ARIMA (Autoregressive Integrated Moving Average) is a statistical analysis model that uses time series data to understand and predict future trends. If you want to learn how to interpret ARIMA results, read this article.

##### Understanding ARIMA Results

In order to interpret the results, you need to know if:

- the model meets the assumptions using Jlung-Box chi-square statistics and autocorrelation of residuals
- each term is significant using p-values
- your model fits well using mean-squared error

In this article, as an example, we will review the results of a simple AR model trying to predict Bitcoinâ€™s future results.

##### Review General Information

First things first, you need to review the general information.

Here is some basic information:

- SARIMAX – Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors
- Dep. Variable â€“ What weâ€™re trying to predict.
- Model â€“ The type of model weâ€™re using. AR, MA, ARIMA.
- Date â€“ The date we ran the model
- Time â€“ The time the model finished
- Sample â€“ The range of the data
- No. Observations â€“ The number of observations

Note: The dependent variable is the close weâ€™re trying to predict. The independent variables are the constant beta. The error term is sigma2 or epsilon in our equation above. Our lag variables are ar.L1, ar.L2, and ar.L3.

##### Determine Significance

Next, you need to make sure that the model is statistically significant.

The null means NOT statistically significant. So,Â each term should have a p-value of less than 0.05, so we can reject the null hypothesis with statistically significant values.

Based on the data, Ll and L2 are not statistically significant as their p-values are above the 0.05 threshold.

##### Review Assumptions

It is not time to check and review if our model meets the assumptions – that the residuals are independent. If the residuals are not independent, we can extract the non-randomness to make a better model.

##### Ljung-Box Test

Pronounced â€śYoung,â€ť the Ljung-Box test checks that the errors are white noise

The Ljung-Box (L1) (Q) is the LBQ test statistic at lag 1 is, the Prob(Q) is 0.01, and the p-value is 0.94. Since the probability is above 0.05, we canâ€™t reject the null that the errors are white noise.

You can use a Ljung-Box diagnostic function to see all the statistics and p-values for the lags. Hereâ€™s how:

##### Heteroscedasticity Test

This method checks whether the error residuals are homoscedastic or have the same variance. The summary performs Whiteâ€™s test.

The summary shows a test statistic of 1.64 and a p-value of 0.00, which means we reject the null hypothesis and our residuals show variance.

##### Jarque-Bera Test

Jarque-Bera tests for the normality of errors. It checks if null that the data is normally distributed against an alternative of another distribution.

In our stats, we have a test statistic of 4535.14 with a probability of 0, which means we reject the null hypothesis, and the data is not normally distributed.

##### Fit Analysis

The Log-Likelihood, AIC (Akaikeâ€™s Information Criterion), BIC (Bayesian Information Criterion), and HQIC (Hannan-Quinn Information Criterion) help compare one model with another.

Check this data:

Log-Likelihood – It identifies a distribution that fits best with the sampled data.

AIC (Akaikeâ€™s Information Criterion) – It helps determine the strength of the linear regression model and penalizes a model for adding parameters.

BIC (Bayesian Information Criterion) – Like AIC, it punishes a model for complexity but also incorporates the number of rows in the data.

HQIC (Hannan-Quinn Information Criterion) – Like BIC and AIC, it is another criterion for model selection, but it is not used as frequently in practice.

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