Methods and apparatus to determine effects of promotional activity on sales

A computer-implemented process for determining expected base sales for a sold product, comprising:

• obtaining sales data for a product sold at a point of sale location, the sales data organized in a time series according to a time period;
• obtaining causal data identifying a promotional event for at least one of the product and the point of sale location;
• excluding sales data corresponding to the promotional event to determine a time series of non-promoted sales data for the product;
• processing, using a processor, the non-promoted sales data using a double exponentially smoothed moving average model including a smoothing constant that assigns exponentially decreasing weights to older sales data values as the sales data becomes older in time, the processing comprising:
• executing a preliminary backward pass through the remaining sales data;
• executing a preliminary forward pass through the remaining sales data;
• averaging the preliminary backward pass and the preliminary forward pass;
• updating the remaining sales data for the product based on second sales data for an additional time period received for the product to provide updated sales data for the product;
• executing an updated backward pass through the updated sales data;
• executing an updated forward pass through the updated sales data;
• and
• averaging the updated backward pass and the forward pass;
• generating, using the processor, expected base data for the product based on the double exponentially smoothed moving average model;
• and
• outputting the expected base data for the product to a user.