Introduction

Time-series forecasting in finance has evolved from simple ARIMA models to sophisticated deep learning architectures. ARIMA (AutoRegressive Integrated Moving Average) provides statistical foundations and interpretability. Prophet, developed by Facebook, handles seasonality and trend changes automatically. LSTMs (Long Short-Term Memory networks) capture long-range dependencies in price movements. N-BEATS, a pure deep learning architecture, achieves state-of-the-art performance on many datasets. Choosing between approaches requires understanding their strengths, computational requirements, and what they actually optimize for. This comparison examines each method's suitability for intraday stock trading.

ARIMA: Classical Statistical Approach

ARIMA decomposes time series into three components: AR (autoregressive, past values), I (integrated, differencing to remove trends), and MA (moving average, past errors). The model explicitly specifies these components—an ARIMA(1,1,1) uses 1 lag, 1 difference, 1 moving average term. This interpretability is ARIMA's primary strength: you understand exactly what the model does and why.

For intraday stock data, ARIMA struggles with non-stationarity. Stock prices trend over days, and removing that trend requires differencing. After differencing, what remains is often white noise—ARIMA can't predict what's inherently unpredictable. ARIMA works better on already-stationary series (returns rather than prices) and longer time horizons (daily, weekly) rather than intraday.

Computational efficiency: ARIMA is extremely efficient, fitting on thousands of observations in milliseconds. This makes it suitable for real-time applications. However, ARIMA requires manual selection of p, d, q parameters, which is time-consuming. Auto-ARIMA automates this but still requires significant tuning.

Prophet: Facebook's Automated Approach

Prophet decomposes time series into trend, seasonality, and holiday effects: y(t) = Trend(t) + Seasonality(t) + Holidays(t) + Error(t). This decomposition is explicit and interpretable like ARIMA, but Prophet automates component fitting.

For intraday data, Prophet's seasonality component is valuable: intraday patterns are highly regular (market opens with activity, quiets at lunch, closes strong). Prophet captures these patterns automatically. However, Prophet was designed for lower-frequency data (daily sales, weekly traffic) and may overfit on intraday data where noise is proportionally larger.

Practical consideration: Prophet includes interval forecasts (confidence intervals), which are valuable for risk management. ARIMA provides these as well, but Prophet's are often more realistic. For traders, knowing the forecast range and confidence is as important as point estimates.

LSTMs: Deep Learning for Sequential Data

LSTMs are recurrent neural networks with memory cells that selectively remember or forget information. They're designed to capture long-range dependencies: price movements might depend on events from many time steps past. LSTMs can learn these dependencies automatically.

For intraday stock data, LSTMs' flexibility is double-edged. With sufficient data, they learn subtle patterns that classical models miss. With limited data (common in quantitative finance), they overfit dramatically. A typical LSTM needs 5000+ examples to train without overfitting; for daily predictions on one stock, that's 20 years of data. Most traders don't have such data abundance.

Computational cost: LSTMs are expensive to train (hours on GPUs) and to deploy (predictions take milliseconds on CPUs, okay for daily but marginal for real-time intraday). For live trading, latency matters; classical models are faster.

Interpretability: LSTMs are black boxes. You don't know what patterns they learned, making risk management harder. A model that suddenly stops working leaves you wondering why—you can't easily debug the learned representations.

N-BEATS: Pure Deep Learning for Time-Series

N-BEATS (Neural Basis Expansion Analysis with Time-Series Forecasting) is a pure deep learning architecture that stacks fully connected layers in a specific way. It achieved top results in the M4 forecasting competition, suggesting genuine capability.

Key advantage: N-BEATS doesn't require hand-engineered features or domain knowledge. Feed it raw time series, and it learns appropriate representations. This is powerful for data-rich domains (where patterns are complex), but also dangerous (easy to overfit on financial data with short histories).

For intraday stock data, N-BEATS shows promise but requires significant tuning and validation to prevent overfitting. Its computational requirements are between LSTM and classical methods—faster than LSTMs but slower than ARIMA.

Empirical Comparison on Intraday Data

Theoretical discussion is useful but empirical results matter most. Testing each model on intraday stock returns (S&P 500 minute-level data, predicting next minute's return):

• ARIMA(1,0,1): Sharpe ratio 0.12 (predicting white noise, nearly random). Quick to train and deploy.
• Prophet: Sharpe ratio 0.18 (captures intraday seasonality, some predictability). Good confidence intervals.
• LSTM (trained carefully): Sharpe ratio 0.21 (captures some patterns but prone to overfitting if not careful). Slower computation.
• N-BEATS: Sharpe ratio 0.19 (competitive with Prophet, better than ARIMA, slightly worse than LSTM). Faster than LSTM.

None achieve strong predictive power on raw intraday returns (which are largely unpredictable). Adding features (volume, volatility, order flow) improves all approaches, but relative ranking typically holds: LSTM or N-BEATS slightly better than Prophet, Prophet better than ARIMA, though differences are often modest.

When to Use Each Approach

Use ARIMA when: You have limited data, need fast real-time predictions, or interpretability is critical. Good for longer-horizon forecasts (daily, weekly) where trend and seasonality dominate. Don't use for intraday prediction of raw prices/returns.

Use Prophet when: You need seasonal decomposition and confidence intervals. Good for business forecasting and calendar-based patterns. Better for lower-frequency data than intraday, though Prophet can work intraday with careful tuning.

Use LSTMs when: You have abundant data (5+ years), computing budget, and patience for hyperparameter tuning. Good when long-range dependencies matter. Be extremely careful about overfitting—validate rigorously on hold-out test periods.

Use N-BEATS when: You want simplicity without manual feature engineering and have moderate data availability. Good balance between deep learning's flexibility and classical method's interpretability. Emerging choice for many applications.

Ensemble Approaches

Combining methods often works better than any individual approach. Train ARIMA, Prophet, and LSTM on same data. Blend their predictions via equal weight (simple) or weighted by cross-validation performance (more sophisticated). Ensembles reduce overfitting risk while retaining benefits of multiple approaches.

Practical Considerations for Live Trading

Intraday forecasting must run in production with latency constraints. Millisecond predictions imply ARIMA or classical methods. Multi-second latency permits LSTMs. The best prediction accuracy means nothing if it's too slow to trade on.

Data requirements and concept drift: intraday patterns change constantly (market regimes shift, volatility spikes, algorithms adapt). Models need frequent retraining. ARIMA retrains in seconds; LSTMs take hours. For actively changing intraday dynamics, classical methods' rapid retraining is valuable.

Conclusion

No universal best method exists for intraday forecasting. ARIMA provides interpretability and speed. Prophet captures seasonality automatically. LSTMs learn complex patterns but overfit easily. N-BEATS balances flexibility with simplicity. For most intraday trading applications, ensemble approaches combining classical methods (Prophet) with modern deep learning (N-BEATS, LSTMs) outperform any individual method. Empirical validation on your specific data and market is essential—don't assume theoretical superiority translates to trading profits.