Six years of quarterly data of a seasonally adjusted series are used to estimate

Question

Six years of quarterly data of a seasonally adjusted series are used to estimate a linear trend model as cap T_t = 128.20 + 1.06tt. In addition, quarterly seasonal indices are calculated as cap S_1 = 0.93, cap S_2 = 0.88, cap S_3 = 1.14, and cap S_4 = 1.05. a-1. Interpret the first quarterly index. In other words, what is the value of the series in the first quarter as compared to the average? 7% above 7% below 93% above 93% below 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? 5% above 5% below 95% above 95% below b. Make a forecast for all four quarters of next year. (Round your answers to 2 decimal places.) Quarter 1 Quarter 2 Quarter 3 Quarter 4

Explanation / Answer

Each index is a percent, with the average for the year equal to 100.0; that
is, each monthly index indicates the level of sales, production, or another variable in
relation to the annual average of 100.0.

a- 1 7% below since s1=0.93 (93%) which is 7% less than the average 100%

a-2 5% above since s2=1.05(105%) which is 5% more than the average 100%

b For 7th year

Quarter 1

t=25

substituting in trend line we get: y=154.7

quarter 2

t=26 y=155.76

quareter 3

t=27 y=156.82

quarter 4

t=28 y =157.88

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