Package 'geoFKF'

Computing coefficients Fourier.

Description

This function computes minimum square estimates for Fourier coefficients.

Usage

coef_fourier(f, m)

Arguments

f	A time series to be smoothed.
m	Order of the Fourier polynomial. Default value is computed using the Sturge's rule.

Value

A vector with the fourier coefficients.

Examples

x <- seq(from = -pi, to = pi, by = 0.01)
y <- x^2 + rnorm(length(x), sd = 0.1)
v_coef <- coef_fourier(y)

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Temperature datasets from Canada.

Description

Temperature time series from 35 weather stations from Canada. This dataset is a classic one and was used in famous package fda. We have made a few changes in this dataset.

Usage

data("datasetCanada")

Format

A list with two entries: m_cood and m_data.

m_coord

a tibble with latitude, logitude and the name of stations.

m_data

a tibble where each column is the time series from a weather station.

Source

the CanadianWeather dataset from the R package fda.

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Smoothed curve in Fourier Series.

Description

This function computes the smoothed curve using Fourier coefficients.

Usage

fourier_b(coef, x)

Arguments

coef	Fourier coefficients.
x	a time series to evaluate the smoothed curve.

Value

a time series with the smoothed curve.

Examples

v_coef <- rnorm(23)
fourier_b(v_coef)

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Kriging method for Spatial Functional Data.

Description

geo_fkf implements the kriging method for spatial functional datasets.

Usage

geo_fkf(m_data, m_coord, new_loc, p, t = seq(from = -pi, to = pi, by = 0.01))

Arguments

m_data	a tibble where each column or variable is data from a station
m_coord	a tibble with two columns: latitude and longitude
new_loc	a tible with one observation, where the columns or variables are latitude and longitude
p	order in the Fourier Polynomial
t	a time series with values belonging to $[-\pi, \pi]$ to evaluate the estimate curve

Value

a list with three entries: estimates, Theta and cov_params

estimates

the estimate curve

Theta

weights (matrices) of the linear combination

cov_params

estimate $\sigma^2$, $\phi$ and $\rho$

Examples

data("datasetCanada")

m_data <- as.matrix(datasetCanada$m_data)
m_coord <- as.matrix(datasetCanada$m_coord[, 1:2])
pos <- sample.int(nrow(m_coord), 1)
log_pos <- !(seq_len(nrow(m_coord)) %in% pos)
new_loc <- m_coord[pos, ]
m_coord <- m_coord[log_pos, ]
m_data <- m_data[, log_pos]

geo_fkf(m_data, m_coord, new_loc)

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Maximum likelihood estimate for $\sigma^2$, $\phi$ and $\rho$.

Description

This function maximum likelihood estimate for $\sigma^2$, $\phi$ and $\rho$ in the random field model for the covariance.

Usage

log_lik_rf(m_coef, m_coord)

Arguments

m_coef	Matrix where each column is an observed vector
m_coord	Matrix where each observation contains the latitude and longitude

Value

Return a list with

par

A vector with the estimates of $\sigma^2$, $\phi$ and $\rho$.

m_cov

A matrix of covariances of the estimates.

Examples

data("datasetCanada")

m_data <- as.matrix(datasetCanada$m_data)
m_coord <- as.matrix(datasetCanada$m_coord[, 1:2])

p <- ceiling(1 + log2(nrow(m_data)))
m_coef <- sapply(seq_len(nrow(m_coord)), function(i) {
    coef_fourier(m_data[, i], p)
})
log_lik_rf(m_coef, m_coord)

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Log likelihood function for multivariate normal with spatial dependency.

Description

Log likelihood function for multivariate normal with spatial dependency.

Arguments

mCoef	coefficient matrix. Each column is the coefficient from a curve;
mDist	distance matris;
s2	variance from the covariance model;
phi	variance from the covariance model;
rho	variance from the covariance model;

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