Package 'DCSmooth' reference manual

Title:	Nonparametric Regression and Bandwidth Selection for Spatial Models
Description:	Nonparametric smoothing techniques for data on a lattice and functional time series. Smoothing is done via kernel regression or local polynomial regression, a bandwidth selection procedure based on an iterative plug-in algorithm is implemented. This package allows for modeling a dependency structure of the error terms of the nonparametric regression model. Methods used in this paper are described in Feng/Schaefer (2021) <https://ideas.repec.org/p/pdn/ciepap/144.html>, Schaefer/Feng (2021) <https://ideas.repec.org/p/pdn/ciepap/143.html>.
Authors:	Bastian Schaefer [aut, cre], Sebastian Letmathe [ctb], Yuanhua Feng [ths]
Maintainer:	Bastian Schaefer <[email protected]>
License:	GPL-3
Version:	1.1.2
Built:	2024-11-04 19:57:27 UTC
Source:	CRAN

Nonparametric Regression and Bandwidth Selection for Spatial Models

Description

Nonparametric smoothing techniques for data on a lattice and functional time series. Smoothing is done via kernel regression or local polynomial regression, a bandwidth selection procedure based on an iterative plug-in algorithm is implemented. This package allows for modeling a dependency structure of the error terms of the nonparametric regression model. Methods used in this paper are described in Feng/Schaefer (2021) <https://ideas.repec.org/p/pdn/ciepap/144.html>, Schaefer/Feng (2021) <https://ideas.repec.org/p/pdn/ciepap/143.html>.

Package Content

Index of help topics:

DCSmooth-package        Nonparametric Regression and Bandwidth
                        Selection for Spatial Models
dcs                     Nonparametric Double Conditional Smoothing for
                        2D Surfaces
kernel.assign           Assign a Kernel Function
kernel.list             Print a list of available kernels in the
                        DCSmooth package
plot.dcs                Contour Plot for the Double Conditional
                        Smoothing
print.dcs               Summarize Results from Double Conditional
                        Smoothing
print.dcs_options       Print and Summarize Options for Double
                        Conditional Smoothing
print.summary_dcs       Print the Summary of a DCS estimation
print.summary_sarma     Print the Summary of a "sarma"/"sfarima" object
residuals.dcs           Residuals of "dcs"-object
returns.alv             Returns of Allianz SE
sarma.est               Estimation of an SARMA-process
sarma.sim               Simulation of a SARMA(p, q)-process
set.options             Set Options for the DCS procedure
sfarima.est             Estimation of a SFARIMA-process
sfarima.sim             Simulation of a SFARIMA(p, q, d)-process
summary.dcs             Summarizing Results from Double Conditional
                        Smoothing
summary.dcs_options     Print and Summarize Options for Double
                        Conditional Smoothing
summary.sarma           Summarizing SARMA/SFARIMA Estimation or
                        Simulation
surface.dcs             3D Surface Plot of "dcs"-object or numeric
                        matrix
temp.nunn               Temperatures from Nunn, CO
temp.yuma               Temperatures from Yuma, AZ
volumes.alv             Volumes of Allianz SE
wind.nunn               Wind Speed from Nunn, CO
wind.yuma               Wind Speed from Yuma, AZ
y.norm1                 Single Gaussian Peak
y.norm2                 Double Gaussian Peak
y.norm3                 Double Gaussian Ridges

Further information is available in the following vignettes:

`DCSmooth`	DCSmooth (source, pdf)

Maintainer

Bastian Schaefer <[email protected]>

Author(s)

Bastian Schaefer [aut, cre], Sebastian Letmathe [ctb], Yuanhua Feng [ths]

Nonparametric Double Conditional Smoothing for 2D Surfaces

Description

dcs provides a double conditional nonparametric smoothing of the expectation surface of a functional time series or a random field on a lattice. Bandwidth selection is done via an iterative plug-in method.

Usage

dcs(Y, dcs_options = set.options(), h = "auto", parallel = FALSE, ...)
dcs(Y, dcs_options = set.options(), h = "auto", parallel = FALSE, ...)

Arguments

`Y`	A numeric matrix that contains the observations of the random field or functional time-series.
`dcs_options`	An object of class `"dcs_options"`, specifying the parameters for the smoothing and bandwidth selection procedure.
`h`	Bandwidth for smoothing the observations in `Y`. Can be a two-valued numerical vector with bandwidths in row- and column-direction. If the value is `"auto"` (the default), bandwidth selection will be carried out by the iterative plug-in algorithm.
`parallel`	A logical value indicating if parallel computing should be used for faster computation. Default value is `parallel = FALSE`. Parallelization seems to be efficient at above 400,000 observations.
`...`	Additional arguments passed to `dcs`. Currently supported are numerical vectors `X` and/or `T` containing the exogenous covariates with respect to the rows and columns.

