Time Series Analysis Seasonal Decomposition 1 — Questions and Answers
Question 1: What are the four classical components of a time series decomposition?
- Trend, Seasonality, Cyclical, and Irregular (Residual) (Correct answer)
- Mean, Variance, Skewness, Kurtosis
- AR, MA, Integration, Seasonal
- Level, Slope, Damping, Error
Correct answer: Trend, Seasonality, Cyclical, and Irregular (Residual)
Classical decomposition separates a series into trend, seasonal, cyclical, and irregular (noise) components.
Question 2: In additive decomposition, how are the components combined?
- Y = Trend + Seasonal + Residual (Correct answer)
- Y = Trend × Seasonal × Residual
- Y = Trend / Seasonal + Residual
- Y = Trend + Seasonal × Residual
Correct answer: Y = Trend + Seasonal + Residual
Additive decomposition assumes the components sum together, appropriate when seasonal fluctuations are roughly constant in magnitude.
Question 3: When should multiplicative decomposition be preferred over additive?
- When seasonal variation grows proportionally with the trend level (Correct answer)
- When the series is stationary
- When residuals are normally distributed
- When the series has no trend
Correct answer: When seasonal variation grows proportionally with the trend level
Multiplicative decomposition suits series where seasonal swings increase as the series level increases, reflecting proportional variation.
Question 4: What is STL decomposition?
- Seasonal and Trend decomposition using Loess (Correct answer)
- Standard Time Lag decomposition
- Stochastic Trend Linearization
- Seasonal Temporal Leveling
Correct answer: Seasonal and Trend decomposition using Loess
STL uses locally weighted regression (Loess) to flexibly extract trend and seasonal components, handling complex and changing seasonality.
Question 5: What does the seasonal index represent in classical decomposition?
- The average deviation from the trend for each period within a season (Correct answer)
- The overall average of the series
- The residual after removing trend
- The slope of the trend line
Correct answer: The average deviation from the trend for each period within a season
A seasonal index captures how much a given seasonal period (e.g., month) typically deviates from the overall trend level.
Question 6: What is the X-13ARIMA-SEATS method used for?
- Seasonal adjustment of economic time series (Correct answer)
- Detecting outliers in non-seasonal data
- Fitting VAR models
- Computing spectral densities
Correct answer: Seasonal adjustment of economic time series
X-13ARIMA-SEATS is the US Census Bureau's official seasonal adjustment program, combining ARIMA modeling with signal extraction.
Time Series Analysis Seasonal Decomposition 1
What are the four classical components of a time series decomposition?