Ridiculously Simple Time Series Forecasting

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Ridiculously Simple Time Series Forecasting

• We will review the following techniques
• Simple extrapolation (the naïve model).
• Moving average model
• Weighted moving average model

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The Naïve Model
If your time series exhibits little variation
from one period to the next, has no discernible
trend, and is unaffected by seasonality, the
naïve model is just what you need.
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The Moving Average Model
For example, if n 4, you have a 4-period moving
average model.
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The Weighted Moving Average Model
The ?s are the weights attached to past
observations of the time series variable and
there are n periods weighted. Notice that S?i
1.
The trick is to select the valueof n and
corresponding values of so as to minimize MSE
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Example Forecasting Retail Sales of Womens
Clothing

• Our data set contains 163 monthly observations on
  retail sales of womens clothing in the U.S.
  (January 1992 to August 2005) measuring in
  millions of dollars.
• We will perform in-sample forecasts using the 3
  techniques to determine which has the best fit.

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Techniques 2 and 3

• We will do a 6-month moving average for technique
  2
• We will do a 4-month weighted moving average for
  technique 3. The weights are as follows

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Results
YR MO WRCS Naïve Naïve eSq 6 mo MA 6 mo MA esq 4 mo. WMA 4 Mo. WMA eSq
2005 1 2347 4498 4626801 3070.8 523934.7 3613.6 782163.4
2005 2 2461 2347 12996 3036.8 331584.0 3211.1 746668.8
2005 3 3115 2461 427716 3090.2 616.7 2899.0 191844.0
2005 4 3186 3115 5041 3119.3 4444.4 2903.5 44732.3
2005 5 3175 3186 121 3130.3 1995.1 2935.8 62600.0
2005 6 3059 3175 13456 2890.5 28392.3 3094.9 6416.0
2005 7 2750 3059 95481 2957.7 43125.4 3124.8 4329.6
      ESS(1) 82925024 ESS (2) 34161676 ESS(3) 22718665.1
      MSE (1) 511882.86 MSE(2) 217590.3 MSE(3) 142884.7
      root MSE(1) 715.46 root MSE(2) 466.5 root MSE (3) 378.0
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