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5. Conduct an Ljung-box text 6. Plot the ACF and PACF of the data and find out whether AR or MA models are suitable for the data

Question

  1. Conduct an Ljung-box text
  2. Plot the ACF and PACF of the data and find out whether AR or MA models are suitable for the data
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Solution

Sure, here are the steps to conduct a Ljung-Box test, plot the ACF and PACF, and determine if AR or MA models are suitable for the data:

  1. Conduct a Ljung-Box Test

    • Import the necessary libraries in Python: import pandas as pd and from statsmodels.stats.diagnostic import acorr_ljungbox.
    • Load your data: data = pd.read_csv('your_data.csv').
    • Conduct the Ljung-Box test: ljungbox_results = acorr_ljungbox(data).
    • The Ljung-Box test returns two arrays: the first contains the test statistic for each lag, and the second contains the p-value for each lag. If the p-value is less than your chosen significance level (e.g., 0.05), you would reject the null hypothesis that the data are independently distributed.
  2. Plot the ACF and PACF

    • Import the necessary libraries: `from statsmodels.graphics.tsap

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In a pure auto-regressive process, AR(p), the value of p can be identified usingSelect one:a. Auto-correlation functionb. Ljung−Box testc. Partial auto-correlation functiond. Auto-correlation and partial auto-correlation function

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According to Appendix 3, AR (1) Model Coefficients:ar1 intercept0.2969 -0.0003s.e. 0.0576 0.0018sigma^2 estimated as 0.0004528: log likelihood = 675.81, aic = -1345.62ϕ0 = -0.0003*(1-0.2969)2 Details are in Apendix 3 and Apendix 5= -0.00002109AR (1) Model Form:rt = ϕ0 + ϕ1rt-1 + at , σa2rt = -0.00002109 + 0.2969rt-1+at , 0.0004528

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