Sales Analysis:

Impact of Product Price Change

December 2014


Objectives


  • Identify the impact of product price change on its sales
  • The impact is estimated by:
  • Forming two segments of customers:
    • customers that took advantage of a Special Offer
    • customers that did not take advantage of a Special Offer
  • Applying Intervention Time Series Analysis, Robust and Segmented Regression to each segment of customers


Customers that took advantage of the special offer


  • Have no obvious global trend in weekly sales data
    • Pre-Price Intervention Period: no significant linear trend
    • Special Order Period: there is a significant positive linear trend, slope=736 units/day
    • Post-Price Increase Period: significant positive linear trend, slope=127 units/day
  • Price Increase has significant negative impact on sales


Customers that took advantage of special offer (Cont.)


  • Special Offer has significant positive impact on sales
    • Number of stocking customers has a maximum of 4,235 in Special Offer Period
      • In Pre Price Intervention Period the number of stocking customers was just 3% smaller than the maximum
      • In Post Price Increase Period the number of stocking customers was 27% smaller than the maximum
    • Average number of units has a maximum of 77.55 units per customer in Special Offer Period
      • In Pre Price Intervention Period the average units was 35% smaller than the maximum
      • In Post Price Increase Period the average units was 23% smaller than the maximum
    • Total number of units per week has a maximum of 86,060 units per week in Special Offer Period
      • In Pre Price Intervention Period the total units per week was 38% smaller than the maximum
      • In Post Price Increase Period the total units per week was 56% smaller than the maximum


Customers that did not take advantage of special offer


  • Have significant negative trend in weekly sales data (number of units sold)
  • Have significant negative trend in number of stocking customers
  • Price Change (Special Offer and Price Increase) do not affect average number of units


Data Structure


  • Time Frame:  Aug2013 – May2014
    • Number of weeks: 44
  • Number of purchasing customers: 33,091
  • Number of customers that took advantage of special offer: 4,235
  • Number of customers that did not take advantage of special offer: 28,856


Product Sales Statistics (in units)



Example One


Trend: Linear (Holt) Exponential Smoothing of Product Units (Non-Users of a Special Offer)



Example Two


Intervention Time Series Analysis/ARIMA Modeling


  • Intervention Time Series Analysis (ITSA) is an important method within ARIMA class of models for analyzing the effect of sudden events on time series data
  • The acronym ARIMA stands for "Auto-Regressive Integrated Moving Average" 
  • ITSA has become a standard statistical method for assessing the impact of an intervention (usually a planned policy change) on a time series 
  • ARIMA models are the most general class of models for analysis and forecasting a time series.
  • Type of Intervention:
    • Step: Intervention variable is zero before the specified date and equals one after the date


Weekly Product Sales (users of a special offer)



Example Three


Break Point  Analysis  (Chow Test)

Product Units: weekly dynamics from 01Aug2013 through 30May2014 (Users of a Special Offer)


  • If there is a suspicion or knowledge of structural change (the underlying process is not the same across all observations),  a special tool – Chow’s Breakpoint Test can help to identify the structural change in time series data
  • The Chow test divides the data into two sub-samples. It then estimates the same trend equation to see whether there are significant differences in the estimated equations.
  • A significant difference indicates a structural change in the relationship under consideration (mechanism of the time series generation is changed)
  • Results: the data strongly supports the hypothesis that the date 01JAN2014  (a special offer starting point) is a break point (p-value < 0.006)


Weekly Dynamics of Number of Stocking Customers Among Special Offer Users



Example Four


Weekly Dynamics of Number of Stocking Customers among Special Offer Non Users



Example Five