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 unadjusted forecast value of sales (in millions of dollars) for the first 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 unadjusted forecast value of sales (in millions of dollars) for the first 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 unadjusted forecast value of sales for the first quarter of 2020, we first need to calculate the forecasted sales value for the time period X=16 (since the time period is coded as 0, 1, ..., n and we have 4 years of quarterly data, which gives us 16 quarters).
The linear trend model is given by Y = a + bX, where a is the intercept, b is the slope (or coefficient of X), and X is the time period. Substituting the given values, we get:
Y = 153.93 + 6.01 * 16 = 249.05
This is the deseasonalised forecast for the first quarter of 2020. To get the seasonally unadjusted forecast, we need to adjust this value using the seasonal index for the first quarter, which is given as 1.04.
So, the seasonally unadjusted forecast value for the first quarter of 2020 is:
249.05 * 1.04 = 258.612
Rounding this to two decimal places, we get 258.61 million dollars.
Similar Questions
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