Ridiculously Simple Time Series Forecasting We will review

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Ridiculously Simple Time Series Forecasting We will review the following techniques: • Simple extrapolation

Ridiculously Simple Time Series Forecasting We will review the following techniques: • Simple extrapolation (the “naïve” model). • Moving average model • Weighted moving average model

The Naïve Model If your time series exhibits little variation from one period to

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.

The Moving Average Model For example, if n = 4, you have a 4

The Moving Average Model For example, if n = 4, you have a 4 -period moving average model.

The Weighted Moving Average Model The ω’s are the weights attached to past observations

The Weighted Moving Average Model The ω’s are the weights attached to past observations of the time series variable and there are n periods weighted. Notice that: Σωi = 1. The trick is to select the value of n and corresponding values of so as to minimize MSE

Example: Forecasting Retail Sales of Women’s Clothing • Our data set contains 175 monthly

Example: Forecasting Retail Sales of Women’s Clothing • Our data set contains 175 monthly observations on retail sales of women’s clothing in the U. S. (January 1996 to August 2010) measuring in millions of dollars. • We will perform in-sample forecasts using the 3 techniques to determine which has the best fit.

Techniques 2 and 3 • We will do a 6 -month prior moving average

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

Results YR MO WRCS Naïve 6 MO MA 4 Mo WMA 2010 1 2278

Results YR MO WRCS Naïve 6 MO MA 4 Mo WMA 2010 1 2278 4149 3129. 5 3106. 2 2010 2 2426 2278 3064. 167 3224. 9 2010 3 3183 2426 2988. 833 3219. 3 2010 4 3249 3183 3042 3146. 5 2010 5 3233 3249 3079. 333 2600. 5 2010 6 2949 3233 3086. 333 2898. 4 2010 7 2731 2949 2886. 333 3189. 4

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Millions of Dollars In-Sample Forecasts of Sales of Women's Clothing Stores 6000 5000 4000 3000 2000 1000 0 Year Actual Naïve Model 6 Month Moving Average 4 Month Weighted Moving Average

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