Complete the following steps to interpret an ARIMA analysis. Key output includes the p-value, coefficients, mean square error, Ljung-Box chi-square statistics, and the autocorrelation function of the residuals.
Step 1: Determine whether each term in the model is significant
To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the term is not significantly different from 0, which indicates that no association exists between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the term is not significantly different from 0 when it is significantly different from 0.
P-value ≤ α: The term is statistically significant
If the p-value is less than or equal to the significance level, you can conclude that the coefficient is statistically significant.
P-value > α: The term is not statistically significant
If the p-value is greater than the significance level, you cannot conclude that the coefficient is statistically significant. You may want to refit the model without the term.
Step 2: Determine how well the model fits the data
Use the mean square error (MS) to determine how well the model fits the data. Smaller values indicate a better fitting model.
Step 3: Determine whether your model meets the assumption of the analysis
Use the Ljung-Box chi-square statistics and the autocorrelation function of the residuals to determine whether the model meets the assumptions that the residuals are independent. If the assumption is not met, the model may not fit the data and you should use caution when you interpret the results.
Ljung-Box chi-square statistics
To determine whether the residuals are independent, compare the p-value to the significance level for each chi square statistic. Usually, a significance level (denoted as α or alpha) of 0.05 works well. If the p-value is greater than the significance level, you can conclude that the residuals are independent and that the model meets the assumption.
Autocorrelation function of the residuals
If no significant correlations are present, you can conclude that the residuals are independent. However, you may see 1 or 2 significant correlations at higher order lags that are not seasonal lags. These correlations are usually caused by random error instead and are not a sign that the assumption is not met. In this case, you can conclude that the residuals are independent.
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