Economic Forecasting Seminar

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Economic Forecasting Seminar

• The Holt-Winters Exponential Smoothing Technique

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Simple Exponential Smoothing

• The major advantage of exponential smoothing
  algorithms lies in their ability to produce
  reliable short-term forecasts relatively quickly
  for a large variety of time series.
• Good forecasts require a great deal of judgment
  on the part of the forecaster.

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Forecasting

• Forecasts are a constant value.
• Intuition. Values of the
• series will differ over the
• forecast horizon.
• However, the observed
• data provide no useful information about what
  this difference will be, so the best prediction
  is that it will be zero.

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Series with Trends

• In some situations there is information in the
  observed data that can be useful for forecasting
  future values.
• Few time series exhibit no trend over their
  entire historical range.
• A linear trend forecasting function allows for
  the possibility of an evolving local linear trend
  over time.

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Linear Trend Model

• Yt d0 d1t et
• Period-to-period change in Yt is d1.
• d1 is the constant rate of growth in Y.

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2 x 12 Moving Average

• The result is an estimate of the trend-cycle
  component

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Holts Linear Trend Algorithm

• where and bT are estimates of the level and
  slope at time T, and a and b g are smoothing
  constants whose values are generally (but not
  always) between 0 and 1.

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Holts Linear Trend Algorithm

• Forecasts of future observations follow from the
  assumption of a continued period-by-period
  increase in the amount of the latest slope
  estimate from a base provided by the latest level
  estimate.

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Choosing a and b

• Difficult to do based simply on a visual
  examination.
• Some Guidelines
• As in the simple model, as the evolution of the
  level of the time series appears smoother, the
  appropriate value of a becomes higher.
• Similarly, if the slope (trend) appears to change
  smoothly over time, this suggests a higher value
  for b.

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• Can also
• for a grid of values of a and b.

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Smoothing with Seasonality

• Additive decomposition
• yt (d0 d1t) snt et
• Recall seasonal dummy variables
• Multiplicative decomposition
• yt (d0 d1t) snt et
• Recall centered moving average adjustment

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Holt-Winters Algorithm

• For seasonal time series.
• Algorithm varies depending on whether we assume
  an additive or multiplicative seasonal component.
• Additive seasonality (L is the periodicity of y)

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• Multiplicative seasonality.
• EViews can estimate a, b g

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Other Algorithms

• Other exponential smoothing algorithms exist for
  series which exhibit linear, exponential, or
  damped trends.
• Many of these are attributed to R.G. Brown, e.g.,
  Browns Double Exponential Smoothing.

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