Assessing the effects of recent events on Chipotle sales revenue

Transcription

1 Assessing the effects of recent events on Chipotle sales revenue 1Dr. Simon Sheather SAS Day 2016

2 2 In February 2005, I moved from

3 Head of the Department of Statistics: March 1, 2005 until February 28,

4 In Fall 2007, MS (Statistics) online began with 20 students 4

5 5 In 2012, Texas A&M Statistical Services LP was formed

6 6 In Fall 2013, MS (Analytics) face to face and online began

7 Predicting quarterly revenue for Chipotle Mexican Grill We wish to develop a time series model for the quarterly revenue of Chipotle Mexican Grill, in order to provide forecasts of quarterly revenue for the next two quarters, namely quarters 3 and 4 of We shall consider Chipotle s quarterly revenue from the first quarter of 2004 until the latest available results namely, the second quarter of We shall develop 2 models, namely, 1. A time series model 2. A regression model (with time series errors) using the following predictors 1) Total number of existing Chipotle stores at the beginning of each quarter 2) Number of new Chipotle stores opened during each quarter 7

8 8 Source: timeline of chipotles five outbreaks/#.waz H3nrvbh

9 9

10 Regression model Conclusions: Evidence of non constant variance in the residuals, we shall consider a logarithmic transformation of revenue and the predictors. 10

11 Regression model Conclusions: Evidence of outliers in the residuals Evidence of autocorrelation in the residuals 11

12 12 Residuals from regression model

13 Residuals from regression model Conclusions: We shall consider an AR(5) model for the residuals from the least squares regression model 13

14 Residuals from regression model Conclusions: We shall begin by considering an AR(5) model for the residuals from the least squares regression model 14

15 Regression model with AR(5) errors Notice that the coefficient of Log[New Store Openings] is positive and statistically significant 15

16 16 Regression model with AR(5) errors

17 17 Comparison of regression models

18 Regression model with AR gap model errors Conclusions: For every 1% increase in Existing stores, Chipotle s quarterly revenue is predicted to increase by 100*( ) = 1.27% New stores, Chipotle s quarterly revenue is predicted to increase by 100*( ) = 0.04% 18

19 19 Regression models with AR gap model errors

20 20 Regression model with AR gap model errors

21 Time series model Conclusions: Quarterly revenue increases over time, as does the variability in the quarterly revenue. In order to stabilize the variability, we shall consider a logarithmic transformation of revenue. 21

22 Time series model Conclusions: A logarithmic transformation of revenue stabilizes the variability of the series With an increasing trend in Log[Revenue ($M)] there is a need for differencing 22

23 Time series model Conclusions: Apart from 2013, Log[Revenue ($M)] is lower in the first quarter when compared to the other three quarters, for which Log[Revenue ($M)] is similar each year. In other words, there is evidence of seasonality in the log transformed revenue data. 23

24 Time series model Conclusions: The Ljung Box Q statistic is statistically significant at lags 1, 7 and 8, with lag 1 being the most statistically significant. With parsimony in mind, we begin by considering models just based on lag 1 autoregressive (AR) and/or moving average (MA) terms. 24

25 Time series model Conclusions: The seasonal ARIMA(0,1,1)(0,1,0)4 model produces the lowest values of AIC (Akaike Information Criterion) and SBC (Schwartz Bayesian Criterion) and hence is deemed to be the best of the four models considered. 25

26 Time series model Conclusions: The seasonal ARIMA(0,1,0)(0,1,0)4 is a valid model. A number of outliers are evident in the plot of the residuals 26

27 Time series model Time 2014Q1 2013Q2 2016Q1 2015Q4 2006Q1 Type Level Shift (LS) Level Shift (LS) Additive Outlier (AO) Level Shift (LS) Level Shift (LS) 27

28 28 Time series model allowing for 1 AO and 4 LS

29 Estimated percentage change in Chipotle s quarterly revenue due to 4 level shifts and an additive outlier Time Type % change 2006Q1 Level Shift (LS) Q2 Level Shift (LS) Q1 Level Shift (LS) Q4 Level Shift (LS) Q1 Additive Outlier (AO) 13.1 Chipotle ( reports on the following food safety incidents of 2015 Norovirus in August and December, 2015 Salmonella in August, 2015 E. coli in October November,

30 Time series model allowing for 1 AO and 4 LS Level shift Level shift Additive outlier 30

31 31 Time series model allowing for 1 AO and 4 LS

32 32 Time series model predictions

33 Source: newsarticle&id=

34 34 Source: newsarticle&id=

35 35 Analyst s expectations about revenue