Value

dcs returns an object of class "dcs", including

`Y`	matrix of original observations.
`X, T`	vectors of covariates over rows (`X`) and columns (`T`).
`M`	resulting matrix of smoothed values.
`R`	matrix of residuals of estimation, $Y - M$ .
`h`	optimized or given bandwidths.
`c_f`	estimated variance coefficient.
`var_est`	estimated variance model. If the variance function is modeled by an SARMA/SFARIMA, `var_est` is an object of class "sarma"/ "sfarima".
`dcs_options`	an object of class `cds_options` containing the initial options of the dcs procedure.
`iterations`	number of iterations of the IPI-procedure.
`time_used`	time spend searching for optimal bandwidths (not overall runtime of the function).

Details

See the vignette for a more detailed description of the function.

References

Schäfer, B. and Feng, Y. (2021). Fast Computation and Bandwidth Selection Algorithms for Smoothing Functional Time Series. Working Papers CIE 143, Paderborn University.

Examples

# See vignette("DCSmooth") for examples and explanation

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs(y)

# See vignette("DCSmooth") for examples and explanation

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs(y)

Assign a Kernel Function

Description

Assign a Kernel Function

Usage

kernel.assign(kernel_id)
kernel.assign(kernel_id)

Arguments

kernel_id

a string specifying the kernel identifier as given in the details.

Value

kernel.assign returns an object of class "function". This function takes two arguments, a numeric vector in the first argument and a single number in the second. The function itself will return a matrix with one column and the same number of rows as the input vector.

Details

kernel.assign sets a pointer to a specified kernel function available in the DCSmooth package. The kernels are boundary kernels of the form $K(u,q)$ , where $u \in [-1, q]$ and $q \in [0, 1]$ q = [0, 1]. Kernels are of the Müller-Wang type ("MW"), Müller type ("M") or truncated kernels ("TR").

References

Müller, H.-G. and Wang, J.-L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics, 50:61-76.

Müller, H.-G. (1991). Smooth optimum kernel estimators near endpoints. Biometrika, 78:521-530.

Feng, Y. and Schäfer B. (2021). Boundary Modification in Local Regression. Working Papers CIE 144, Paderborn University.

Examples

 # See vignette("DCSmooth") for further examples and explanation

u <- seq(from = -1, to = 0.5, length.out = 151)
kern_MW220 <- kernel.assign("MW_220")
k <- kern_MW220(u, 0.5)
plot(u, k, type = "l") 

# See vignette("DCSmooth") for further examples and explanation

u <- seq(from = -1, to = 0.5, length.out = 151)
kern_MW220 <- kernel.assign("MW_220")
k <- kern_MW220(u, 0.5)
plot(u, k, type = "l")

Print a list of available kernels in the DCSmooth package

Description

Print a list of available kernels in the DCSmooth package

Usage

kernel.list(print = TRUE)
kernel.list(print = TRUE)

Arguments

print

Logical value. Should the list be printed to the console? If TRUE (the default), the list is printed to the console, if FALSE the list of identifiers is returned from the function as (surprise!) a list.

Value

If print = FALSE, a list is returned containing the kernel identifiers

Details

kernel.list is used to get a list of available kernels in the DCSmooth package.

kernel.list prints a list of identifiers kernel_id of available kernels in the DCSmooth package. The available kernel types are "T": truncated, "MW": Müller-Wang boundary correction, "M": Müller boundary correction.

References

Müller, H.-G. and Wang, J.-L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics, 50:61-76.

Müller, H.-G. (1991). Smooth optimum kernel estimators near endpoints. Biometrika, 78:521-530.

Feng, Y. and Schäfer B. (2021). Boundary Modification in Local Regression. Working Papers CIE 144, Paderborn University.

Examples

 # See vignette("DCSmooth") for further examples and explanation
 
 kernel.list()

# See vignette("DCSmooth") for further examples and explanation
 
 kernel.list()

Contour Plot for the Double Conditional Smoothing

Description

plot method for class "dcs"

Usage

## S3 method for class 'dcs'
plot(x, ...)
## S3 method for class 'dcs'
plot(x, ...)

Arguments

`x`	an object of class "dcs_options", usually, a result of a call to `set.options`.
`...`	Additional arguments passed to `print.dcs_options`. The argument `plot_choice` overrides the prompt to specify a plot, can be `c(1, 2, 3)`.

