how about DX and ADXR?

The deep research logic is organized as follows: 

Okay, let's tackle the user's question about DX and ADXR. The user is interested in technical analysis, specifically in the context of TradingView, and wants to understand how DX and ADXR work. From the references provided, I need to extract the key points about these indicators.

First, I'll start by recalling what DX and ADXR are. From the references, DX is the Directional Movement Index, which measures the direction and strength of a trend. It's calculated using the difference between +DI and -DI, divided by their sum, then multiplied by 100. ADXR, on the other hand, is the Average Directional Movement Index Rating, which smoothens the ADX by averaging it with its value from a certain number of periods ago. 

The user is asking about how DX and ADXR work, so I need to explain their definitions, calculations, and how they're used in trading. I should also compare them to clarify their differences. 

Looking at the references, Number 1 explains DX as part of the Directional Movement System, which includes ADX. Number 5 mentions that ADXR is a smoothed version of ADX. Number 15 and 17 discuss ADXR's calculation as the average of ADX and its past value. 

I should structure the answer by first defining each indicator, then explaining their calculations, followed by their interpretations and uses. It's important to highlight how DX and ADXR differ in terms of their sensitivity and lag. For example, DX is more sensitive to short-term changes, while ADXR is smoother and less reactive to noise. 

The user is interested in TradingView, so mentioning how these indicators are typically plotted there would be helpful. Also, since the user focuses on technical analysis, including how DX and ADXR can be used together for trend confirmation would add value. 

I need to ensure that the answer is clear and concise, using the provided references to back up each point. Including examples or key thresholds (like ADX above 25 indicating a strong trend) would make the explanation more practical. 

Finally, I should wrap up with a conclusion that summarizes the main points and their relevance to the user's trading strategy, especially in the context of short-term trading and trend analysis.

### Conclusion 🎯
The **Directional Movement Index (DX)** and **Average Directional Movement Index Rating (ADXR)** are critical components of the Directional Movement System (DMS) developed by J. Welles Wilder. DX measures the **direction and strength of a trend** using the spread between the Positive Directional Indicator (+DI) and Negative Directional Indicator (-DI), while ADXR smoothens the ADX to provide a **lagging, more stable trend strength signal**. Together, they help traders identify **trend strength, direction, and potential reversals**.

---

### Analysis 📊

#### 1. **Directional Movement Index (DX)**
- **Definition**: DX is calculated as the ratio of the difference between +DI and -DI to their sum, multiplied by 100 .
\[
DX = \left( \frac{|+DI - -DI|}{+DI + -DI} \right) \times 100
\]
- **Interpretation**:
- **Range**: 0–100.
- **Thresholds**:
- **DX > 25**: Strong trend (bullish if +DI > -DI, bearish if -DI > +DI).
- **DX < 20**: Weak trend or consolidation .
- **Use Case**: Identifies **immediate trend direction** and strength.

| Metric | Description |
|--------------|-----------------------------------------------------------------------------|
| +DI | Measures upward price momentum (bullish). |
| -DI | Measures downward price momentum (bearish). |
| DX | Combines +DI and -DI to show trend direction and strength. |

---

#### 2. **Average Directional Movement Index Rating (ADXR)**
- **Definition**: ADXR is the average of the current ADX and its value from a specified number of periods ago .
\[
ADXR = \frac{ADX + ADX_{n}}{2}
\]
(where \(n\) is the lookback period, typically 14).
- **Interpretation**:
- **Smoothing**: ADXR reduces noise in ADX signals, making it less reactive to short-term fluctuations .
- **Thresholds**:
- **ADXR > 25**: Strong trend confirmation.
- **ADXR < 20**: Weak trend or range-bound market .
- **Use Case**: Confirms **long-term trend strength** and helps avoid false signals.

| Metric | Description |
|--------------|-----------------------------------------------------------------------------|
| ADX | Smoothed DX, measures trend strength (0–100). |
| ADXR | Smoothed ADX, provides lagging confirmation of trend changes. |

---

#### 3. **Key Differences Between DX and ADXR**
| Feature | DX | ADXR |
|--------------|--------------------------------------------------------------------|-------------------------------------------------------------------|
| **Calculation** | Direct ratio of +DI and -DI spread. | Average of ADX and its past value. |
| **Sensitivity** | High (reacts quickly to price changes). | Low (smoother, less reactive to noise). |
| **Lag** | Minimal (real-time trend direction). | High (lagging, confirms trend changes after they occur). |
| **Use Case** | Identify immediate trend direction and strength. | Confirm long-term trend strength and avoid false signals. |

---

### Practical Implications 🚨
- **For Traders**: Use DX to **enter trades** based on immediate trend direction and ADXR to **confirm trend strength** before scaling positions.
- **For Analysts**: Combine DX and ADXR with other indicators (e.g., RSI, Bollinger Bands) to refine entry/exit strategies.
- **For Investors**: Monitor ADXR > 25 as a **buy/sell signal** for trending assets, especially in volatile markets like cryptocurrencies .

---

### Final Takeaway 🎯
DX and ADXR are **complementary tools** for trend analysis. DX provides **real-time directionality**, while ADXR offers **lagging confirmation** of trend strength. Together, they help traders balance **speed** (DX) and **accuracy** (ADXR) in their decision-making.