1. Calculate the True Range, +DI, and –DI for each period: True Range is the greater of: Current High – Current Low Absolute value of Current High – Previous Close Absolute value of Current Low – Previous Close +DI IF Current High – Previous High > Previous Low – Current Low THEN +DI = the greater of Current High – Previous High OR 0    -DI IF Previous Low – Current Low > Current High – Previous High THEN –DI = the greater of Previous Low – Current Low OR 0 IF +DI AND -DI are both negative THEN both +DI and –DI = 0 IF +DI AND -DI are both positive AND +DI > -DI THEN +DI = Current High – Previous High AND –DI = 0 Else IF +DI < -DI THEN +DI = 0 AND –DI = Previous Low – Current Low
2. Smooth the True Range, +DI, and –DI using Wilder’s smoothing technique.
3. Divide the smoothed +DI by the smoothed True Range and multiply by 100 (this is the +DI that is plotted for the specified period).
4. Divide the smoothed –DI by the smooth True Range and multiply by 100 (this is the –DI that is plotted for the specified period).
5. Next calculate the Directional Movement Index (DX) which equals the (absolute value of the smoothed +DI – the smoothed –DI) /( the sum of the smoothed +DI and smoothed –DI )and multiply by 100.
6. Next calculate the Average Directional Index (ADX). The first value for ADX is an average of the DX over the specified period. The following values are smoothed by multiplying the previous ADX value by the specified period – 1, adding the current DX value, and dividing this total by the period specified.
7. Finally the Directional Movement Rating (ADXR) is calculated by the averaging the current ADX and the ADX value n-periods ago.

1. The DMI is mainly used to determine the direction and strength of market trends:
   3.1 Buy Signal: When +DI crosses above -DI, it is a buy signal, indicating the market is starting an uptrend.
   3.2 Sell Signal: When -DI crosses above +DI, it is a sell signal, indicating the market is starting a downtrend.
   3.3 Trend Strength: When the ADX is above 20 or 25, it indicates a strong trend, whether up or down. When ADX is below 20, it indicates a non-trending market.
   3.4 Trend Confirmation: When the ADX is rising, it indicates the current trend is strengthening. Conversely, when the ADX is falling, it indicates the current trend is weakening.

4.1 Multi-dimensional Analysis: The DMI not only identifies the market direction (through +DI and -DI) but also evaluates trend strength (through ADX). 
4.2 Wide Applicability: The DMI is suitable for various markets and time frames, including stocks, futures, and forex. 
4.3 Early Warning: By observing the crossover of +DI and -DI, investors can receive early buy or sell signals. 
4.4 Trend Confirmation: Through the ADX, investors can confirm the strength of the current trend, avoiding trading in non-trending markets and reducing risk.

The Rate of Change (ROC) is a commonly used tool in technical analysis to measure the speed of price changes over a specific period. It calculates the percentage change between the current price and the price from a number of periods ago to reflect the intensity and speed of price movements. The ROC is often used to identify price trends and to determine overbought or oversold conditions.

The formula for ROC can be expressed as: ROC = (Today's Closing Price - n-day ago Closing Price) / n-day ago Closing Price For example, if the closing price of Apple on May 23, 2022, was $143.11, and the closing price on May 5, 2022, was $156.54, then the 12-day ROC is -8.579, calculated as [($143.11 - $156.54) / $156.54] * 100.

The ROC is mainly used to determine price trends and overbought or oversold conditions: 3.1 Buy Signal: When the ROC rises from negative territory and crosses the zero line, it is a buy signal, indicating the price is starting to rise.
3.2 Sell Signal: When the ROC falls from positive territory and crosses the zero line, it is a sell signal, indicating the price is starting to fall.
3.3 Overbought Signal: When the ROC reaches a relatively high positive value, it indicates the price may be overbought and a pullback is likely.
3.4 Oversold Signal: When the ROC reaches a relatively low negative value, it indicates the price may be oversold and a rebound is likely.
3.5 Divergence Signal: When the price trend and the ROC trend diverge (e.g., the price makes a new high but the ROC does not), it is a signal of a potential price reversal.

4.1 High Sensitivity: The ROC is very sensitive to price changes and can quickly reflect the speed and intensity of price movements. 
4.2 Simple and Intuitive: The ROC is relatively simple to calculate and interpret, making it suitable for all types of investors. 
4.3 Trend Determination: Through the zero line crossover and divergence, the ROC can effectively determine price trends and potential reversal points. 
4.4 Multi-period Application: The ROC can be applied to different time periods, allowing investors to adjust the N value based on their needs for short-term or long-term analysis.