Value

No return value.

Details

plot.dcs provides a contour plot of either the original data (1), smoothed surface (2) or residuals (3).

Examples

## Contour plot of smoothed surface
y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
plot(dcs_object, plot_choice = 2)

## Contour plot of smoothed surface
y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
plot(dcs_object, plot_choice = 2)

Summarize Results from Double Conditional Smoothing

Description

print method for class "dcs"

Usage

## S3 method for class 'dcs'
print(x, ...)
## S3 method for class 'dcs'
print(x, ...)

Arguments

`x`	an object of class "dcs", usually, a result of a call to `dcs`.
`...`	Additional arguments passed to `print.dcs`.

Value

No return value.

Details

print.dcs prints a short summary of an object of class dcs, only including bandwidths and the estimated variance coefficient (only if automatic bandwidth selection is used).

Examples

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
print(dcs_object)
dcs_object

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
print(dcs_object)
dcs_object

Print and Summarize Options for Double Conditional Smoothing

Description

print method for class "dcs_options"

Usage

## S3 method for class 'dcs_options'
print(x, ...)
## S3 method for class 'dcs_options'
print(x, ...)

Arguments

`x`	an object of class "dcs_options", usually, a result of a call to `set.options`.
`...`	Additional arguments passed to `print.dcs_options`.

Value

No return value.

Details

print.dcs_options prints the main options and summary.dcs_options prints main and advanced (IPI) options used for the dcs function. Arguments should be an object of class "dcs_options".

Examples

## Default options
myOpt <- set.options()
print(myOpt)
summary(myOpt)

## Use Kernel regression
myOpt <- set.options(type = "KR")
print(myOpt)
summary(myOpt)

## Default options
myOpt <- set.options()
print(myOpt)
summary(myOpt)

## Use Kernel regression
myOpt <- set.options(type = "KR")
print(myOpt)
summary(myOpt)

Print the Summary of a DCS estimation

Description

print method for class "summary_dcs"

Usage

## S3 method for class 'summary_dcs'
print(x, ...)
## S3 method for class 'summary_dcs'
print(x, ...)

Arguments

`x`	An object of class `"summary_dcs"`.
`...`	Additional arguments passed to `print.summary_dcs`.

Value

No return value.

Print the Summary of a "sarma"/"sfarima" object

Description

print methods for class "summary_sarma"/ "summary_sfarima"

Usage

## S3 method for class 'summary_sarma'
print(x, ...)

## S3 method for class 'summary_sfarima'
print(x, ...)
## S3 method for class 'summary_sarma'
print(x, ...)

## S3 method for class 'summary_sfarima'
print(x, ...)

Arguments

`x`	An object of class `"summary_sarma"` or `"summary_sfarima"`.
`...`	Additional arguments passed to `print.summary_sarma`/ `print.summary_sfarima`.

Value

No return value.

Residuals of "dcs"-object

Description

Returns the residuals of an object of class "dcs".

Usage

## S3 method for class 'dcs'
residuals(x, ...)
## S3 method for class 'dcs'
residuals(x, ...)

Arguments

`x`	an object of class `"dcs"`, usually the result of a call to `dcs`.
`...`	Additional arguments passed to `residuals.dcs`.

Value

Returns the $n_x \times n_t$ -matrix of residuals.

Examples

y = y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object = dcs(y)
residuals(dcs_object)

y = y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object = dcs(y)
residuals(dcs_object)

Returns of Allianz SE

Description

The (log-) returns of the shares of the German insurance company Allianz SE from 2007-01-02 to 2010-12-30 aggregated to 5-minute observations. The data is adjusted to matrix form for direct use with the DCSmooth-functions.

Usage

returns.alv
returns.alv

Format

A numeric matrix with 1016 rows representing the days and 101 columns representing the intraday time points.

Estimation of an SARMA-process

Description

Parametric Estimation of an $SARMA(p, q)$ -process on a lattice.

Usage

sarma.est(Y, method = "HR", model_order = list(ar = c(1, 1), ma = c(1, 1)))

qarma.est(Y, model_order = list(ar = c(1, 1), ma = c(1, 1)))
sarma.est(Y, method = "HR", model_order = list(ar = c(1, 1), ma = c(1, 1)))

qarma.est(Y, model_order = list(ar = c(1, 1), ma = c(1, 1)))

Arguments

`Y`	A numeric matrix that contains the demeaned observations of the random field or functional time-series.
`method`	Method used for estimation of the parameters. One of `"HR", "sep", "RSS"`, default value is `"HR"`
`model_order`	A list containing the orders of the SARMA model in the form `model_order = list(ar = c(p1, p2), ma = c(q1, q2))`. Default value is a $SARMA((1, 1), (1, 1))$ model.

