Question

We consider data in the following table, summarizing sales of a product (in thousands). For each of the questions, justify your answer.

Year	Quarter	Sales
2015	1 2 3 4	4.95 4.25 6.15 6.65
2016	1 2 3 4	5.85 5.35 6.95 7.55
2017	1 2 3 4	6.15 5.75 7.65 7.95

(3.3) Ignoring seasonality and assuming the the time-series as given follows an AR(1) process, what is the expected sales value for the first quarter of 2018? (5)

Answer 1

Here I attach the R code

x=c(4.95,4.25,6.15,6.65,5.85,5.35,6.95,7.55,6.15,5.75,7.65,7.95)
m=arima(x,order=c(1,0,0))
m
forecast::forecast(m,1)

Here I attach the data and fit AR(1) model. The model summary is

Z_t=6.2887+0.4865Z_t-1+

The forecasted value for 2018 first quarter is :7.04