11.9 Simple Forecasting Method #1:  Naive Method

The naive method for forecasting is sometimes referred to as LOCF, or Last Observation Carried Forward.  To apply this method is to predict the value for period t + 1 using the observed value from period t.  

While the naive method might sound too simplistic to be of much use, there are some instances in which it is quite handy.  For example, look at weather forecasting.  Suppose you are trying to predict tomorrow’s weather.  (Let’s also assume that you’re an amateur weather forecaster who lacks any sophisticated equipment).  To estimate the high temperature for tomorrow, you could simply use today’s high temperature.  Let’s take a look at how this would have done for the first seven days in January in Boston, in 1980.  (For the first day, the forecaster used the high temperature from December 31st). 

Not bad, eh?  If we calculate the average error to allow negative and positive predictions to cancel out, the mean error across the 7-day period was just 2.286 degrees.  Even if we use the average absolute error, it’s still just 5.71 degrees for the period.  Admittedly, the practical value of this is low — weather forecasts with even just a slightly longer range are much more useful in helping people to plan things like commuting choices and travel.  

For a time series with seasonality, we can use a naive approach that is slightly more nuanced than simply predicting the last observation from the time series.  

Instead of using the most recent observation from any time period, we would use the most recent observation that corresponded to the seasonal period that we wished to predict.  Suppose, for instance, that it’s June of 1970, and we are working with a dataset that exhibits monthly seasonality.  To make a seasonal naive forecast for the following month, we would use the observed data from July of 1969.  To make the August 1970 forecast, we would use the August 1969 data, and so on.