weighted averages i+ = (/n)(σ i ) where i+ = forecast for next n = number of historical s Σ i = sum of the results for each of the n historical s 0/ = 0 0 forecast Get the forecast for the next 0 forecast Get the forecast for the next Using Total Historical verage 0/ = 0 (0+)/ = 0/ = 0 (0+)/ = (0++)/ = (0+++)/ =. (0++++)/ =. (0+++++)/ =... Disadvantage Really lags behind a trend! because Uses all historical data Puts equal weight on every piece of historical information ( )/ =. ( )/ =...

historical s Σ i = sum of the results for each of the n historical s 0/ = 0 0 forecast Get the forecast for the next 0 forecast Get the forecast for the next Using Total Historical verage 0/ = 0

3 Moving verage 0 orecast using a moving average on last s 0 orecast using a moving average on last s Pick the last n s that are most relevant i+ = (/n) (Σ i ) where i+ = the forecast for next n = the number of s in the moving average (Σ i ) = the sum of the last n s (0++)/ = (0++)/ = (++)/ =. 0 orecast using a moving average on last s 0 orecast using a moving average on last s Moving verage (0++)/ = (++)/ =. (++)/ =. (0++)/ = (++)/ =. (++)/ = (++)/ =. Still lags behind a trend Puts equal weight on each of the historical results being used Gives bias when seasonal data is involved (++)/ =. (++)/ =. If you want more weight on the most recent data you need a weighted average

0 orecast using a moving average on last s 0 orecast using a moving average on last s Moving verage (0++)/ = (++)/ =. (++)/ =. (0++)/ = (++)/ =. (++)/ = (++)/ =.

4 Weighted Moving verage Three average with equal weight jun = ( mar + apr + may ) / or jun = ( mar + apr + may ) / Weighted average with more on May jun = ( mar + apr + may ) / Naïve gain jun = (0 mar +0 apr + may ) / (()+()+())/ = (()+()+())/ =. (()+()+())/ =. (()+()+())/ =. (()+()+())/ = orecast using a WEIGHTED moving average on last s ((0)+()+())/ =.. Weighted Moving verage Weighted Moving verage is better at responding to a trend because it puts more weight on recent data and less weight on old data They get the appropriate weights by doing a statistical fit to the data Trends Simple Trend Projection Simple Growth and Slope or Trends Ted Mitchell Trends in the data are not handled well by moving averages or exponential smoothing methods. Before the era of simple statistical tools on every PC managers used simple calculations of trends based on the naïve forecast. The naïve forecast is sales in next t = sales in the last (t-) or R t = R t-

. Weighted Moving verage Weighted Moving verage is better at responding to a trend because it puts more weight on recent data and less weight on old data They get the appropriate weights by doing a

5 Sales Do a orecast for Period Two Periods go Last Last plus X Percent The sales in the last plus the percentage growth over the last two s Sales Do a orecast for Period Two Periods go Last Simple Percentage Projection uses the same growth as between the last two s g 0 0 Getting the slope Example Calculate historical g g = Growth rate between 0 and The percentage growth over the last two s = g Prediction for the last would be R = g R 0 We know R and R 0 so we can calculate g R = g R 0 where R 0 = $0 R = $ then calculate g = g(0) g = / 0 g =. or growth is % Sales Two Periods go Last g = R /R 0 Simple last plus percent growth Projection uses the same slope as the last two s 0

between 0 and The percentage growth over the last two s = g Prediction for the last would be R = g R 0 We know R and R 0 so we can calculate g R = g R 0 where R 0 = $0 R

6 Prediction of in ( in ) = g ( in ) R = gr Where R = revenue in = g =. Then R =.() = 0. Sales Prediction for R R 0 = 0 R =.() = 0 R = g =. = Sales Prediction for R in R 0 = 0 R = R = 0. g =. = 0 0 The Problem with The last result + percent improvement method Very dependent on the base used in the percentage. If you use the same percentage as passes then the method inflates the forecasted values But it is simple and very popular! Examples: Naïve Method & Last Period Plus Rate of Change Method Ted Mitchell New Shoes Home Market Spring Home Market in this example is experiencing a long run decline in sales as it nears the end of the Product Life Cycle

= 0 0 The Problem with The last result + percent improvement method Very dependent on the base used in the percentage.

7 Period ctual Units,,000,,000 Period ctual Units,,000,0,000,,000 0,000 Period ctual Units,,000,0,000,,000,0,000 0,000 What to do Next You have two pieces of information Industry Sales in =,,000 Industry Sales in =,0,000 nd the idea that the market is in decline phase of the Product Life Cycle (PLC) Do you naïve or last + decline % Last + change % Consider the last plus the decline rate from the two previous s What is the decline rate Sales in = decline rate (Sales in ),0 = decline rate (, ) Decline rate =,0 /, =.% orecasting Sales in = decline rate (sales in ) Sales in =.% (,0,000) Sales in =, units

(PLC) Do you naïve or last + decline % Last + change % Consider the last plus the decline rate from the two previous s What is the decline rate Sales

8 Period ctual Units,,000,0,000,,000. 0,000 Period ctual Units,,000,0,000,000,000,,000. or the naïve method,0,000 0,000 Smallest is naive Period ctual Units,,000,0,000,000,000,000,,000. or the naïve method,0,000, or the naïve method,000,000 0,000 Smallest is naive Smallest is last + decline rate Use last and decline rate to forecast Use last and decline rate to forecast or naïve method Use last and decline rate to forecast

or the naïve method,0,000, or the naïve method,000,000 0,000 Smallest is naive Smallest is last + decline

Forecasting DISCUSSION QUESTIONS

4 C H A P T E R Forecasting DISCUSSION QUESTIONS 1. Qualitative models incorporate subjective factors into the forecasting model. Qualitative models are useful when subjective factors are important. When