ARMA(Autoregressive Moving Average) Model -DeepALGO-

📊 ARMA Model Indicator

This script is a custom indicator based on the ARMA (Autoregressive Moving Average) model, one of the fundamental and widely used models in time series analysis.
While ARMA is typically employed in statistical software, this implementation makes it accessible directly on TradingView, allowing traders to visualize and apply the dynamics of ARMA in financial markets with ease.

🧩 What is the ARMA Model?

The ARMA model explains time series data by combining two components: Autoregression (AR) and Moving Average (MA).

AR (Autoregression) component
Captures the dependence of current values on past values, modeling the inherent autocorrelation of the series.

MA (Moving Average) component
Incorporates past forecast errors (residuals), smoothing out randomness and noise while improving predictive capability.

By combining these two aspects, ARMA models can capture both the underlying structure of the data and the random fluctuations, providing a more robust description of price behavior than simple averages alone.

⚙️ Design of This Script

In classical statistics, ARMA coefficients are estimated using the ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function). However, this process is often too complex for trading environments.

This script simplifies the approach:

The coefficients theta (θ) and epsilon (ε) are fixed, automatically derived from the chosen AR and MA periods.

This eliminates the need for statistical estimation, making the indicator easy to apply with simple parameter adjustments.

The goal is not academic rigor, but practical usability for traders.

🔧 Configurable Parameters

AR Period (p): Order of the autoregressive part.

MA Period (q): Order of the moving average part. Shorter periods yield faster responsiveness, while longer periods produce smoother outputs.

Offset: Shifts the line forward or backward for easier comparison.

Smoothing Period: Additional smoothing to reduce noise.

Source: Choose from Close, HL2, HLC3, High, or Low.

🎯 Advantages Compared to Traditional Moving Averages

Commonly used moving averages such as SMA (Simple Moving Average) and EMA (Exponential Moving Average) are intuitive but have limitations:

SMA applies equal weights to past data, which makes it slow to respond to new price changes.

EMA emphasizes recent data, providing faster response but often introducing more noise and reducing smoothness.

The ARMA-based approach provides two key advantages:

Balance of Responsiveness and Smoothness
AR terms capture autocorrelation while MA terms correct residuals, resulting in a smoother line that still reacts more quickly than SMA or EMA.

Flexible Adaptation
By adjusting the MA period (q), traders can fine-tune how closely the model follows price fluctuations—ranging from rapid short-term responses to stable long-term trend recognition.

📈 Practical Use Cases

The ARMA indicator can be applied in several practical ways:

Trend Direction Estimation
The slope and position of the ARMA line can provide a straightforward read of bullish or bearish market conditions.

Trend Reversal Identification
Changes in the ARMA line’s direction may signal early signs of a reversal, often with faster reaction compared to traditional moving averages.

Confirmation with Other Indicators
Combine ARMA with oscillators such as RSI or MACD to improve the reliability of signals.

Combination with Heikin-Ashi
Heikin-Ashi candles smooth out price action and highlight trend changes. When used together with ARMA, they can significantly enhance reversal detection. For example, if Heikin-Ashi indicates a potential reversal and the ARMA line simultaneously changes direction, the confluence provides a stronger and more reliable trading signal.

⚠️ Important Notes

Risk of Overfitting
Excessive optimization of AR or MA periods may lead to overfitting, where the indicator fits historical data well but fails to generalize to future market conditions. Keep parameter choices simple and consistent.

Weakness in Sideways Markets
ARMA works best in trending environments. In range-bound conditions, signals may become noisy or less reliable. Consider combining it with range-detection tools or volume analysis.

Not a Standalone System
This indicator should not be used in isolation for trading decisions. It is best employed as part of a broader analysis framework, combining multiple indicators and fundamental insights.

💡 Summary

This script brings the theoretical foundation of ARMA into a practical, chart-based tool for traders.
It is particularly valuable for those who find SMA too lagging or EMA too noisy, offering a more nuanced balance between responsiveness and smoothness.

By capturing both autocorrelation and residual structure, ARMA provides a deeper view of market dynamics.
Combined with tools such as Heikin-Ashi or oscillators, it can significantly enhance trend reversal detection and strategy reliability.