Statistical modelling of annual retail sales of good and services in the United States using generalized Pareto distribution model

Abstract

The total retail sales of goods and services in the US is modelled using generalized pareto distribution (GPD) model from Extreme Value Theory. The trend test which is Mann-Kendall (MK) suggests that retail sales data exhibit a non-stationarity. Thus, the non-stationary GPD with a linear dependence in time is proposed. The maximum likelihood estimation (MLE) method is used to estimate the parameters of GPD model. The return level of US annual retail sales for the next 20, 50 and 100 years are being calculated. Results showed that both stationary and non-stationary GPD produce the commendable results in fitting the data. The assessment on Q-Q plot suggest that GPD distribution provides a good fit to the annual retail sales data using MLE method. However, non-stationary GPD with time as a linear covariate does improve the model. This is supported by the goodness-of-fit test where the AIC, BIC and LRT conclude the non-stationary performed quite well compared to the stationary model. Consequently, the non-stationary GPD model is the most appropriate, comprising linear effect in the location of extremal behavior, but homogeneity in all other aspects. The return levels provided in this study could provide some useful information to the country where the government should focus more on the retail industry as the retail industry has high potential to be primary sector of the economy in the country. In addition, the government should be more creative in strategizing the marketing plan into a global market and building up the alternative way to increase the profits while coping the challenges during the pandemic period.