Question

Six years of quarterly data of a seasonally adjusted series are used to estimate a linear trend model as T1 = 194.40 + 1.23t. In addition, quarterly seasonal indices are calculated as S, = 0.94, S2 = 0.88, S3 = 1.20, and S4 = 1.02. 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? 94% below O 6% above 94% above 6% 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? 98% above 2% below 98% below 2% above 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

Answer 1

tokenast is solution: a-l. 6% below Si=0.94 which means 94% of the it is 6% below a-2 2% above Su = 1.02 which means 102% of the i H 2 % above the seasonal average. average, forecast is the seasonal average, average b. Six years of quarterly data has been used to estimate the trend model. time period index Cts for the first quarter of next year = 6*4+1=95 for second quarta, t= 26 » for third quarter t = 27 and for the → Powerth quarter, t= 28 forecast for next year is calculated as below Quarter la prend A Seasonal factor - l *s, =(194.40+1-23 *35)40.4 - 211.64

Quartea 2 = les 9 (194.404 1.93 *26) *0188 - 199.21 Quarter 3 - lat 83 = (194.40 +1:33 * 2+) * 120 a 273,13 Quarter u = lag * Su = (194.40 + 1.23 * 28)* 1.02 gille Gu
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