Question

1. We regressed M&Ms yearly sales in period t (S_t) with an AR(4) model including an intercept. Our hypothesized model is given as follows:

S_t= β₀  + β₁ (S_t-1)    ₊    β₂ (S_t-2)     +  β₃ (S_{t -3}) + β₄ (S_t-4) + .

Our OLS-estimated model is given below. Numbers in the parentheses under the coefficients are p-valuesfor the corresponding parameter estimation. Significance level=5%.

= 5.60   1.05S_t-1        0.57S_t-2        0.32S_t-3    0.051S_t-4

(0.3)      (0.006)           (0.32)            (0.040)        (0.562)

           N=36      R²= 0.55     Adj- =0.53     Coefficient Var=1.57

1. What is the value of R^2 ? How to interpret it?

2. Which lag variables are significant based on the p-values?

3. Given the historical sales of M&Ms in the table, using this model, predict the sales of M&Ms in 2018 () and 2019 ()

Years	M&M Sales (100 million dollars)
2013	5.8
2014	6.5
2015	7
2016	7.1
2017	7.5

Answer 1