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    Question

    In time series decomposition, which component is removed

    to achieve stationarity?
    A Trend Correct Answer Incorrect Answer
    B Seasonality Correct Answer Incorrect Answer
    C Residuals Correct Answer Incorrect Answer
    D Both Trend and Seasonality Correct Answer Incorrect Answer
    E Irregular Component Correct Answer Incorrect Answer

    Solution

    To achieve stationarity, a time series must have a constant mean and variance over time. Removing both the trend and seasonality components ensures that the data's systematic variations are eliminated, leaving behind only the residuals (or irregular components). This stationary data is then ready for advanced forecasting methods, like ARIMA. For instance, when analyzing stock prices, trends and seasonal fluctuations are removed to focus on the unpredictable residuals. Why Other Options Are Wrong : A) Trend : Removing only the trend does not ensure stationarity if seasonal patterns persist. B) Seasonality : Isolating seasonality alone leaves the trend intact, preventing full stationarity. C) Residuals : Residuals are the noise left after decomposition; they do not need removal. E) Irregular Component : Irregular components are random and do not affect stationarity.

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