Bitcoin Expectile Model [LuxAlgo]The Bitcoin Expectile Model is a novel approach to forecasting Bitcoin, inspired by the popular Bitcoin Quantile Model by PlanC. By fitting multiple Expectile regressions to the price, we highlight zones of corrections or accumulations throughout the Bitcoin price evolution.
While we strongly recommend using this model with the Bitcoin All Time History Index INDEX:BTCUSD on the 3 days or weekly timeframe using a logarithmic scale, this model can be applied to any asset using the daily timeframe or superior.
Please note that here on TradingView, this model was solely designed to be used on the Bitcoin 1W chart, however, it can be experimented on other assets or timeframes if of interest.
🔶 USAGE
The Bitcoin Expectile Model can be applied similarly to models used for Bitcoin, highlighting lower areas of possible accumulation (support) and higher areas that allow for the anticipation of potential corrections (resistance).
By default, this model fits 7 individual Expectiles Log-Log Regressions to the price, each with their respective expectile ( tau ) values (here multiplied by 100 for the user's convenience). Higher tau values will return a fit closer to the higher highs made by the price of the asset, while lower ones will return fits closer to the lower prices observed over time.
Each zone is color-coded and has a specific interpretation. The green zone is a buy zone for long-term investing, purple is an anomaly zone for market bottoms that over-extend, while red is considered the distribution zone.
The fits can be extrapolated, helping to chart a course for the possible evolution of Bitcoin prices. Users can select the end of the forecast as a date using the "Forecast End" setting.
While the model is made for Bitcoin using a log scale, other assets showing a tendency to have a trend evolving in a single direction can be used. See the chart above on QQQ weekly using a linear scale as an example.
The Start Date can also allow fitting the model more locally, rather than over a large range of prices. This can be useful to identify potential shorter-term support/resistance areas.
🔶 DETAILS
🔹 On Quantile and Expectile Regressions
Quantile and Expectile regressions are similar; both return extremities that can be used to locate and predict prices where tops/bottoms could be more likely to occur.
The main difference lies in what we are trying to minimize, which, for Quantile regression, is commonly known as Quantile loss (or pinball loss), and for Expectile regression, simply Expectile loss.
You may refer to external material to go more in-depth about these loss functions; however, while they are similar and involve weighting specific prices more than others relative to our parameter tau, Quantile regression involves minimizing a weighted mean absolute error, while Expectile regression minimizes a weighted squared error.
The squared error here allows us to compute Expectile regression more easily compared to Quantile regression, using Iteratively reweighted least squares. For Quantile regression, a more elaborate method is needed.
In terms of comparison, Quantile regression is more robust, and easier to interpret, with quantiles being related to specific probabilities involving the underlying cumulative distribution function of the dataset; on the other expectiles are harder to interpret.
🔹 Trimming & Alterations
It is common to observe certain models ignoring very early Bitcoin price ranges. By default, we start our fit at the date 2010-07-16 to align with existing models.
By default, the model uses the number of time units (days, weeks...etc) elapsed since the beginning of history + 1 (to avoid NaN with log) as independent variable, however the Bitcoin All Time History Index INDEX:BTCUSD do not include the genesis block, as such users can correct for this by enabling the "Correct for Genesis block" setting, which will add the amount of missed bars from the Genesis block to the start oh the chart history.
🔶 SETTINGS
Start Date: Starting interval of the dataset used for the fit.
Correct for genesis block: When enabled, offset the X axis by the number of bars between the Bitcoin genesis block time and the chart starting time.
🔹 Expectiles
Toggle: Enable fit for the specified expectile. Disabling one fit will make the script faster to compute.
Expectile: Expectile (tau) value multiplied by 100 used for the fit. Higher values will produce fits that are located near price tops.
🔹 Forecast
Forecast End: Time at which the forecast stops.
🔹 Model Fit
Iterations Number: Number of iterations performed during the reweighted least squares process, with lower values leading to less accurate fits, while higher values will take more time to compute.
