The Accumulative Swing Index created by Welles Wilder attempts to find the swing line within the bar. Originally created to apply to daily bars, as there is a market or user defined value of the maximum price change that can occur during the trading session. Using the study on intra-day bar data will require the user to specify a limit value for the given bar interval.
\[ASI_{t} = ASI_{t-1} + SI_{t}\]
where\(SI_{t}\) is the current bar's swing index calculated by the formula:
\[SI_{t} = 50 \times \left ( \frac{Close_{t} - Close_{t-1}+0.5\times(Close_{t}-Open_{t})+0.25 \times (Close_{t-1}-Open_{t-1})}{R} \right ) \times \frac{K}{T}\]
where
\[K = max\left ( High_{t} - Close_{t-1}\;,\;Close_{t-1} - Low_{t} \right )\]
\(T\) is a user defined value which means the maximum price change during a trading session.
\(R\) is a value calculated on the base of the relationship between current close price and previous high and low prices. The formula is:
\[R = TR - 0.5 \times ER + 0.25 \times SH\]
where
\[TR = max(High_{t} - Close_{t-1} , Close_{t-1} - Low_{t} , High_{t} - Low_{t})\]
\[ER = \left\{\begin{matrix} High_{t} - Close_{t-1} & if Close_{t-1} > High_{t} \\ 0 & if Low_{t} \leq Close_{t-1} \leq High_{t} \\ Close_{t-1} - Low_{t} & if Close_{t-1} < Low_{t} \end{matrix}\right.\]
\[SH = Close_{t-1} - Open_{t-1}\]