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 T_t = 183.40 + 1.07t. In addition, quarterly seasonal indices are calculated as S_1 = 0.80, S _2 = 0.98, S_3 = 1.02, and S_4 = 1.04. 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? 20% below 80% below 80% above 20% 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? 96% above 4% above 4% below 96% below b. Make a forecast for all four quarters of next year. (Round your answers to 2 decimal places.)

Explanation / Answer

Average: (0.80 + 0.98 + 1.02 + 1.04) / 4 = 0.96

1) Difference is 0.8 - 0.96 = -0.16

Percentage = -0.16 / 0.96 = -0.16.67 = -16.67 * 100 = -16%

Ans: 20% below

2) Difference is 1.04 - 0.96 = 0.08

Percentage = 0.08 / 0.96 = 0.08 = 0.08 * 100 = 8%

Ans: 20% below

3) Tt = 183.40 + 1.07 t

Subtitute 5,6,7 and 8 in above equation which represent next year Q1, Q2 Q3 and Q4

Note: If you substitute 1,2,3 and 4 which represent current year

T1 = 183.4 + 1.07(5)

T1 = 183.4 + 5.35

T1 = 188.75 (Q1)

T2 = 183.4 + 1.07 (6)

T2 = 189.82 (Q2)

T3 = 183.4 + 1.07 (7)

T3 = 190.89 (Q3)

T4 = 183.4 + 1.07 (8)

T4 = 191.96 (Q4)

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