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    Question

    Which of the following is the correct decomposition of

    time series data into its components?
    A Trend, seasonality, residuals, and correlation. Correct Answer Incorrect Answer
    B Trend, cyclical patterns, irregular components, and residuals. Correct Answer Incorrect Answer
    C Trend, seasonality, cyclic behavior, and random noise. Correct Answer Incorrect Answer
    D Trend, seasonality, and residuals. Correct Answer Incorrect Answer
    E Trend, outliers, seasonal effects, and forecast errors. Correct Answer Incorrect Answer

    Solution

    Time series decomposition involves breaking down a time series into three main components: 1. Trend: The long-term direction or movement in the data (e.g., increasing or decreasing). 2. Seasonality: The repeating fluctuations at regular intervals due to seasonal factors (e.g., monthly, quarterly). 3. Residuals (or irregular components): The random, unexplained fluctuations that remain after removing the trend and seasonality. These are the "noise" or errors in the data. This decomposition is critical because it allows for better understanding and forecasting by isolating predictable patterns from random variations. Option A is incorrect because correlation is not a component of time series decomposition. Option B is incorrect as the cyclical component is different from seasonality and is often linked to economic cycles, not necessarily regular time intervals. Option C is incorrect because "cyclic behavior" and "random noise" are not formal components in standard time series decomposition. Option E is incorrect because outliers and forecast errors are not part of the standard decomposition process.

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