Interpret the first quarterly index. In other words, what is the value of the se

Question

Interpret the first quarterly index. In other words, what is the value of the series in the first quarter as compared to the average?

Interpret the fourth quarterly index. In other words, what is the value of the series in the fourth quarter as compared to the average?

Make a forecast for all four quarters of next year. (Round your answers to 2 decimal places.)

Six years of quarterly data of a seasonally adjusted series are used to estimate a linear trend model as t = 194.40 + 1.23t. In addition, quarterly seasonal indices are calculated as 1 = 0.94, 2 = 0.88, 3 = 1.20,and 4 = 1.02.

Explanation / Answer

a-1. 6% below.

s1 = 0.94, which means the seasonal forecast is 94% of the average. Therefore, it is 6% below average.

a-2. 2% above

s4 = 1.02, which means the seasonal forecast is 102% of the average. Therefore, it is 2% above average.

b.

Six years of quarterly data has been used to estimate the trend model. Therefore, time period index (t) for the first quarter of next year = 6*4+1 = 25; for second quarter, t = 26; for third quarter, t = 27 and for the fourth quarter, t = 28

Forecast for next year is calculated as below:

Quarter 1 = Trend * seasonal factor = I25*S1 = (194.40+1.23*25)*0.94 = 211.64

Quarter 2 = I26*S2 = (194.40+1.23*26)*0.88 = 199.21

Quarter 3 = I27*S3 = (194.40+1.23*27)*1.20 = 273.13

Quarter 4 = I28*S4 = (194.40+1.23*28)*1.02 = 211.64

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