Quant Methodology
Evaluation & Metrics
OptiCampus-X isn't a black box. Our systems are built on verifiable statistical models and rigorous mathematical optimization.
Seasonal ARIMA
Time-series demand prediction for electricity and water.
// ARIMA(p,d,q)
$$\Phi_P(B^s)\phi_p(B)(1-B)^d(1-B^s)^D Y_t = \Theta_Q(B^s)\theta_q(B)\epsilon_t$$
We decompose VIT-AP usage into Trend ($T_t$), Seasonality ($S_t$), and Residual ($R_t$). This allows the system to anticipate high-load periods like exam weeks or hostel peak hours.
Accuracy Metrics
How we measure forecasting success.
RMSE$$RMSE = \sqrt{\frac{1}{n} \sum_{t=1}^{n} (y_t - \hat{y}_t)^2}$$
MAPE$$MAPE = \frac{100\%}{n} \sum_{t=1}^{n} \left| \frac{y_t - \hat{y}_t}{y_t} \right|$$