Value

The function returns an object of class "sarma" including

`Y`	The matrix of observations, inherited from input.
`innov` The estimated innovations.
`model`	The estimated model consisting of the coefficient matrices `ar` and `ma` and standard deviation of innovations `sigma`.
`stnry`	An logical variable indicating whether the estimated model is stationary.

Details

The MA- and AR-parameters of a top-left quadrant ARMA process are estimated by the specified method. The lag-orders of the $SARMA(p, q)$ are given by $p = (p_1, p_2), q = (q_1, q_2)$ , where $p_1, q_1$ are the lags over the rows and $p_2, q_2$ are the lags over the columns. The estimation process is based on the model

$\phi(B_{1}B_{2})X_{i,j} = \theta(B_{1}B_{2})u_{i,j}$

Examples

# See vignette("DCSmooth") for examples and explanation

## simulation of SARMA process
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma <- 0.5
sarma_model <- list(ar = ar, ma = ma, sigma = sigma)
sarma_simulated <- sarma.sim(100, 100, model = sarma_model)
sarma_simulated$model

## estimation of SARMA process
sarma.est(sarma_simulated$Y)$model
sarma.est(sarma_simulated$Y, 
           model_order = list(ar = c(1, 1), ma = c(1, 1)))$model

# See vignette("DCSmooth") for examples and explanation

## simulation of SARMA process
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma <- 0.5
sarma_model <- list(ar = ar, ma = ma, sigma = sigma)
sarma_simulated <- sarma.sim(100, 100, model = sarma_model)
sarma_simulated$model

## estimation of SARMA process
sarma.est(sarma_simulated$Y)$model
sarma.est(sarma_simulated$Y, 
           model_order = list(ar = c(1, 1), ma = c(1, 1)))$model

Simulation of a $SARMA(p, q)$ -process

Description

sarma.sim simulates a specified SARMA-model on a lattice with normally distributed innovations.

Usage

sarma.sim(n_x, n_t, model)

qarma.sim(n_x, n_t, model)
sarma.sim(n_x, n_t, model)

qarma.sim(n_x, n_t, model)

Arguments

`n_x`	Number of simulated observation rows.
`n_t`	Number of simulated observation columns.
`model`	A list containing the coefficient matrices `ar` and `ma` of the SARMA model as well as the standard deviation of innovations `sigma`.

Value

The function returns an object of class "sarma", consisting of

`Y`	A $n_x \times n_t$ -matrix of simulated values of the specified SARMA process.
`innov`	The innovations used for simulation, iid. drawn from a normal distribution with zero mean and variance $\sigma^2$ .
`model`	The model used for simulation, inherited from input.
`stnry`	An logical variable indicating whether the simulated model is stationary.

Details

Simulation of a top-left dependent spatial ARMA process (SARMA). This function returns an object of class "sarma". The simulated innovations are created from a normal distribution with specified variance $\sigma^2$ .

see the vignette for further details.

Examples

# See vignette("DCSmooth") for examples and explanation
 
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma <- 0.5
sarma_model <- list(ar = ar, ma = ma, sigma = sigma)

sarma_sim <- sarma.sim(100, 100, model = sarma_model)
summary(sarma_sim)

# See vignette("DCSmooth") for examples and explanation
 
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma <- 0.5
sarma_model <- list(ar = ar, ma = ma, sigma = sigma)

sarma_sim <- sarma.sim(100, 100, model = sarma_model)
summary(sarma_sim)

Set Options for the DCS procedure

Description

Set Options for the DCS procedure

Usage

set.options(
  type = "LP",
  kerns = c("MW_220", "MW_220"),
  drv = c(0, 0),
  var_model = "iid",
  ...
)
set.options(
  type = "LP",
  kerns = c("MW_220", "MW_220"),
  drv = c(0, 0),
  var_model = "iid",
  ...
)

