What are the limitations of ARIMA models?

ARIMA (AutoRegressive Integrated Moving Average) models are widely used for time series forecasting but have several key limitations. First, ARIMA requires the time series to be stationary, meaning its statistical properties (like mean and variance) must remain constant over time. If the data has trends, seasonality, or other non-stationary patterns, it must be manually transformed—often through differencing or logging—before modeling. For example, stock price data often contains trends and volatility clusters that ARIMA struggles with, requiring multiple rounds of differencing to stabilize the mean. Over-differencing can strip meaningful patterns from the data, leading to poor forecasts. This reliance on manual preprocessing makes ARIMA inflexible for datasets with complex non-stationary behavior.

Second, ARIMA assumes linear relationships between past and future values. Real-world data often includes nonlinear interactions (e.g., sudden market crashes or holiday sales spikes) that linear models can’t capture. For instance, a retailer’s sales might surge nonlinearly during Black Friday due to external factors like promotions, which ARIMA cannot model unless explicitly added as covariates. While extensions like SARIMA (Seasonal ARIMA) handle seasonality, they still lack native support for external variables or nonlinear effects. This makes ARIMA less adaptable compared to machine learning models (e.g., Random Forests or LSTMs) that can automatically learn complex patterns and incorporate multiple input features.

Finally, ARIMA’s parameter selection process is cumbersome. Developers must manually choose the order of autoregressive §, differencing (d), and moving average (q) terms using tools like ACF/PACF plots, which can be ambiguous. For example, if autocorrelation decays slowly in an ACF plot, selecting the right “q” value becomes subjective. While tools like auto_arima automate parameter tuning, they may not always converge to the optimal model. Additionally, ARIMA scales poorly with large datasets or high-frequency data (e.g., minute-level sensor readings) due to its computational complexity. Retraining the model for real-time updates is inefficient, making it impractical for dynamic environments like algorithmic trading, where low-latency predictions are critical. These limitations drive many developers toward hybrid or alternative models for complex forecasting tasks.