Modified Box-Pierce (Ljung-Box) Chi-Square statistics ARIMA

Find definitions and interpretation guidance for every modified Box-Pierce (Ljung-Box) chi-square statistic.

Lag

The lag is the time period that separates the data that are ordered in time. Minitab displays lags that are in multiples of 12. The lag is used to calculate the partial autocorrelation coefficient. The maximum number of lags (as suggested by Box and Jenkins) is approximately n/4 for a series with less than 240 observations or for a series with more than 240 observations, where n is the number of observations.

Chi-Square

The chi-square value is the test statistic that Minitab uses to determine whether the residuals are independent.

Interpretation

Minitab uses the chi-square value to calculate the p-value, which you use to make a decision about whether the residuals are independent. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

DF

The degrees of freedom are the amount of information in your data. Minitab uses the degrees of freedom for the chi-square statistics to calculate the p-value.

P-Value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Minitab displays p-values for accumulated lags that are multiples of 12.

Interpretation

Use the p-values to determine whether the model meets the assumptions that the residuals are independent. 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. If the assumption is not met, the model may not fit the data and you should use caution when you interpret the results.

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