Arguments

`type`	either local polynomial regression (`"LP"`, the default) or kernel regression (`"KR"`).
`kerns`	a character vector of length 2 containing the identifier for the kernels to be used in kernel regression. Weighting functions in local polynomial regression are computed according to the identifier. Default value is `MW_220`, the Mueller-Wang kernel of order $(2, 2, 0)$ . If only a single value is provided, it is used as kernel in both directions.
`drv`	A non-negative vector of length 2, containing the derivative orders to be estimated from the given data. The default is `c(0, 0)`. For LP-regression, polynomial order is selected as $(\nu_1 + 1, \nu_2 + 1)$ . If only a single value is provided, it is used as derivative in both directions.
`var_model`	the method of estimating the variance coefficient $c_f$ . Currently available are `var_model = c("iid", "sarma_HR", "sarma_sep", "sarma_RSS", "sfarima_RSS")`. Replacing the argument `var_model`. For code using `var_est`, the argument is converted to `var_model`.
`...`	Additional arguments passed to `set.options()`. This includes `IPI_options`, a list containing further options used by the iterative plug-in algorithm. For convenience, any of the options usually included in the list `IPI_options` can be passed as argument directly to `set.options` and will be converted into the `IPI_options` list. Further arguments accepted are `model_order` controlling the order of the variance model, if either an SARMA or SFARIMA model is used. This argument is either a list of the form `list(ar = c(1, 1), ma = c(1, 1))` or specifies an order selection criterion from `c("aic", "bic", "gpac")`. If an order selection criterion is used, the argument `order_max` controls the maximum order to be tested.

Value

An object of class "dcs_options".

Details

This function is used to set the options for bandwidth selection in the dcs function. Detailed information can be found in the vignette.

Examples

# See vignette("DCSmooth") for examples and explanation

set.options()

myOpt <- set.options(type = "KR", var_model = "iid")
y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs(y, dcs_options = myOpt)
# See vignette("DCSmooth") for examples and explanation

set.options()

myOpt <- set.options(type = "KR", var_model = "iid")
y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs(y, dcs_options = myOpt)

Estimation of a SFARIMA-process

Description

Parametric Estimation of a $SFARIMA(p, q, d)$ -process on a lattice.

Usage

sfarima.est(Y, model_order = list(ar = c(1, 1), ma = c(1, 1)))
sfarima.est(Y, model_order = list(ar = c(1, 1), ma = c(1, 1)))

Arguments

`Y`	A numeric matrix that contains the demeaned observations of the random field or functional time-series.
`model_order`	A list containing the orders of the SFARIMA model in the form `model_order = list(ar = c(p1, p2), ma = c(q1, q2))`. Default value is a $SFARIMA((1, 1), (1, 1), d)$ model.

Value

The function returns an object of class "sfarima" including

`Y`	The matrix of observations, inherited from input.
`innov` The estimated innovations.
`model`	The estimated model consisting of the coefficient matrices `ar` and `ma`, the estimated long memory parameters `d` and standard deviation of innovations `sigma`.
`stnry`	An logical variable indicating whether the estimated model is stationary.

Details

The MA- and AR-parameters as well as the long-memory parameters

$d$

of a SFARIMA process are estimated by minimization of the residual sum of squares RSS. Lag-orders of $SFARIMA(p, q, d)$ are given by $p = (p_1, p_2), q = (q_1, q_2)$ , where $p_1, q_1$ are the lags over the rows and $p_2, q_2$ are the lags over the columns. The estimated process is based on the (separable) model

$\varepsilon_{ij} = \Psi_1(B) \Psi_2(B) \eta_{ij}$

, where

$\Psi_i = (1 - B_i)^{-d_i}\phi^{-1}_i(B_i)\psi_i(B_i), i = 1,2$

Examples

# See vignette("DCSmooth") for examples and explanation

## simulation of SFARIMA process
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d <- c(0.1, 0.1)
sigma <- 0.5
sfarima_model <- list(ar = ar, ma = ma, d = d, sigma = sigma)
sfarima_sim <- sfarima.sim(50, 50, model = sfarima_model)

## estimation of SFARIMA process
sfarima.est(sfarima_sim$Y)$model
sfarima.est(sfarima_sim$Y, 
           model_order = list(ar = c(1, 1), ma = c(0, 0)))$model

# See vignette("DCSmooth") for examples and explanation

## simulation of SFARIMA process
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d <- c(0.1, 0.1)
sigma <- 0.5
sfarima_model <- list(ar = ar, ma = ma, d = d, sigma = sigma)
sfarima_sim <- sfarima.sim(50, 50, model = sfarima_model)

## estimation of SFARIMA process
sfarima.est(sfarima_sim$Y)$model
sfarima.est(sfarima_sim$Y, 
           model_order = list(ar = c(1, 1), ma = c(0, 0)))$model

Simulation of a $SFARIMA(p, q, d)$ -process

Description

sfarima.sim simulates a specified SFARIMA-model on a lattice with normally distributed innovations.

Usage

sfarima.sim(n_x, n_t, model)
sfarima.sim(n_x, n_t, model)

Arguments

`n_x`	Number of simulated observation rows.
`n_t`	Number of simulated observation columns.
`model`	A list containing the coefficient matrices `ar` and `ma` of the QARMA model, the long memory parameter vector `d` as well as the standard deviation of innovations `sigma`.

