TASC's September 2022 edition of Traders' Tips includes an article by Vitali Apirine titled "The Linear Regression-Adjusted Exponential Moving Average". This script implements the titular indicator presented in this article.
█ CONCEPT
The Linear Regression-Adjusted Exponential Moving Average (LRAdj EMA) is a new tool that combines a linear regression indicator with exponential moving averages. First, the indicator accounts for the linear regression deviation, that is, the distance between the price and the linear regression indicator. Subsequently, an exponential moving average (EMA) smooths the price data and and provides an indication of the current direction.
As part of a trading system, LRAdj EMA can be used in conjunction with an exponential moving average of the same length to identify the overall trend. Alternatively, using LRAdj EMAs of different lengths together can help identify turning points.
█ CALCULATION
The script uses the following input parameters:
EMA Length
LR Lookback Period
Multiplier
The calculation of LRAdj EMA is carried out as follows:
where MLTP is a weighting multiplier defined as MLTP = 2 ⁄ (EMA Length + 1), and LRAdj is the linear regression adjustment (LRAdj) multiplier: LRAdj = (Abs(Current LR Dist)−Abs(Minimum LR Dist)) ⁄ (Abs(Maximum LR Dist)−Abs(Minimum LR Dist))
When calculating the LRAdj multiplier, the absolute values of the following quantities are used: Current LR Dist is the distance between the current close and the linear regression indicator with a length determined by the LR Lookback Period parameter, Minimum LR Dist is the minimum distance between the close and the linear regression indicator for the LR lookback period, Maximum LR Dist is the maximum distance between the close and the linear regression indicator for the LR lookback period.