# Model statistics for ARIMA

Find definitions and interpretation guidance for every model statistic that is provided with ARIMA.

## Iteration

This value indicates the number of iterations required to obtain the sum of squared errors (SSE). The ARIMA algorithm performs up to 25 iterations to fit a model. If the solution does not converge, store the estimated coefficients on the Storage subdialog, and run the analysis again entering the column of stored coefficients in Starting values for coefficients. You can store the estimated parameters and use them as starting values for a subsequent fit as often as necessary.

The algorithm may also fail to converge because you include a constant in the model. You can try performing the analysis again without the constant.

## SSE

The SSE is the sum of the squared residuals. It quantifies the variation in the data that the ARIMA model does not explain. Minitab displays the SSE for each iteration of the ARIMA algorithm.

### Interpretation

The SSE indicates the accuracy of the fitted model, at each iteration. The smaller the value, the more accurate the fit of the model. If you are comparing models or starting conditions, comparing multiple final SSE values can be meaningful. However, a single final SSE value may not be intuitively meaningful.

## Parameters

The parameters are the estimated coefficients for the parameters in the model, at each iteration. The table shows the progress of the ARIMA algorithm as it attempts to converge on a solution. For each subsequent iteration, the algorithm adjusts the parameter estimates in a manner that it predicts should reduce the SSE compared to the previous iteration. The iterations continue until the algorithm is unable to reduce the sum of squares any further, a problem prevents the subsequent iteration, or Minitab reaches the maximum number of iterations.

## Back forecasts

The back forecasts are the fitted values for time intervals before the start of your series. The back forecast values are the same as if you reversed the order of your time series and generated forecasts at the end of the reversed series.

## Coef

The coefficients are the final estimates of the values for the parameters in the model. Coefficients are the numbers by which the values of the term are multiplied in the ARIMA model.

## SE Coef

The standard error of the coefficient (SE Coef) estimates the variability between parameter estimates that you would obtain if you took samples from the same population again and again. Use the standard error of the estimate to measure the precision of the parameter estimate. The smaller the standard error, the more precise the estimate.

## T

The t-value measures the ratio between the coefficient and its standard error.

### Interpretation

Minitab uses the t-value to calculate the p-value, which you use to test whether the coefficient is significantly different from 0.

You can use the t-value to determine whether to reject the null hypothesis. However, the p-value is used more often because the threshold for the rejection of the null hypothesis does not depend on the degrees of freedom.

## P for the final estimate of parameters

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

### Interpretation

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.

## SS

The sum of squares for the residuals is the summation of the residuals using the final parameter estimates, excluding back forecasts. Minitab uses the sum of squares to calculate the mean square error.

## MS

The mean square error is a measure of the accuracy of the fitted model. Smaller values of the mean square error usually indicate a better fitting model. Use the mean square error to compare fits of different ARIMA models.

## DF

The degrees of freedom are the amount of information in your data. Minitab uses the degrees of freedom for the residuals to calculate the mean square error.

## Correlation matrix of the estimated parameters

The correlation matrix displays the correlation for every pair of terms in the model. If parameter estimates are highly correlated, consider reducing the number of parameters to simplify the model.

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