Refer to the quarterly value of Gross Domestic Product (GDP in billions of current dollars) in China from 2021q1 to 2023q4. You are going to analyze GDP by an additive model with a trend component (Tt) and a seasonal component (St), and forecast GDP using the seasonal decomposition method. Year Quarter t GDP (Y₁) CM(4) Detrended 2021 1 1 24920 2 2 28284.9 3 3 29128.8 ? ? 4 4 32589.9 ? ? 2022 1 5 27034.4 ? ? 2 6 29244.7 ? ? 3 7 30794.2 ? ? 4 8 33399.1 ? ? 2023 1 9 28442.3 ? ? 2 10 30829.3 ? ? 3 11 31997.6 4 12 34789 a. Use an CM(t|4) [centered moving average of order 4] series to estimate the GDP series from t = 3 to 10. b. Calculate the seasonal factors for each quarter with a zero mean, by first obtaining the detrended revenue series from t = 3 to 10. c. In this seasonal decomposition method, why is it necessary to use moving averages to process time series data first? How about using moving average of order 5?
Refer to the quarterly value of Gross Domestic Product (GDP in billions of current dollars) in China from 2021q1 to 2023q4. You are going to analyze GDP by an additive model with a trend component (Tt) and a seasonal component (St), and forecast GDP using the seasonal decomposition method. Year Quarter t GDP (Y₁) CM(4) Detrended 2021 1 1 24920 2 2 28284.9 3 3 29128.8 ? ? 4 4 32589.9 ? ? 2022 1 5 27034.4 ? ? 2 6 29244.7 ? ? 3 7 30794.2 ? ? 4 8 33399.1 ? ? 2023 1 9 28442.3 ? ? 2 10 30829.3 ? ? 3 11 31997.6 4 12 34789 a. Use an CM(t|4) [centered moving average of order 4] series to estimate the GDP series from t = 3 to 10. b. Calculate the seasonal factors for each quarter with a zero mean, by first obtaining the detrended revenue series from t = 3 to 10. c. In this seasonal decomposition method, why is it necessary to use moving averages to process time series data first? How about using moving average of order 5?
Chapter11: Gross Domestic Product
Section: Chapter Questions
Problem 4SQ
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