Technical Studies Reference


Inertia 2

This study calculates and displays the Inertia 2 study for the Price Data.

Let \(C\) be a random variable denoting the Close Price, and let the Standard Deviation Length, Relative Volatility Index Length, and Linear Regression Length Inputs be denoted as \(n_\sigma\), \(n_{RVIX}\), and \(n_{LR}\), respectively. We denote the Relative Volatility Index Up and Relative Volatility Index Down at Index \(t\) as \(RVIX^{(U)}_t(n_\sigma)\) and \(RVIX^{(D)}_t(n_\sigma)\), respectively, and we compute them in terms of a Standard Deviation for \(t \geq \max\{n_\sigma, n_{RVIX}, n_{LR}\}\) as follows.

\(\displaystyle{RVIX^{(U)}_t(n_\sigma) = \left\{ \begin{matrix} \sigma_t(C,n_\sigma) & C_t > C_{t - 1} \\ 0 & C_t \leq C_{t - 1} \end{matrix}\right .}\)

\(\displaystyle{RVIX^{(D)}_t(n_\sigma) = \left\{ \begin{matrix} 0 & C_t > C_{t - 1} \\ \sigma_t(C,n_\sigma) & C_t \leq C_{t - 1} \end{matrix}\right .}\)

Next we compute the Smoothed Relative Volatility Index Up and Smoothed Relative Volatility Index Down. The values of these at Index \(t\) are denoted as \(\overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX})\) and \(\overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX})\), respectively. These both have the value \(0\) for \(t < \max\{n_\sigma, n_{RVIX}, n_{LR}\}\). We compute them for \(t \geq \max\{n_\sigma, n_{RVIX}, n_{LR}\}\) as follows.

\(\displaystyle{\overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX}) = \frac{\overline{RVIX}^{(U)}_{t - 1}(n_\sigma,n_{RVIX})\cdot(n_{RVIX} - 1) + RVIX^{(U)}_t(n_\sigma)}{n_{RVIX}}}\)

\(\displaystyle{\overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX}) = \frac{\overline{RVIX}^{(D)}_{t - 1}(n_\sigma,n_{RVIX})\cdot(n_{RVIX} - 1) + RVIX^{(D)}_t(n_\sigma)}{n_{RVIX}}}\)

We denote the Relative Volatility Index at Index \(t\) as \(RVIX_t(n_\sigma,n_{RVIX})\), and we compute it for \(t \geq \max\{n_\sigma, n_{RVIX}, n_{LR}\}\) as follows.

\(\displaystyle{RVIX_t(n_\sigma,n_{RVIX}) = \left\{ \begin{matrix} 100\cdot\frac{\overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX})}{\overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX}) + \overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX})} & \overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX}) + \overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX}) \neq 0 \\ 0 & \overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX}) + \overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX}) = 0 \end{matrix}\right .}\)

Finally, we denote Inertia 2 at Index \(t\) as \(Inertia^{(2)}_t(n_\sigma,n_{RVIX},n_{LR})\). It is a Moving Linear Regression of the Relative Volatility Index, and we compute it for \(t \geq \max\{n_\sigma,n_{RVIX},n_{LR}\}\) as follows.

\(Inertia^{(2)}_t(n_\sigma,n_{RVIX},n_{LR}) = MLR_t(RVIX(n_\sigma,n_{RVIX}),n_{LR})\)

Inputs

Spreadsheet

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Inertia_2.288.scss


*Last modified Thursday, 05th April, 2018.