Class definition for the fBM model.

Class definition for the fBM model.

Details

Fractional Brownian motion X_t is the only (zero-mean) continuous stationary increments (CSI) Gaussian process having mean square displacement (MSD) function given by the power law

E[(X_t-X_0)^2] = t^alpha,

with subdiffusion exponent 0 < alpha < 2. The resulting MSD as a function of alpha is what gets passed to the csi_model base class to construct the fbm_model derived class.

Super class

subdiff::csi_model -> fbm_model

Public fields

phi_names

Kernel parameter names. In this case, the character string alpha. See csi_model.

Methods

Public methods

• fbm_model$acf()

• fbm_model$trans()

• fbm_model$itrans()

• fbm_model$get_subdiff()

• fbm_model$clone()

Inherited methods

• subdiff::csi_model$drift()
• subdiff::csi_model$fisher()
• subdiff::csi_model$fit()
• subdiff::csi_model$get_omega()
• subdiff::csi_model$get_vcov()
• subdiff::csi_model$initialize()
• subdiff::csi_model$itrans_full()
• subdiff::csi_model$loglik()
• subdiff::csi_model$msd()
• subdiff::csi_model$nlp()
• subdiff::csi_model$nu_hat()
• subdiff::csi_model$resid()
• subdiff::csi_model$sim()
• subdiff::csi_model$trans_full()

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Method acf()

Increment autocorrelation function.

Usage

fbm_model$acf(phi, dt, N)

Arguments

phi, dt, N

See csi_model.

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Method trans()

Transform kernel parameters from regular to computational basis.

Usage

fbm_model$trans(phi)

Arguments

phi

See csi_model.

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Method itrans()

Transform kernel parameters from computational to regular basis.

Usage

fbm_model$itrans(psi)

Arguments

psi

See csi_model.

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Method get_subdiff()

Transform parameters from computational basis to subdiffusion parameters.

Usage

fbm_model$get_subdiff(omega)

Arguments

omega

See csi_model.

Returns

Vector with named elements alpha and logD.

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Method clone()

The objects of this class are cloneable with this method.

Usage

fbm_model$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# simulate data from the fbm model
alpha <- .8

dt <- 1/60
N <- 1800
ndim <- 2

Xt <- csi_sim(drift = matrix(0, N-1, ndim),
              acf = fbm_acf(alpha, dt, N-1),
              Sigma = diag(ndim),
              X0 = rep(0, ndim))


# create fbm model object
model <- fbm_model$new(Xt = Xt, dt = dt, drift = "linear")

# evaluate loglikelihood
model$loglik(phi = c(alpha = alpha),
             mu = rep(0, ndim),
             Sigma = diag(ndim))
#> [1] 859.9225