How do you choose between parametric and non-parametric time series models?

Choosing between parametric and non-parametric time series models depends on the data’s characteristics, the assumptions you’re willing to make, and the problem’s goals. Parametric models require predefined assumptions about the data’s distribution and structure, while non-parametric models avoid strict assumptions, relying instead on data-driven patterns. The decision often hinges on factors like data complexity, interpretability needs, and available computational resources.

Parametric models (e.g., ARIMA, SARIMA, or linear regression-based approaches) are ideal when the data aligns with known statistical assumptions. For example, ARIMA assumes stationarity (constant mean and variance over time) and uses parameters like autoregressive (AR) and moving average (MA) terms to model trends. These models are efficient with small datasets, computationally lightweight, and produce interpretable results. For instance, if you’re forecasting monthly sales with a clear seasonal pattern, SARIMA can explicitly model seasonality by extending ARIMA with seasonal differencing and coefficients. However, parametric models struggle with nonlinear relationships or complex patterns. If your data has erratic spikes (e.g., cryptocurrency prices) or irregular seasonality, forcing a parametric structure might lead to poor performance.

Non-parametric models (e.g., Gaussian Processes, decision trees, or neural networks) excel when the data’s underlying patterns are unclear or highly nonlinear. Methods like Random Forests or Long Short-Term Memory (LSTM) networks adapt to complex interactions without requiring explicit formulas. For example, LSTMs can capture long-term dependencies in sequences, making them useful for tasks like energy demand forecasting where weather, holidays, and economic factors interact unpredictably. Non-parametric approaches often require larger datasets to avoid overfitting and are computationally intensive. A downside is reduced interpretability: while a Gaussian Process provides uncertainty estimates, it’s harder to explain than an ARIMA model’s coefficients. These models are better suited for scenarios where accuracy trumps transparency, such as anomaly detection in high-frequency sensor data.

When deciding, consider your data size, interpretability requirements, and deployment constraints. If you have limited data and need explainability (e.g., business planning where stakeholders want to understand drivers), parametric models are preferable. For large, noisy datasets where flexibility matters (e.g., real-time stock price prediction), non-parametric methods may perform better. Also, evaluate computational costs: retraining a neural network daily might be impractical in resource-constrained environments, whereas updating an ARIMA model is simpler. Always validate with metrics like AIC (for parametric) or cross-validation error (for non-parametric) to compare performance objectively.