Value

The function returns an object of class "sfarima", consisting of

`Y`	A $n_x \times n_t$ -matrix of simulated values of the specified SFARIMA process.
`innov`	The innovations used for simulation, iid. drawn from a normal distribution with zero mean and variance $\sigma^2$ .
`model`	The model used for simulation, inherited from input.
`stnry`	An logical variable indicating whether the simulated model is stationary.

Details

Simulation of a separable spatial fractionally ARIMA process (SFARIMA). This function returns an object of class "sfarima". The simulated innovations are created from a normal distribution with specified variance $\sigma^2$ .

see the vignette for further details.

Examples

# See vignette("DCSmooth") for examples and explanation
 
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d <- c(0.1, 0.1)
sigma <- 0.5
sfarima_model <- list(ar = ar, ma = ma, d = d, sigma = sigma)

sfarima_sim <- sfarima.sim(100, 100, model = sfarima_model)
surface.dcs(sfarima_sim$Y)

# See vignette("DCSmooth") for examples and explanation
 
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d <- c(0.1, 0.1)
sigma <- 0.5
sfarima_model <- list(ar = ar, ma = ma, d = d, sigma = sigma)

sfarima_sim <- sfarima.sim(100, 100, model = sfarima_model)
surface.dcs(sfarima_sim$Y)

Summarizing Results from Double Conditional Smoothing

Description

summary method for class "dcs"

Usage

## S3 method for class 'dcs'
summary(object, ...)
## S3 method for class 'dcs'
summary(object, ...)

Arguments

`object`	an object of class "dcs", usually, a result of a call to `dcs`.
`...`	Additional arguments passed to the `summary.dcs` function.

Value

The function summary.dcs returns an object of class summary_dcs including

`h_opt`	estimated optimal bandwidth from the IPI-procedure.
`c_f`	estimated variance factor.
`iterations`	number of iterations of the IPI-procedure.
`time_used`	time spend searching for optimal bandwidths (not overall runtime of the function).
`var_est`	estimated variance model. Has class "sarma" if an SARMA model is used and class "sfarima" if an SFARIMA model is used.
`var_model_id`	identifier for the variance model estimated.
`var_model_order`	order of the estimated variance model, if either SARMA or SFARIMA is used.
`dcs_options`	an object of class `cds_options` containing the initial options of the dcs procedure.

Details

summary.dcs strips an object of class "dcs" from all large matrices (Y, X, T, M, R), allowing for easier handling of meta-statistics of the bandwidth selection procedure.

print.summary_dcs returns a list of summary statistics from the dcs procedure. The output depends on the use of the dcs- function. If automatic bandwidth selection is chosen, summary.dcs prints detailed statistics of the type of regression, the estimated bandwidths h_x, h_t, the variance coefficient c_f and performance statistics such as the number of iterations of the IPI-algorithm and the time used for bandwidth selection.

The method used for estimation of the variance coefficient is printed and the results of an SARMA/SFARIMA-estimation, if available.

If bandwidths are supplied to dcs, summary.dcs only prints the given bandwidths.

Examples

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
summary(dcs_object)

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs_object <- dcs(y)
summary(dcs_object)

Print and Summarize Options for Double Conditional Smoothing

Description

summary method for class "dcs_options"

Usage

## S3 method for class 'dcs_options'
summary(object, ...)
## S3 method for class 'dcs_options'
summary(object, ...)

Arguments

`object`	an object of class "dcs_options", usually, a result of a call to `set.options`.
`...`	Additional arguments passed to `summary.dcs_options`.

Value

No return value.

Details

print.dcs_options prints the main options and summary.dcs_options prints main and advanced (IPI) options used for the dcs function. Arguments should be an object of class "dcs_options".

Examples

## Default options
myOpt <- set.options()
print(myOpt)
summary(myOpt)

## Use Kernel regression
myOpt <- set.options(type = "KR")
print(myOpt)
summary(myOpt)

## Default options
myOpt <- set.options()
print(myOpt)
summary(myOpt)

## Use Kernel regression
myOpt <- set.options(type = "KR")
print(myOpt)
summary(myOpt)

Summarizing SARMA/SFARIMA Estimation or Simulation

Description

summary method for class "sarma" or "sfarima"

Usage

## S3 method for class 'sarma'
summary(object, ...)

## S3 method for class 'sfarima'
summary(object, ...)
## S3 method for class 'sarma'
summary(object, ...)

## S3 method for class 'sfarima'
summary(object, ...)

Arguments

`object`	an object of class "sarma" or "sfarima", usually a result of a call to the estimation functions `sarma.est`, `sfarima.est` or to the corresponding simulation functions `sarma.sim` and `sfarima.sim`.
`...`	Additional arguments passed to the `summary.sarma`/ `summary.sfarima` function.

