Assume you first collected a quarterly sales data (in millions of dollars) over a four-year period from the first quarter 2016 to the fourth quarter 2019 then computed (the normalised) seasonal index for each quarter using ratio-to-moving-average method, and finally fitted a linear trend model based on the deseasonalised sales data and a time period (X), coded as 0, 1, ......, n. If the estimated coefficients of the intercept and X (time period) are 153.93 and 6.01, respectively, what is the seasonally adjusted forecast value of sales (in millions of dollars) for the third quarter of 2020? Round your final answer to two decimal places. Assume the (normalised) seasonal indices for the quarterly sales data are 1.04, 1.02, 0.96 and 0.98 for quarters 1, 2, 3 and 4, respectively.
Question
Assume you first collected a quarterly sales data (in millions of dollars) over a four-year period from the first quarter 2016 to the fourth quarter 2019 then computed (the normalised) seasonal index for each quarter using ratio-to-moving-average method, and finally fitted a linear trend model based on the deseasonalised sales data and a time period (X), coded as 0, 1, ......, n. If the estimated coefficients of the intercept and X (time period) are 153.93 and 6.01, respectively, what is the seasonally adjusted forecast value of sales (in millions of dollars) for the third quarter of 2020? Round your final answer to two decimal places. Assume the (normalised) seasonal indices for the quarterly sales data are 1.04, 1.02, 0.96 and 0.98 for quarters 1, 2, 3 and 4, respectively.
Solution
To calculate the seasonally adjusted forecast value of sales for the third quarter of 2020, we need to follow these steps:
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First, we need to calculate the forecasted sales value without considering the seasonality. This can be done by plugging the time period value into the linear trend model. The time period for the third quarter of 2020 is 18 (from the first quarter of 2016 to the third quarter of 2020, we have 18 quarters). So, the forecasted sales value without considering the seasonality is:
Y = a + bX Y = 153.93 + 6.01 * 18 Y = 261.11 (in millions of dollars)
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Then, we need to adjust this forecasted value for seasonality. The seasonal index for the third quarter is 0.96. So, the seasonally adjusted forecast value of sales for the third quarter of 2020 is:
Y_adjusted = Y * seasonal_index Y_adjusted = 261.11 * 0.96 Y_adjusted = 250.67 (in millions of dollars)
So, the seasonally adjusted forecast value of sales for the third quarter of 2020 is approximately $250.67 million, rounded to two decimal places.
Similar Questions
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