Auto-ARIMA Picks the Best Model So You Do Not Have To
ARIMA models are powerful but they have a parameter problem. Before you can use one, you need to choose three numbers; p (the autoregressive order, how many past values to include), d (how many times to difference the series), and q (the moving average order, how many past errors to include). Choosing the wrong combination gives you a model that either underfits the data (missing structure that was there to capture) or overfits it (fitting noise instead of signal, which collapses on out-of-sample data).
The traditional approach is to use ACF and PACF plots to read off the orders, which requires some skill and judgment and is not always unambiguous. Auto-ARIMA automates this by fitting a range of candidate models and selecting the one with the best information criterion score; typically the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).
The FatNarwhal Auto-ARIMA tool does this search automatically. You give it a time series and it gives you the best-fit ARIMA model along with the forecast, diagnostic plots, and the full comparison table of candidate models.
How to Use It
Go to fatnarwhal.com/auto-arima and enter a ticker or data series.
The tool searches over a grid of (p, d, q) combinations up to a specified maximum order (typically p and q up to 5, d up to 2), fits each model, and ranks them by AIC. The best model is selected and used to generate the forecast.
The output shows you which model won (e.g., ARIMA(1,1,1) or ARIMA(2,1,0)), the coefficient estimates, the AIC scores of the top candidates so you can see how close the competition was, the forecast with confidence bands, and the residual diagnostics.
Pay attention to the residual diagnostics, which show the ACF of the model residuals. If the best model is well-specified, the residuals should look like white noise; no significant autocorrelation at any lag. If the residual ACF still shows significant spikes, the model has not fully captured the series and the forecast should be treated with additional skepticism.
Compare the Auto-ARIMA selection to what you would have chosen manually using the ACF and PACF plots from the autocorrelation tool. They should usually agree, but when they differ it is informative.
The Math Behind It
Auto-ARIMA selects models by minimizing AIC, defined as:
Where k is the number of estimated parameters and log(L) is the log-likelihood of the model fit. AIC rewards goodness of fit but penalizes complexity; adding more parameters only improves the score if the improvement in fit outweighs the complexity penalty.
BIC applies a stronger penalty for complexity:
BIC = k × log(n) − 2 × log(L)
Where n is the number of observations. BIC tends to select simpler models than AIC, particularly when n is large.
The search over the model grid is typically done using a stepwise algorithm that starts from a simple baseline model and adds or removes terms based on whether each change improves the information criterion. Full grid search is also available but is slower for large grids.
When to Use It and When Not To
Auto-ARIMA is the right starting point when you want a well-specified time series model quickly without manually working through ACF/PACF diagnostic plots. It is also a useful sanity check on a model you have already specified manually; if the automated search arrives at the same model, you can be more confident in your choice.
The limitation is that Auto-ARIMA optimizes for statistical fit on the training data, not necessarily for forecasting accuracy out of sample. A model with the best AIC is not guaranteed to have the best forecast; it is the best description of the in-sample data within the ARIMA family of models.
Also worth knowing; if the series has seasonal patterns (daily, weekly, monthly cycles), standard ARIMA will not capture them well. Seasonal ARIMA (SARIMA) handles this case and can be selected in the tool by specifying a seasonal period.
Try It
Go to fatnarwhal.com/auto-arima and run it on a series you have already explored with the basic ARIMA tool. Compare the model selection; does Auto-ARIMA agree with what you would have chosen? Look at the AIC table and see how close the runner-up models are. A large gap means the winning model is clearly better; a small gap means several models fit the data similarly and the choice is not critical.
Let the algorithm do the search. Spend your time on the interpretation.