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    Question

    In time series analysis, the Dickey-Fuller test is used

    to:
    A Test for the presence of seasonality in the data. Correct Answer Incorrect Answer
    B Test for autocorrelation in the residuals. Correct Answer Incorrect Answer
    C Test whether the time series data is stationary or non-stationary. Correct Answer Incorrect Answer
    D Calculate the moving average for a time series. Correct Answer Incorrect Answer
    E Forecast future values of a time series. Correct Answer Incorrect Answer

    Solution

    The Dickey-Fuller test is a statistical test used to check for stationarity in time series data. Stationarity refers to a property of a time series where the mean, variance, and autocovariance are constant over time. Non-stationary data, on the other hand, often requires transformation (such as differencing) to become stationary before applying many time series forecasting models, like ARIMA. The Dickey-Fuller test specifically tests the null hypothesis that a unit root is present in the data, which implies non-stationarity. If the test rejects the null hypothesis, it indicates that the data is stationary. Why Other Options Are Incorrect: • A: The Dickey-Fuller test does not directly test for seasonality. Seasonality would be identified through decomposition or by analyzing seasonal patterns in the data. • B: Autocorrelation is typically tested using the autocorrelation function (ACF), not the Dickey-Fuller test. • D: The moving average is a technique used for smoothing or forecasting, not for testing stationarity. • E: While stationarity is important for forecasting, the Dickey-Fuller test does not directly forecast future values; it assesses whether the data needs to be differenced before forecasting.

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