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 ...
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
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
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
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.
Time Series: Techniques
• Moving Average
• Weighted Moving Average
• Exponential Smoothing
• Adjusted Exponential Smoothing
• Linear Trend
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:
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.
• 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
• 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
• 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
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
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
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
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
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
A variation on MAD
Measures absolute error as a percentage of demand rather than per period
Formula:
tDtFtDMAPD
Mean Absolute Deviation
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
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
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
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
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
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