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1

Quantitative Forecasting Methods Types:

There are two types of Quantitative Forecasting Methods:

  1. Time Series Models -- are based on the premise that data patterns from the past will continue more or less unchanged into some future period. 
  2. Causal Models -- assume the variable being forecasted (dependent variable) is related to one or more other variables (independent variable) and makes forecasts based on those associations. 

2

Time Series Methodologies or Models:

Time Series Models: a number of specific models have been developed to predict a future value (or values) from past values, Here are the most significant models, beginning with the simplest method:

  1. Naive -- Uses the immediate prior period's actual value as a forecast for the next period.
    • "Next year is expected to be just like this year".
  2. Simple Mean (Average) -- Uses the average of past values as the forecast for a future period or periods.
    • E.g. average the last 2 yrs as the forecast for next year.
  3. Simple Moving Average -- Uses the average of a specific number of the most recent values as the forecast for future period(s). Values are not adjusted.
  4. Weighted Moving Average -- Uses the average of a specific number of most recent values with each receiving a different emphasis or weight.
    • Average the last 3 months with the last month weight being .5, two months ago weight being .3, and three months ago weighted .2
    • E.g.: Forecasted value = (1 month ago x .5) + (2 months ago x .3) + (3 month ago x .2)
    • Weights must equal 1.0 
  5. Exponential Smoothing -- Uses the average of a specific number of most recent values with weights assigned to each which decline exponentially as data becomes older. 
    • A weight is assigned to the most recent period; that weight is called "smoothing factor"
    • All other weights for earlier periods are computed asa function of the smoothing factor. 
  6. Trend-adjusted Exponential Smoothing -- An exponential smoothing method which makes adjustments to past data when strong trend patterns are evident in the data.
    • This trend can be used when the forecast period is long enough to have a trend.
  7. Seasonal Indexes -- Adjusts past data to accomodate seasonal patterns in data
  8. Linear Trend Line -- Uses least squares to fit a straight line to past data and extends trendline to establish forecast. 

3

Time Series Patterns:

Over time, actual time series data will relect a pattern. Commom patterns in Time Series Data include:

  1. Level or Horizontal -- Data are relatively constant or stable over time; little increase or decrease in values.
  2. Seasonal -- Data reflects upward or downward swings over a short to intermediate time period, with each swing about same timing and level of change.
  3. Cycles -- Data reflects upward and downward swings over long period of time.
  4. Trend -- Data reflects a steady and persistent upward and downward movement over some long time period.
  5. Random -- Data reflects unpredictable, erratic variations over time. 

4

Time Series Decomposition:

Time series data that shows pattern often can be decomposed (i.e., separated into multiple causes).

  • Decomposition is the removal of effects of each pattern component from the data.

Decomposition Process:

  • 1. Removing the seasonal effects from the data, typically using smoothing;
  • 2. Removing the overall trend from the deseasonalized data, typically using regression;
  • 3. Removing the cyclic effects from the remaining data values, typically using a cyclic index. 

5

Causal Models:

Causal Models: Assume the variable being forecasted (dependent variable) is related to one or more other variables (independent variable) and makes forecasts based on those associations. 

Common Causal Model Types:

  • Regression Models
  • Input-Output Models
  • Economic Models

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Causal Model Types:

  1. Regression Models -- Uses mathematical equations that relate a dependent variable to one or more independent variables that influence the dependent variable:
    • Regression fits a curve to the data points to minimize error
    • Curve may be linear or non-linear
    • Trend analysis uses regression with time as the independent (explanatory) variable.
  2. Input-Output Models -- Describe the flow from one stage of a process or sector to another stage or sector. 
    • Outputs of one stage or sector determines inputs to a subsequent stage or sector.
      • Crude oil production > refining > gasoline
    • Can be used at macroeconomic level
  3. Economic Models -- Specify statistical relationship believed to exist between economic quantities.
    • Black Scholes model is economic model.