136 Case: the Market of Health and Personal Care Products
A time series is an ordered sequence of observations \(\{Y_t\}\) indexed by time \(t\), usually sampled at fixed intervals. In this part we work with monthly observations (\(t=1,2,\dots,T\)), so the spacing is one month throughout.
136.1 Problem
A company sells an exclusive variety of pharmaceutical and health-related products through numerous retail stores in the USA. The production manager needs accurate information about the monthly US retail sales for the purpose of production planning and maintaining an adequate inventory of produced items (to be shipped to customers on demand). The primary objective of this analysis is to:
- gain insight into the dynamics of the Retail Market of Health and Personal Care products
- examine the role of the long-run trend and seasonality
- create extrapolation forecasts without the need of exogenous variables
- evaluate the impact of past events (such as promotions, strikes, etc.)
136.2 Data
The monthly time series under investigation (i.e. the “HPC” time series) is available in most R modules. The first observation corresponds to January 2001 and the last observation to December 2007. The retail sales are measured in millions USD and have not been adjusted for seasonality nor inflation. In this handbook, the stored series is a teaching extract of US monthly retail sales for health and personal care products (US Census Bureau retail trade statistics).
The stored time series is shown in the following plot:
Observe how the time series exhibits a long-term trend and strong seasonality. Some key descriptive statistics are also shown at the bottom. If we set the Sample Range slider to 1 - 12, we see the observations of the first year with a peak in December.
For a refresher on the graphical tools used in this section, see the Time Series Plot example in Section 79.5, the Mean Plot chapter (Chapter 80), and the Periodogram chapter (Chapter 85).