conditions influence human behavior and the choices people make. Ice-cream
sales, success of a garage sale, number of hot-dogs sold by a New York vendor, crime
rates, school truancy rates, church attendance, and even stock market returns, are
all affected to a varying extent by weather conditions. In many cases, the ways
in which weather conditions affect behavior have been researched,
documented, and analyzed. The end result of this research and data
analysis is often a theoretic model that describes and quantifies how certain
weather elements (such as wind, rain, temperature, or humidity) influence human
behavior. BrainTech, LLC
uses similar statistical techniques to transform patterns in past
sales into a descriptive
model of behavior that can help a company better understand their customers. These behavioral models include variables such as day-of-week, time of year,
proximity to holidays, general demand trend, and multiple weather elements.
Using modeling techniques, we can identify variables that may have influenced customer
purchasing behavior in the past, and quantify the strength of association
between each variable and behavior. Almost without exception, the models of
customer behavior contain at least one weather element with a quantifiable and
predictable association with daily sales figures.
Although a primary reason to
develop models is to understand customer behavior, many of the models can reproduce
the number of sales made on any given day with a high degree of accuracy.
Using statistical techniques such as cross-validation, we can refine models so
that they reflect current customer behavior and preference with a high degree
of certainty. These cross-validated models can be extremely useful for predicting
short-term, future sales.
The primary challenge of using predictive
models that contain weather-related variables to estimate future sales is dealing
with the variable accuracy of weather forecasts.
In essence, the accuracy of a
weather forecast limits the number of days the model can be expected to produce
reasonable estimates of future sales. As an example, if customers buy fewer
products on days when it is raining, even a perfect model of customer behavior will
fail to accurately estimate sales seven days in advance if the forecasted
rainfall seven days from now turns out to be inaccurate.
This informal report addresses two important factors that
predictably influence the accuracy of weather forecasts. These two factors
are: (1) properties of the geographic location for which the forecast is being
made (i.e. region, elevation, climate), and (2) the weather element being
forecast (i.e. temperature, wind speed, precipitation). By understanding how
forecast accuracy varies based on geographic location and the weather element
being forecast, we are able to estimate how many days in advance a specific model
is likely to predict sales with a high degree of accuracy.
For 3-day weather forecasts in Key West, Florida, the predicted temperature has
been within 3 degrees of the actual temperature 90% of the time. In Seattle, that number is around 75%. The same holds for precipitation predictions; forecasts
of precipitation in Eastern Washington or Los Angeles tend to be more accurate than
forecasts of precipitation in Seattle or tropical regions of Florida. In general,
stable the climate, the better forecasts tend to be. Therefore, clients
in charge of inventory management for stores in Southern California and Eastern
Washington may be able to extend sales estimates further into the future than those
who manage inventory for stores in Western Washington and Oregon.
2. The forecasting
of certain elements (such as rain) in a 1-to-3-day period out is considered to
be extremely accurate, exceeding
90% in 2002. We have been unable to locate a comprehensive, easily
accessible collection of weather forecast accuracy data by region, per weather
Therefore, models that rely heavily on certain weather elements
require that we perform our own analysis of each weather element for each weather
This is why we track
changes in weather forecasts.
There are cases when weather forecasts change at the last
minute due to unexpected movement of storm fronts, or slower-than-anticipated air
movement in zones of high or low pressure. We have received several questions
about how unexpected, last-minute change in a weather forecast affects a predictive
While the answer to this question depends largely on customer
behavior and the predictive model, using statistical models to generate estimates
of future sales carries little or no risk of increasing negative impact when a dramatic
forecast change occurs.
In other words, if a client is using weather forecasts
to estimate demand, the estimates generated by the model are equally likely to
be negatively impacted when an unexpected weather change occurs. However, because
models are updated each night based on actual weather collected during the day,
forecast changes are immediately incorporated into the modeling process and future
estimates are adjusted accordingly. In the rare event a weather system stalls
or arrives early during an important transition period (from weekend to weekday,
or vice versa), estimated sales for the next week remain valid, and shipments
can be reduced or increased by an appropriate amount based on predicted sales for
the upcoming week. In summary, although the negative impact of
last-minute, unexpected changes in weather forecasts on sales estimates cannot
be ignored or brushed aside, using modeling to estimate future sales carries
little risk of increasing or prolonging the impact of such an event.
The two following figures illustrate the effect of weather
forecast accuracy on sales estimated by the same predictive model. In each
figure, the right-most blue bar indicates the date on which the prediction is
made. The diverging lines show the anticipated range of change in prediction
as time progresses, given the accuracy of weather forecasts. In other words,
if the model were used to estimate how many units will be sold six days from
now, the bands indicate how estimates of sales might change over the upcoming
six days due to adjustments made to weather forecasts. The first figure shows a
95% confidence band for estimates produced by the model 6 days into the future assuming
accuracy of forecasts typical of a Southern-California-like climate. In
other words, given the specific model with typical Southern California weather forecast
accuracy, over the next six days, sales estimates will remain within the upper
and lower bands 95% of the time. Figure 2 shows the same model’s 95% band of
prediction assuming weather forecast accuracy typical of a Western-Washington-like
Figure 1. Assuming
forecast accuracy typical of a region with stable climate, 95% of the time
the model will continue to estimate sales within the confidence bands over the
next six days.
Figure 2. Assuming
forecast accuracy typical of a region with variable climate, 95% of the
time the model will continue to estimate sales within the confidence bands over
the next six days.
The 95% confidence bands diverge at an increasing rate in
the second figure due to reduced accuracy of weather forecasts for the region.
However, it is also important to note that the bands remain fairly narrow
within a 3 day forecast window, regardless of Southern-California-like or
Western-Washington-like weather forecast accuracy. In summary, models that
use weather forecasts to estimate future sales for the following three days
remain extremely robust despite variable accuracy of weather forecasts between
regions. However, as can be seen in figure two, the model’s estimate of
sales 4-7 days in the future is likely to change a great deal as the weather
forecast is updated.
In conclusion, weather forecasts are sufficiently accurate
so that companies able to place and receive orders within a three-day window can
be reasonably confident that sales predicted by the model up to three days in
advance will remain fairly stable, despite updates to weather forecasts. Companies
that produce or stock perishable goods are often able to improve inventory management
and better estimate short-term demand using predictive models in conjunction
with weather forecasts. In regions with more stable climates, it may be
reasonable to use predictive models in conjunction with weather forecasts to
estimate sales up to 4-5 days in advance.
Copyright © Owen
Produced for BrainTech, LLC
Curious about how your sales might be related to the
weather? You can easily find out, online; we track and record weather forecasts for
every zipcode in the continental US, and offer a free regression
analysis tool you can use online that combines our weather data with your
sales data to search for possible models of customer behavior. Here is an
example output from the modeling tool. We also offer other services, including
in-house analysis and interpretive reports.