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    Question

    Which of the following statements is true regarding

    the Dickey-Fuller test in time series analysis?
    A It is used to calculate the correlation between time-lagged data points. Correct Answer Incorrect Answer
    B It tests for the presence of stationarity by comparing p-values to a significance level. Correct Answer Incorrect Answer
    C It ensures time series data is decomposed into trend, seasonality, and residuals. Correct Answer Incorrect Answer
    D It measures the degree of randomness in the residuals of a time series. Correct Answer Incorrect Answer
    E It models autoregressive relationships to predict future values. Correct Answer Incorrect Answer

    Solution

    Explanation: The Dickey-Fuller test is a statistical test used to check whether a time series is stationary. Stationarity implies that the statistical properties of the series, such as mean and variance, do not change over time. In this test, the null hypothesis assumes that the series has a unit root (non-stationary), while the alternative hypothesis assumes stationarity. By examining the p-value, we determine whether to reject the null hypothesis. A p-value below a chosen significance level (e.g., 0.05) indicates stationarity. This test is essential for models like ARIMA, which require stationary data for accurate forecasting. Option A: This describes autocorrelation, not the Dickey-Fuller test. Option C: Decomposition separates components but does not test stationarity. Option D: Measuring randomness pertains to residual analysis, not Dickey-Fuller. Option E: This describes autoregressive modeling, not stationarity testing.

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