# Technical Studies Reference

### Chikou Span

Calculates and displays a Chikou Span (aka Lagging Span) of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Input Chikou Span Length be denoted as $$n$$. Let $$i$$ denote a value of the Index between $$0$$ and the current Index $$t$$. Then we denote the Chikou Span at Index $$i$$ for the given Inputs as $$CS_i(X,n)$$, and we compute it as follows.

$$\displaystyle{CS_{i - n}(X,n) = \left\{ \begin{matrix} 0 & 0 \leq i < n \\ X_i & n \leq i \leq t \end{matrix}\right .}$$

This is equivalent to the following, more intuitive, formula.

$$\displaystyle{CS_i(X,n) = \left\{ \begin{matrix} X_{i + n} & 0 \leq i \leq t - n \\ 0 & t - n < i \leq t \end{matrix}\right .}$$