- #1

#### member 428835

The autocorrelation coefficient ##\rho## is defined as $$\rho_k \equiv \frac{\sum_{t=k+1}^T (x_t - \bar x)(x_{t-k} - \bar x)}{\sum_{t=1}^T(x_t-\bar x)^2}$$

Now suppose we calculate ##\rho## through ##T##, but are then given a new data at time ##T + \Delta t##. Is there a way to approximate the new autocorrelation without recalculating from scratch? Obviously if we use the definition we'd have to recalculate the mean ##\bar x## and therefore the entire computation.