Log Regression Oscillator

18小时前

The Log Regression Oscillator transforms the logarithmic regression curves into an easy-to-interpret oscillator that displays potential cycle tops/bottoms.

🔶 USAGE


Calculating the logarithmic regression of long-term swings can help show future tops/bottoms. The relationship between previous swing points is calculated and projected further. The calculated levels are directly associated with swing points, which means every swing point will change the calculation. Importantly, all levels will be updated through all bars when a new swing is detected.


The "Log Regression Oscillator" transforms the calculated levels, where the top level is regarded as 100 and the bottom level as 0. The price values are displayed in between and calculated as a ratio between the top and bottom, resulting in a clear view of where the price is situated.

The main picture contains the Logarithmic Regression Alternative on the chart to compare with this published script.


Included are the levels 30 and 70. In the example of Bitcoin, previous cycles showed a similar pattern: the bullish parabolic was halfway when the oscillator passed the 30-level, and the top was very near when passing the 70-level.



🔹 Proactive

A "Proactive" option is included, which ensures immediate calculations of tentative unconfirmed swings.


Instead of waiting 300 bars for confirmation, the "Proactive" mode will display a gray-white dot (not confirmed swing) and add the unconfirmed Swing value to the calculation.

The above example shows that the "Calculated Values" of the potential future top and bottom are adjusted, including the provisional swing.


When the swing is confirmed, the calculations are again adjusted, showing a red dot (confirmed top swing) or a green dot (confirmed bottom swing).

🔹 Dashboard


When less than two swings are available (top/bottom), this will be shown in the dashboard.

The user can lower the "Threshold" value or switch to a lower timeframe.

🔹 Notes

Logarithmic regression is typically used to model situations where growth or decay accelerates rapidly at first and then slows over time, meaning some symbols/tickers will fit better than others.

Since the logarithmic regression depends on swing values, each new value will change the calculation. A well-fitted model could not fit anymore in the future.


Users have to check the validity of swings; for example, if the direction of swings is downwards, then the dataset is not fitted for logarithmic regression.


In the example above, the "Threshold" is lowered. However, the calculated levels are unreliable due to the swings, which do not fit the model well.


Here, the combination of downward bottom swings and price accelerates slower at first and faster recently, resulting in a non-fit for the logarithmic regression model.

Note the price value (white line) is bound to a limit of 150 (upwards) and -150 (down)

In short, logarithmic regression is best used when there are enough tops/bottoms, and all tops are around 100, and all bottoms around 0.

Also, note that this indicator has been developed for a daily (or higher) timeframe chart.

🔶 DETAILS

In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (arrays) and returns a single number, the sum of the products of the corresponding entries of the two sequences of numbers.

The usual way is to loop through both arrays and sum the products.

In this case, the two arrays are transformed into a matrix, wherein in one matrix, a single column is filled with the first array values, and in the second matrix, a single row is filled with the second array values.

After this, the function matrix.mult() returns a new matrix resulting from the product between the matrices m1 and m2.

Then, the matrix.eigenvalues() function transforms this matrix into an array, where the array.sum() function finally returns the sum of the array's elements, which is the dot product.

Pine Script®

🔶 SETTINGS

• Threshold: Period used for the swing detection, with higher values returning longer-term Swing Levels.
  
• Proactive: Tentative Swings are included with this setting enabled.
  
• Style: Color Settings
  
• Dashboard: Toggle, "Location" and "Text Size"
  

18小时前

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