1. **Problem Statement:** We are given a piecewise function $$\Psi(t)$$ defined as: $$\Psi(t) = \begin{cases} 1, & \text{if } \left( \frac{CVD_t - CVD_{t-x}}{\left| \left( \frac{P_t - P_{t-x}}{P_{t-x}} \right) \cdot 100 \right| + \epsilon} \geq S_{min} \right) \land (\Delta CVD_t \geq \Phi_{min}) \land (\alpha_x > 0) \land (\Delta P_x < \Theta_{max}) \\ 0, & \text{otherwise} \end{cases}$$ 2. **Explanation of the formula:** - The function $$\Psi(t)$$ outputs 1 if all the following conditions are true: - The ratio $$\frac{CVD_t - CVD_{t-x}}{\left| \left( \frac{P_t - P_{t-x}}{P_{t-x}} \right) \cdot 100 \right| + \epsilon}$$ is greater than or equal to $$S_{min}$$. - The change in $$CVD$$ over time $$\Delta CVD_t$$ is at least $$\Phi_{min}$$. - The parameter $$\alpha_x$$ is positive. - The change in price $$\Delta P_x$$ is less than $$\Theta_{max}$$. - Otherwise, $$\Psi(t) = 0$$. 3. **Important notes:** - $$CVD_t$$ and $$CVD_{t-x}$$ represent cumulative volume delta at times $$t$$ and $$t-x$$. - $$P_t$$ and $$P_{t-x}$$ are prices at times $$t$$ and $$t-x$$. - $$\epsilon$$ is a small positive number to avoid division by zero. - The absolute value in the denominator ensures the ratio is well-defined. 4. **Intermediate work:** - The ratio inside the condition can be rewritten as: $$\frac{CVD_t - CVD_{t-x}}{\left| \frac{P_t - P_{t-x}}{P_{t-x}} \cdot 100 \right| + \epsilon} = \frac{\Delta CVD_t}{|\text{percentage price change}| + \epsilon}$$ - This ratio compares the change in cumulative volume delta to the adjusted percentage price change. 5. **Interpretation:** - If the volume change relative to price change is sufficiently large (above $$S_{min}$$), and other conditions on $$\Delta CVD_t$$, $$\alpha_x$$, and $$\Delta P_x$$ hold, then $$\Psi(t) = 1$$. - Otherwise, $$\Psi(t) = 0$$. This function can be used as a signal indicator in trading or data analysis contexts.