Advance forecasting

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Advance forecasting
Forecasting by identifying patterns in the past
data

• Chapter outline
• Extrapolation from the past
• Cause and effect relationships
• Trend analysis
• - Regression analysis
• - Simple linear regression analysis
• - Multiple linear regression analysis
• - Quadratic regression analysis
• 3. Cyclical and seasonal issues
• Seasonal decomposition of time series data
• Type of seasonal variation
• Computing Multiplication seasonal indices
• Using seasonal indices to forecast
• A caution regarding seasonal indices

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Extrapolation from the pastCause-and-effect
Relationships

• Causal forecasting seeks to identify specific
  cause-effect relationships that will influence
  the pattern of future data. Causes appear as
  independent variables, and effects as dependent ,
  response variables in forecasting models.
• Independent variable Dependent, response
  variable
• Price demand
• Decrease in population decrease in demand
• Number of teenager demand for jeans
• Causal relationships exist even when there is no
  specific time series aspect involved.
• The most common technique used in causal modeling
  is least squares regression.

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Extrapolation from the past Linear Trend
analysis
Its noticed from this figure that there is a
growth trend influencing the demand, which should
be extrapolated into the future.
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Extrapolation from the pastLinear Trend
analysis
The linear trend model or sloping line rather
than horizontal line. The forecasting equation
for the linear trend model is Y ??X
or Y a bX Where X is the
time index (independent variable). The parameters
alpha and beta ( a and b) (the intercept and
slope of the trend line) are usually estimated
via a simple regression in which Y is the
dependent variable and the time index X is the
independent variable.
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Extrapolation from the past Linear Trend
analysis
Although linear trend models have their uses,
they are often inappropriate for business and
economic data. Most naturally occurring business
time series do not behave as though there are
straight lines fixed in space that they are
trying to follow real trends change their slopes
and/or their intercepts over time. The linear
trend model tries to find the slope and intercept
that give the best average fit to all the past
data, and unfortunately its deviation from the
data is often greatest near the end of the time
series, where the forecasting action is.
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Extrapolation from the pastLinear Trend analysis
Using a data table (what if analysis ) to
determine the best-fitting straight line with the
lowest MSE
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Extrapolation from the past Linear Trend analysis
Simple linear Regression Analysis
Regression analysis is a statistical method of
taking one or more variable called independent or
predictor variable- and developing a mathematical
equation that show how they relate to the value
of a single variable- called the dependent
variable. Regression analysis applies
least-squares analysis to find the best-fitting
line, where best is defined as minimizing the
mean square error (MSE) between the historical
sample and the calculated forecast. Regression
analysis is one of the tools provided by Excel.
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Simple linear Regression Analysis
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Extrapolation from the past Linear Trend analysis
Multiple linear Regression Analysis
Simple linear regression analysis use one
variable (quarter number) as the independent
variable in order to predict the future value. In
many situations, it is advantageous to use more
than one independent variable in a forecast.
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Multiple linear Regression Analysis
Two factors that control the frequency of
breakdown. So they are the independent
variables. Y a bX1 cX2
Intercept
Slope 1 Slope2
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Multiple linear Regression Analysis
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Extrapolation from the past Linear Trend analysis
Quadratic Regression Analysis
Quadratic regression analysis fits a second-order
curve of the form Y a bX
cX2 Quadratic regression is prepared by adding
the squared value of the time periods. The
coefficients in the quadratic formula are
calculated again using regression, where time
periods and the squared time periods are the
independent variables and the demand remains the
dependent variable.
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Quadratic Regression Analysis
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Quadratic Regression Analysis
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Extrapolation from the past Cyclical and Seasonal
Issues

• The fundamental approach to including cyclical or
  seasonal factors is to break the forecast into
  two components
• The underlying growth component
• The seasonal variations
• To prepare a forecast model
• Use a method to fit a growth curve to the
  historical record
• Determine the pattern of the seasonal variability
• In general, two sets of parameters to be
  estimated
• ( the coefficients in the trend line, and the
  percents in the seasonal patterns )

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Extrapolation from the past Cyclical and Seasonal
Issues
Basically two things must be done 1- determine
the trend line 2- take the trend line out (
calculate deviations from the trend) 3- create a
pie, radar, or polar chart of the average period
value
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Cyclical and Seasonal Issues Seasonal
Decomposition of Time Series Data

• Time series data are usually considered to
  consist of six component
• Average demand is simply the long-term mean
  demand
• Trend component is how rapidly demand is
  growing or shrinking
• Autocorrelation is simply a statement that
  demand next period is related to demand this
  period
• Seasonal component is that portion of demand
  that follows a short-term pattern
• Cyclical component is much like the seasonal
  component, only its period is much longer.
• Random component is the unpredictable component
  of demand

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Cyclical and Seasonal Issues Type of Seasonal
Variation
There are two types of seasonal
variation Additive seasonal variation Occurs
when the seasonal effects are the same regardless
of the trend. Multiplication seasonal variation
Occurs when the seasonal effects vary with the
trend effects. Its the most common type of
seasonal variation
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Cyclical and Seasonal Issues Computing
Multiplicative Seasonal Indices

• Steps of Multiplicative Time Series Model
• Decide that the data is seasonal in nature.
• Then realized that the seasonal variation is
  quarterly
• If the variation of the data is larger to the
  right, then that seasonal variation is
  multiplicative.
• Seasonal indices is needed to produce the
  seasonal forecast model.

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Cyclical and Seasonal Issues Computing
Multiplicative Seasonal Indices

1. Computing seasonal indices requires data that
   match the seasonal period. If the seasonal period
   is monthly, then monthly data are required. A
   quarterly seasonal period requires quarterly
   data.
2. Calculate the centered moving averages (CMAs)
   whose length matches the seasonal cycle. The
   seasonal cycle is the time required for one cycle
   to be completed. Quarterly seasonality requires a
   4-period moving average, monthly seasonality
   requires a 12-period moving average and so on.
3. Determine the Seasonal-Irregular Factors or
   components. This can be done by dividing the raw
   data by the corresponding depersonalized value.
4. Determine the average seasonal factors. In this
   step the random and cyclical components will be
   eliminated by averaging them.

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Cyclical and Seasonal Issues Computing
Multiplicative Seasonal Indices
Step 1
Step 4
Step 2 AVERAGE(B2B5)
Step 3 B3/C3
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Cyclical and Seasonal Issues Using Seasonal
Indices to Forecast
To forecast using seasonal indices 1- Compute the
forecast using an annual values. Any forecasting
techniques can be used. 2- Use the seasonal
indices to share out the annual forecast by
periods
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