Value

The function summary.sarma/summary.sfarima returns an object of class summary_sarma including

`model`	estimated or simulated model parameters including coefficient matrices `ar`, `ma`, the error term standard deviation `sigma` and the vector of long memory parameters `d` (`summary.sarma` only)
`model_order`	order of the estimated/simulated model computed from the matrices `ar`, `ma`.
`stnry`	a flag for stationarity of the short memory part.
`subclass`	a flag indicating whether the object inherits from an estimation (`subclass = "est"`) or simulation procedure (`subclass = "sim"`).

Details

summary.sarma/summary.sfarima strips an object of class "sarma"/"sfarima" from all large matrices (Y, innov), allowing for easier handling of meta-statistics of the bandwidth selection procedure.

print.summary_sarma/print.summary_sarma returns a list of summary statistics from the estimation or simulation procedure.

Examples

# SARMA Simulation and Estimation
ma = matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar = matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma = 0.5
sarma_model = list(ar = ar, ma = ma, sigma = sigma)
sarma_sim = sarma.sim(100, 100, model = sarma_model)
summary(sarma_sim)
sarma_est = sarma.est(sarma_sim$Y)
summary(sarma_est)

# SFARIMA Simulation and Estimation
ma = matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar = matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d = c(0.1, 0.1)
sigma = 0.5
sfarima_model = list(ar = ar, ma = ma, d = d, sigma = sigma)
sfarima_sim = sfarima.sim(100, 100, model = sfarima_model)
summary(sfarima_sim)
sfarima_est = sfarima.est(sfarima_sim$Y)
summary(sfarima_est)

# SARMA Simulation and Estimation
ma = matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar = matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
sigma = 0.5
sarma_model = list(ar = ar, ma = ma, sigma = sigma)
sarma_sim = sarma.sim(100, 100, model = sarma_model)
summary(sarma_sim)
sarma_est = sarma.est(sarma_sim$Y)
summary(sarma_est)

# SFARIMA Simulation and Estimation
ma = matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar = matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d = c(0.1, 0.1)
sigma = 0.5
sfarima_model = list(ar = ar, ma = ma, d = d, sigma = sigma)
sfarima_sim = sfarima.sim(100, 100, model = sfarima_model)
summary(sfarima_sim)
sfarima_est = sfarima.est(sfarima_sim$Y)
summary(sfarima_est)

3D Surface Plot of "dcs"-object or numeric matrix

Description

3D Surface Plot of "dcs"-object or numeric matrix

Usage

surface.dcs(Y, trim = c(0, 0), plot_choice = "choice", ...)
surface.dcs(Y, trim = c(0, 0), plot_choice = "choice", ...)

Arguments

`Y`	an object of class `"dcs"` or a numeric matrix that contains the values to be plotted.
`trim`	a numeric vector with two values specifying the percentage of trimming applied to the boundaries of the surface to plot. Useful for derivative estimation.
`plot_choice`	override the prompt to specify a plot, can be `c(1, 2, 3)`.
`...`	optional arguments passed to the plot function.

Value

dcs.3d returns an object of class "plotly" and "htmlwidget".

Details

surface.dcs uses the plotly device to plot the 3D surface of the given "dcs"-object or matrix. If a "dcs"-object is passed to the function, it can be chosen between plots of the original data (1), smoothed surface (2) and residuals (3).

Examples

# See vignette("DCSmooth") for examples and explanation

smth <-  dcs(y.norm1 + rnorm(101^2))
surface.dcs(smth, trim = c(0.05, 0.05), plot_choice = 2)

# See vignette("DCSmooth") for examples and explanation

smth <-  dcs(y.norm1 + rnorm(101^2))
surface.dcs(smth, trim = c(0.05, 0.05), plot_choice = 2)

Temperatures from Nunn, CO

Description

This dataset contains the 5-minute observations of the 2020 temperature in Nunn, CO. The data is from the U.S. Climate Reference Network database at www.ncdc.noaa.gov. (see Diamond et al., 2013). The observations were adjusted matrix form for direct use with the DCSmooth-functions.

Usage

temp.nunn
temp.nunn

Format

A numeric matrix with 366 rows and 288 columns containing the temperatures in Celsius.

