Quantifying Loss to the Economy Using Interrupted Time Series Models: An Application to the Wholesale and Retail Sales Industries in South Africa

A few recent publications on interrupted time series analysis only conduct preintervention modelling and use it to illustrate postintervention deviation without quantifying the amount lost during the intervention period. Thus, this study aims to illustrate how to estimate and quantify the actual amounts (in South African Rands—ZAR) that the negative impact of the intervention effects of the COVID-19 pandemic had on the South African total monthly wholesale and retail sales using the seasonal autoregressive integrated moving average (SARIMA) with exogenous components (SARIMAX) model. In addition, the SARIMAX model is supplemented with three approaches for interrupted time series fitting (also known as a pulse function covariate vector), which are: (i) trial and error, (ii) quotient of fitted values and actual values, and (iii) a constant value of 1 throughout the intervention period. Model selection and adequacy metrics indicate that fitting a pulse function with a trial-and-error approach produces estimates with the minimum errors on both datasets, so a more accurate loss in revenue in the economy can be approximated. Consequently, using the latter method, the pandemic had an immediate, severe negative impact on wholesale trade sales, lasting for 15 months (from March 2020 to May 2021) and resulted in a loss of ZAR 302,339 million in the economy. Moreover, the retail sales were also negatively affected, but for 8 months (from March 2020 to October 2020), with a 1-month lag or delay, suggesting the series felt the negative effects of the pandemic one month into the intervention period and resulted in a loss of ZAR 87,836 million in the economy.