Forecasting

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• Forecasting
• ??

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Contents ??

• 18.1 Components Of A Time Series ???????
• Trend Component ??
• Cyclical Component ??
• Seasonal Component ??
• Irregular Component ???
• 18.2 Smoothing Methods ???
• Moving Averages ????
• Weighted Moving Averages
  ??????
• Exponential Smoothing ????
• 18.3 Trend Projection ????

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Contents ??

• 18.4 Trend And Seasonal Components ??
  ?????
• Multiplicative
  Model ????
• Calculating The Seasonal
  Indexes ??????
• ?
• Deseasonalizing The Time
  Series ??????????
• Using The Deseasonalized Time
  Series To
• Identify Trend ????????????????
• Seasonal Adjustments ?????
• Models Based On Monthly Data
  ???????
• Cyclical Component ????

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Contents ??

• 18.5 Regression Analysis ????
• 18.6 Qualitative Approaches ????
• Delphi Method ????
• Expert Judgment ?????
• Scenario Writing ???????
• Intutive Approaches ???

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Overview Of Forecasting Methods
???????
Forecasting Methods ????
Quantitative ??
Qualitative ??
Causal ??
Time Series ????
Smoothing ???
Trend Projection ?????
Trend Projection Adjusted For Seasonal
Influence ????????????
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18.1 Components Of A Time Series
???????

• Trend Component ????
• The long-run shift or movement in the time
  series observable over several periods of time.
• Cyclical Component ????
• The component of the time series model
  that results in periodic above-trend and
  below-trend behavior of the time series lasting
  more than one year.

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• Seasonal Component ????
• The component of the time series model
  that shows a periodic pattern over one year or
  less.
• Irregular Component ?????
• The component reflects the random
  variation of the time series values beyond what
  can be explained by the trend, cyclical, and
  seasonal components.

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Examples Of Some Possible Time Series
Trend Patterns

• Nonlinear Linear decreasing trend
  No trend

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18.2 Smoothing Methods
???

• Moving Averages ?????
• A method of forecasting or smoothing a
  time series by averaging each successive group of
  data points.
• Moving Averages?(most recent n data
  values)/n
• NOTE Forecast Accuracy ????
• Mean squared error (MSE) ????
• The average of the sum of the squared
  differences between the forecast values and the
  actual time series values.

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• Weighted Moving Averages ???????
• A method of forecasting or smoothing a
  time series by computing a weight average of past
  data values.
• NOTE The sum of the weights must equal one.

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• Exponential Smoothing ????
• A forecasting technique that uses a
  weighted average of past time series values to
  arrive at smoothed time series values that can be
  used as forecasts.
• Exponential Smoothing Model
• F t1 aY t (1-a)F t
• Ft1 forecast of the time series for
  period t1
• Yt actual value of the time series in
  period t
• Ft forecast of the time series for
  period t
• a smoothing constant ( 0 a 1 )

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18.3 Trend Projection
????

• Trend Projection ?????
• y b0 b1x
• Equation For Linear Trend
• Tt b0 b1t
• Tttrend value of the time series in period
  t
• b0intercept of the trend line
• b1slope of the trend line
• ttime

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• Computing The Slope (b1) And Intercept
  (b0)
• b1 ?tYt - (?t?Yt )/n
• ?t2 - (?t)2/n
• b0 Y - b1t

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18.4 Trend And Seasonal Components
???????

• Multiplicative Time Series Model ????
• A model whereby the separate components
  of the time series are multiplied together to
  identify the actual time series value. When the
  four components of trend, cyclical, seasonal, and
  irregular are assumed present, we obtain
• Yt TtCtStIt
• When the cyclical component is not
  modeled, we obtain
• Yt TtStIt

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• Deseasonalized Time Series ??????????
• A time series from which the effect of
  season has been removed by dividing each original
  time series observation by the corresponding
  seasonal index.

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18.5 Regression Analysis
????

• Causal Forecasting Methods ?????
• Forecasting methods that relate a time
  series to other variables that are believed to
  explain or cause its behavior.
• Autoregressive Model ??????
• A time series model whereby a regression
  relationship based on past time series values is
  used to predict the future time series values.

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18.6 Qualitative Approaches
????

• Delphi Method ????
• A qualitative forecasting method that
  obtains forecasts through group consensus.
• Expert Judgment ?????
• Qualitative forecasts are based on the
  judgment of a single expert or represent the
  consensus of a group of experts.

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• Scenario Writing ???????
• A qualitative forecasting method that
  consists of developing a conceptual scenario of
  the future based on a well-defined set of
  assumptions.
• Intuitive Approaches ???
• Qualitative approaches are based on the
  ability of the human mind to process a variety of
  information.