One way to forecast sales is to calculate the average and predict that $921.43 will be today’s sale. Another way (even simpler) is to assume that yesterday’s demand will be today’s demand as well, because $960 is the closest data point available.

A plot of your sales is as follows:

The plot seems to indicate an upward trend in our demand; therefore, your next sale should be higher than $960. However, if you look at the X-axis (time), you notice that sales are high on weekends. Because the next day is Monday, your sale should be much lower than $960. If you take into consideration last Monday’s sale ($880), you can expect a similar sale on the next Monday. Using this method, you have considered a seasonality effect.

There are a variety of different approaches to demand forecasting, and each approach leads to a different result. More data generally helps choose one approach over another, but nothing is guaranteed. Forecasting algorithms help find patterns in the data to yield the most accurate results possible.

In all the approaches previously mentioned in our example, we utilized only information from the time series itself to predict future values:

• average of last 7 days
• last value
• trend in the data
• seasonality effect

In Univariate Time Series Forecasting, you use only the information from the demand time series for forecasting. But what if an external factor affects your demand?

In our ice cream sales example, it is well known that temperature affects ice cream sales - ice cream sales rise when the temperature is high and drop when the temperature is lower. Should you take that into account for forecasting?

A plot including temperature is shown as:

This plot indicates a high positive correlation between temperature and ice cream sales (if one increases, the other increases). Therefore, a predicted value of temperature for the next day obtained from a weather service should help us to predict the next day’s ice cream sales.

Multivariate Time Series Forecasting incorporates such external factors. This method is also referred to as Causal Forecasting, and in this example temperature is a causal variable that causes changes in ice cream sales.

Another example of causal forecasting is the use of marketing spend as a causal variable to forecast a company’s revenue. In this case, marketing spend is a controllable causal variable because the company can control how much to spend on marketing. In the ice cream sales example, we do not have control over the temperature. Causal variables such as temperature are non-controllable causal variables. Other examples of non-controllable causal variables include macro-economic indices, holidays, and other weather variables such as chance of rain, wind speed, amount of snow, and so on.