Forecasting NoTrend Time Series II: Moving Averages

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Forecasting No-Trend Time Series II Moving
Averages Exponential Smoothing
Topics Moving Average Method Smoothing Effect of
Span/Period Assessment of Forecast with Holdout
Sample Exponential Smoothing Method Effect of
Smoothing Constant Implementation in StatTools
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Moving Average Method

• Apply when time series does not have a pronounced
  trend
• Takes average of past k observations to forecast
  value of the next observation
• Ftk (Yt Yt1Ytk-1)/k

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Moving Average Calculation with k 3
131 (128 135 130)/3 130.7 (135 130
127)/3
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Smoothing Effect of Span Value, k 3

• Small values of k lead to light smoothing
  forecast series closely mirrors original series
• Can lead to misleading forecasts attempting to
  model random noise
• Use small k when movements believed to be true
  pattern

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Smoothing Effect of Span Value, k gt 7

• Large values of k lead to heavy smoothing
  forecast series tracks overall basic movement
• Can lead to misleading forecasts if series
  fluctuations are part of true pattern and not
  random
• Use large k when movements believed to be random

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Graph of Smoothing with Small Span Value, k 3
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Graph of Smoothing with Large Span Value, k 12
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Assessment of Forecast

• Use MAE, RMSE, MAPE
• Choose k that yields smaller values of error
  metrics
• Calculations based on historical values do not
  guarantee better forecasts
• Better based on holdout sample

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Assessment of Forecast Small Span, k 3
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Assessment of Forecast Large Span, k 12
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Simple Exponential Smoothing Method

• Apply when time series does not have a pronounced
  trend

Starting at the end until power equals zero
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Simple Exponential Smoothing vs. Moving Avg.

• Improves on Moving Avg. since no series
  observations are lost due to averaging
• In forecast, it gives weight to all past
  observations but weight depends on smoothing
  constant, a

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Simple Exponential Smoothing Calculation with a
0.1
L1 Y1 to start off process L2 128.7 0.1135
0.9128 L3 128.83 .1130
.1.9135.9.9128
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Effect of Small Smoothing constant, a 0.1

• Small values of a lead to heavy smoothing because
  distant series observations continue to have
  large influence
• Effect is similar to that of moving average with
  large k
• Use small a when series swings believed to be
  random

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Effect of Large Smoothing constant, a 0.9

• Large values of a lead to light smoothing
  forecast series mimics original series
• Only very recent observations influence next
  forecast
• Use large a when swings believed to be true
  pattern

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Graph of Simple Exponential Smoothing with Small
a (0.1)
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Graph of Simple Exponential Smoothing with Large
a (0.9)
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Assessment of Forecast

• Use MAE, RMSE, MAPE
• Choose a that yields smaller values of error
  metrics
• StatTools can find optimal a
• Calculations based on historical values do not
  guarantee better forecasts consider holdout
  sample

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Assessment of Forecast Small Smoothing Constant
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Assessment of Forecast Large Smoothing Constant
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Simple Exponential Smoothing with Optimal a
(0.264)
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Assessment of Forecast Optimal Smoothing Constant
Optimization based on RMSE
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Forecasting with Moving Averages in StatTools

• After naming data set, place cursor anywhere in
  spreadsheet and click on the Time Series
  Forecasting icon (4th from right)
• Select Forecast from drop down menu
• Select variable of interest by clicking in the
  box next to it

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Forecasting with Moving Averages in StatTools

• Accept defaults for Number of Forecasts and
  Method ( Moving Avg.) then enter desired
  number of holdouts and span value
• Check defaults under Time Scale and adjust if
  necessary
• Click O.K. for output in new sheet

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Forecasting with Simple Exponential Smoothing in
StatTools

• After naming data set, place cursor anywhere in
  spreadsheet and click on the Time Series
  Forecasting icon (4th from right)
• Select Forecast from drop down menu
• Select variable of interest by clicking in the
  box next to it

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Forecasting with Simple Exponential Smoothing in
StatTools

• Accept default for Number of Forecasts then
  enter desired number of holdouts
• Click radio button for Expon. Smoothing
  (Simple) then enter parameter value (a) or check
  optimize box
• Accept other defaults and click O.K. to obtain
  forecasts in new sheet