A second-order autoregressive model for four years of the monthly price of apple

Question

A second-order autoregressive model for four years of the monthly price of apples is shown below. The table shows the apple prices for the first year. Using the values from the table, what is the predicted value for January of the second year? MonthJan Feb Mar Apr May Jun Aug Sep Oct Nov Deco Price 0.967 1.004 0.964 0.952 0.996 1.042 1.171 1.213 1.232 1.127 1.092 1.052 Mar Apr May Jun Jul Aug Sep Rsquared : 79.7% Rsquared (adjusted)-78.796 s = 0.0663 42 degrees of freedom SE(Coeff) 0.0882 P-value 0.0417 1.211386 0.1437 8.43 s0.0001 -0.370582 0.1463 -2.53 0.015 Coefficient 0.185329 t-ratio 2.10 Variable Intercept Lag1 Lag2 The forecast value is (Round to three decimal places as needed.)

Explanation / Answer

Here the prediction equation is

Price = intercept + 1.211386 * lag1 - 0.3706 * lag 2

so Price (January - 2nd year) = 0.1853 + 1.2114 * Dec (1st year) - 0.3706 * Nov(1st year)

= 0.1853 + 1.2114 * 1.052 - 0.3706 * 1.092

= 1.055

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