Chapter 13 Forecasting. Components of Forecasting Time Series Methods Accuracy of Forecast ...

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Transcript of Chapter 13 Forecasting. Components of Forecasting Time Series Methods Accuracy of Forecast ...

Page 1: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Chapter 13

Forecasting

Page 2: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Components of Forecasting

Time Series Methods

Accuracy of Forecast

Regression Methods

Topics

Page 3: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Many forecasting methods are available for use

Depends on the time frame and the patterns

Time Frames:

Short-range (one to two months) Medium-range (two months to one or two years) Long-range (more than one or two years)

Patterns:

Trend Random variations Cycles Seasonal pattern

Components of Forecasting

Page 4: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Forecasting Components: Patterns

• Trend: A long-term movement of the item being forecast

• Random variations: movements that are not predictable and follow no pattern

• Cycle: A movement, up or down, that repeats itself over a time span

• Seasonal pattern: Oscillating movement in demand that occurs periodically and is repetitive

Page 5: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Forecasting Components: Forecasting Methods

• Times Series (Statistical techniques)– Uses historical data to predict future pattern

– Assume that what has occurred in the past will continue to occur in the future

– Based on only one factor - time.

• Regression Methods– Attempts to develop a mathematical relationship between the item

being forecast and the involved factors

• Qualitative Methods– Uses judgment, expertise and opinion to make forecasts

Page 6: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Forecasting Components: Qualitative Methods

• Called jury of executive opinion

• Most common type of forecasting method for long-term

• Performed by individuals within an organization, whose judgments and opinion are considered valid

• Includes functions such as marketing, engineering, purchasing, etc.

• Supported by techniques such as the Delphi Method, market research, surveys, etc.

Page 7: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Time Series: Techniques

• Moving Average

• Weighted Moving Average

• Exponential Smoothing

• Adjusted Exponential Smoothing

• Linear Trend

Page 8: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

i periodin data average moving in the periods ofnumber

iDn

niDMAn

Moving Average

• Uses values from the recent past to develop forecasts

• Smoothes out random increases and decreases

• Useful for stable items (not possess any trend or seasonal pattern

• Formula for:

Page 9: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Revisit of 3-Month and 5-Month

• Longer-period moving averages react more slowly to changes in demand

• Number of periods to use often requires trial-and-error experimentation

• Moving average does not react well to changes (trends, seasonal effects, etc.)

• Good for short-term forecasting.

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• Weights are assigned to the most recent data.

• Determining precise weights and number of periods requires trial-and-error experimentation

• Formula:

100% and 0%between i, periodfor weight the

1

iW

n

i iDiWnWMA

Weighted Moving Average

Page 11: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

• Weights recent past data more strongly

• Formula:

Ft + 1 = Dt + (1 - )Ft

where: Ft + 1 = the forecast for the next period Dt = actual demand in the present period Ft = the previously determined forecast for

the present period = a weighting factor (smoothing constant)

• Commonly used values of are between .10 and .50

• Determination of is usually judgmental and subjective

Exponential Smoothing: Simple Exponential Smoothing

Page 12: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

• Forecast that uses the higher smoothing constant (.50) reacts more strongly to changes in demand

• Both forecasts lag behind actual demand

• Both forecasts tend to be lower than actual demand

• Recommend low smoothing constants for stable data without trend; higher constants for data with trends

Comparing Different Smoothing Constants

Page 13: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Exponential smoothing with a trend adjustment factor added

Formula: A Ft + 1 = Ft + 1 + Tt+1

where: T = an exponentially smoothed trend factor

Tt + 1 + (Ft + 1 - Ft) + (1 - )Tt

Tt = the last period trend factor = smoothing constant for trend (between zero and one)

Weights are given to the most recent trend data and determined subjectively

Forecast is higher than the simple exponentially smooth

Useful for increasing trend of the data

Exponential Smoothing: Adjusted

Page 14: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

When demand displays an obvious trend over time, a linear trend line, can be used to forecast

Does not adjust to a change in the trend

Formula: Y= a+ b x

Linear Trend Line

xbyaxnxyxnxyb

2

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Seasonal pattern is a repetitive up-and-down movement in demand

Can occur on a monthly, weekly, or daily basis.

Forecast can be developed by multiplying the normal forecast by a seasonal factor

Seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand: lies between zero and one

Si =Di/D

Seasonal Adjustments

Page 16: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Forecasts will always deviate from actual values

Difference between forecasts and actual values referred to as forecast error

Like forecast error to be as small as possible

If error is large, either technique being used is the wrong one, or parameters need adjusting

Measures of forecast errors:

Mean Absolute deviation (MAD) Mean absolute percentage deviation (MAPD) Cumulative error (E bar) Average error, or bias (E)

Forecast AccuracyOverview

Page 17: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

MAD is the average absolute difference between the forecast and actual demand.

Most popular and simplest-to-use measures of forecast error.

Formula:

The lower the value of MAD, the more accurate the forecast

MAD is difficult to assess by itself

Must have magnitude of the data

ntFtDMAD

Forecast Accuracy: Mean Absolute Deviation

Page 18: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

A variation on MAD

Measures absolute error as a percentage of demand rather than per period

Formula:

tDtFtDMAPD

Mean Absolute Deviation

Page 19: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Sum of the forecast errors (E =et).

A large positive value indicates forecast is biased low A large negative value indicates forecast is biased high Cumulative error for trend line is always almost zero Not a good measure for this method

Cumulative Error

Page 20: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Time series techniques relate a single variable being forecast to time.

Regression is a forecasting technique that measures the relationship of one variable to one or more other variables.

Simplest form of regression is linear regression.

Regression MethodsOverview

Page 21: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

data y the of mean

data x the of mean

:where

22

nyy

nxx

xnx

yxnxyb

xbya

bxay

Linear regression relates demand (dependent variable ) to an independent variable.

Regression MethodsLinear Regression

Page 22: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Measure of the strength of the relationship between independent and dependent variables

Formula:

Value lies between +1 and -1. Value of zero indicates little or no relationship between

variables. Values near 1.00 and -1.00 indicate strong linear

relationship.

2222 yynxxn

yxxynr

Regression Methods: Correlation

Page 23: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Percentage of the variation in the dependent variable that results from the independent variable.

Computed by squaring the correlation coefficient, r. If r = .948, r2 = .899 Indicates that 89.9% of the amount of variation in the

dependent variable can be attributed to the independent variable, with the remaining 10.1% due to other, unexplained, factors.

Regression Methods: Coefficient of Determination

Page 24: Chapter 13 Forecasting.  Components of Forecasting  Time Series Methods  Accuracy of Forecast  Regression Methods Topics.

Multiple Regression

Multiple regression relates demand to two or more independent variables.

General form:

y = 0 + 1x1 + 2x2 + . . . + kxk

where 0 = the intercept

1 . . . k = parameters representing contributions of the independent

variables

x1 . . . xk = independent variables