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Cumulative Adjusted Value
This study calculates and displays a Cumulative Adjusted Value of the data specified by the Input Data Input.
Let \(X\) be a random variable denoting the Input Data Input, and let \(X_t\) be the value of the Input Data at Index \(t\). Let the Input Long Term Smoothing Length be denoted as \(n\). Then we denote the Adjusted Value for the given Inputs at Index \(t\) as \(AdjVal_t(X,n)\), and we compute it for \(t \geq 0\) using an Exponential Moving Average as follows.
\(AdjVal_t(X,n) = X_t - EMA_t(X,n)\)Note: The internal calculations performed in the Exponential Moving Average calculation are used in the calculation of \(AdjVal_t(X,n)\). Consequently, there is no delay of \(n\) units either in this calculation or in the subsequent calculation of the Cumulative Adjusted Value.
We denote the Cumulative Adjusted Value for the given Inputs at Index \(t\) as \(AdjCumVal_t(X,n)\), and we compute it with the following recursion relation.
\(CumAdjVal_0(X,n) = AdjVal_0(X,n)\)\(CumAdjVal_t(X,n) = CumAdjVal_{t - 1}(X,n) + AdjVal_t(X,n)\)
For some background as to why this study was developed, refer to Market Statistics Calculations Compared to Other Data Services.
Inputs
- Input Data
- Long Term Smoothing Length: In the case of when using this study on an Intraday chart of the TICK market statistic with 1 minute bars and where the Session Times are set to a 6.5 hour time range (standard US stock market open time), then set this to 7800 to be equivalent to a 20 day average. Reference: Cumulative Line for the Adjusted NYSE TICK
Spreadsheet
The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.
Open it through File >> Open Spreadsheet.
*Last modified Monday, 26th September, 2022.