estimateAccumulatedVolatilityCI {BSS} | R Documentation |

## Estimate confidence interval for the accumulated volatility processes

### Description

`estimateAccumulatedVolatility`

estimates a confidence interval for 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.

### Usage

```
estimateAccumulatedVolatilityCI(
Y,
n,
p,
method = "nonparametric",
kernel = "gamma",
confidence_level
)
```

### 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 |

`kernel` |
text string representing the choice of kernel when fitting the model to estimate
the scale factor parametrically. Options are |

`confidence_level` |
the required level for the confidence interval, as a probability between 0 and 1. |

### Value

The function returns a list of two vectors of the same length as `Y`

which are the estimates for the
lower and upper values for the confidence interval. 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

```
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')
#'
```

*BSS*version 0.1.0 Index]