Eight years of quarterly data of a seasonally adjusted series are used to estima

Question

Eight years of quarterly data of a seasonally adjusted series are used to estimate an exponential trend model as ln(T_t) = 2.70 + 0.02t with a standard error of the estimate, s_e = 0.06. In addition, quarterly seasonal indices are calculated as S_1 = 0.97, S_2 = 1.14, S_3 = 0.95, and S_4 = 1.05. a-1. Interpret the third quarterly index. In other words, what is the value of the series in the third quarter as compared to the average? 5% below 5% above 95% below 95% above a-2. Interpret the fourth quarterly index. In other words, what is the value of the series in the fourth quarter as compared to the average? 95% below 5% above 5% below 95% above b. Make a forecast for all four quarters of next year. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Explanation / Answer

a-1) 5% below:

a-2) 5% above:

a-3)

for t =97,98,99,100 for next year Quarter 1,2,3,4

therefore unseasoned forecast of 4 quarters:

multiplying above with seasonal index; forecast:

quarter 1 4.64 quarter 2 4.66 quarter 3 4.68 quarter 4 4.7

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