# Estimate accumulated volatility processes `estimateAccumulatedVolatility` estimates the pth power accumulated volatility process for a Brownian semistationary process, using either parametric methods of model fitting first, or using a non-parametric estimator for the scale factor. ```r estimateAccumulatedVolatility( Y, n, p = 2, method = "nonparametric", kernel = "gamma" ) ``` ## Arguments - `Y`: a vector of observations of a BSS process. - `n`: positive integer indicating the number of observations per unit of time. - `p`: the power to evaluate the accumulated power volatility process for. Defaults to 2, in order to estimate the accumulated squared volatility process. - `method`: text string representing the method used to estimate the accumulated volatility. Options are `'acf'`, `'cof'` or `nonparametric`. If `'acf'` is selected, model parameters are fit to the data `Y` using least squares on the autocorrelation function and these parameters are used to estimate the scale factor. If `'cof'` is selected, only the smoothness parameter `alpha` is estimated using the change of frequency method, and then put into an asymptotic expression for the scale factor in the calculation. If `'nonparametric'` is selected then the non-parametric estimator for the scale factor will be used in the calculation. Defaults to `'nonparametric'`. - `kernel`: text string representing the choice of kernel when fitting the model to estimate the scale factor parametrically. Options are `'gamma'` and `'power'`. Defaults to `'gamma'`. ## Returns The function returns a vector of the same length as `Y` which is the estimate for the accumulated volatility process, observed from time 0 to T, at intervals of T/n. Note that the values have been divided by m_p in the output, so that the estimation is of the integral alone. If the non-parametric estimator for tau_n is used then the values will be scaled by the expectation of the squared volatility, as per the theory. ## Examples ```r N <- 10000 n <- 100 T <- 1.0 theta <- 0.5 beta <- 0.125 kappa <- 3 alpha <- -0.2 lambda <- 1.0 vol <- exponentiatedOrnsteinUhlenbeck(N, n, T, theta, beta) bss_simulation <- gammaKernelBSS(N, n, T, kappa, alpha, lambda, sigma = vol) y <- bss_simulation$bss estimateAccumulatedVolatility(y, n, p = 2, method = 'nonparametric', kernel = 'gamma') #' ```

estimateAccumulatedVolatility function