Temperatures from Yuma, AZ

Description

This dataset contains the 5-minute observations of the 2020 temperature in Yuma, AZ. The data is from the U.S. Climate Reference Network database at www.ncdc.noaa.gov. (see Diamond et al., 2013). The observations were adjusted matrix form for direct use with the DCSmooth-functions.

Usage

temp.yuma
temp.yuma

Format

A numeric matrix with 366 rows and 288 columns containing the temperatures in Celsius.

Volumes of Allianz SE

Description

The trading volumes of the shares of the German insurance company Allianz SE from 2007-01-02 to 2010-09-30 aggregated to 5-minute observations. The data is adjusted to matrix form for direct use with the DCSmooth-functions.

Usage

volumes.alv
volumes.alv

Format

A numeric matrix with 1016 rows representing the days and 102 columns representing the intraday time points.

Wind Speed from Nunn, CO

Description

This dataset contains the 5-minute observations of the 2020 wind speed in Nunn, CO. The data is from the U.S. Climate Reference Network database at www.ncdc.noaa.gov. (see Diamond et al., 2013). The observations were adjusted matrix form for direct use with the DCSmooth-functions.

Usage

wind.nunn
wind.nunn

Format

A numeric matrix with 366 rows and 288 columns containing the wind speed in $m/s$ .

Wind Speed from Yuma, AZ

Description

This dataset contains the 5-minute observations of the 2020 wind speed in Yuma, AZ. The data is from the U.S. Climate Reference Network database at www.ncdc.noaa.gov. (see Diamond et al., 2013). The observations were adjusted matrix form for direct use with the DCSmooth-functions.

Usage

wind.yuma
wind.yuma

Format

A numeric matrix with 366 rows and 288 columns containing the wind speeds in $m/s$ .

Single Gaussian Peak

Description

Example data for using the DCSmooth functions. Data resembles a single gaussian peak on the interval $[0,1] \times [0,1]$ with maximum at $(0.5, 0.5)$ and variance matrix $0.1 \cdot {\bf I}$ , where ${\bf I}$ represents the $2 \times 2$ identity matrix.

Usage

y.norm1
y.norm1

Format

A numeric matrix with 101 rows and 101 columns.

Double Gaussian Peak

Description

Example data for using the DCSmooth functions. Data resembles two gaussian peaks on the interval $[0,1] \times [0,1]$ with maxima at $(0.5, 0.3)$ with variance matrix $0.1 \cdot {\bf I}$ and at $(0.2, 0.8)$ with variance matrix $0.05 \cdot {\bf I}$ , where ${\bf I}$ represents the $2 \times 2$ identity matrix.

Usage

y.norm2
y.norm2

Format

A numeric matrix with 101 rows and 101 columns.

Double Gaussian Ridges

Description

Example data for using the DCSmooth functions. Data resembles two gaussian ridges on the interval $[0,1] \times [0,1]$ with maxima at $(0.25, 0.75)$ with variance matrix $(0.01, -0.1) \cdot {\bf I}$ and at $(0.75, 0.5)$ with variance matrix $(0.01, -0.1) \cdot {\bf I}$ , where ${\bf I}$ represents the $2 \times 2$ identity matrix.

Usage

y.norm3
y.norm3

Format

A numeric matrix with 101 rows and 101 columns.

Package 'DCSmooth'

Help Index

Nonparametric Regression and Bandwidth Selection for Spatial Models

Description

Package Content

Maintainer

Author(s)

Nonparametric Double Conditional Smoothing for 2D Surfaces

Description

Usage

Arguments

Value

Details

References

See Also

Examples

Assign a Kernel Function

Description

Usage

Arguments

Value

Details

References

See Also

Examples

Print a list of available kernels in the DCSmooth package

Description

Usage

Arguments

Value

Details

References

See Also

Examples

Contour Plot for the Double Conditional Smoothing

Description

Usage

Arguments

Value

Details

See Also

Examples

Summarize Results from Double Conditional Smoothing

Description

Usage

Arguments

Value

Details

See Also

Examples

Print and Summarize Options for Double Conditional Smoothing

Description

Usage

Arguments

Value

Details

See Also

Examples

Print the Summary of a DCS estimation

Description

Usage

Arguments

Value

See Also

Print the Summary of a "sarma"/"sfarima" object

Description

Usage

Arguments

Value

See Also

Residuals of "dcs"-object

Description

Usage

Arguments

Value

See Also

Examples

Returns of Allianz SE

Description

Usage

Simulation of a $SARMA(p, q)$ -process

Simulation of a $SFARIMA(p, q, d)$ -process