| Type: | Package |
| Title: | Bayesian Modeling of Autoregressive Threshold Time Series Models |
| Version: | 1.0 |
| Date: | 2017-02-19 |
| Author: | Hanwen Zhang, Fabio H. Nieto |
| Maintainer: | Hanwen Zhang <hanwengutierrez@gmail.com> |
| Description: | Identification and estimation of the autoregressive threshold models with Gaussian noise, as well as positive-valued time series. The package provides the identification of the number of regimes, the thresholds and the autoregressive orders, as well as the estimation of remain parameters. The package implements the methodology from the 2005 paper: Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data <doi:10.1081/STA-200054435>. |
| Encoding: | UTF-8 |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | mvtnorm |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-02-24 02:41:45 UTC; hanwenzhang |
| Repository: | CRAN |
| Date/Publication: | 2017-02-24 08:31:45 |
Identify the autoregressive orders for a log-normal TAR model given the number of regimes and thresholds.
Description
This function identify the autoregressive orders for a log-normal TAR model given the number of regimes and thresholds.
Usage
ARorder.lognorm(Z, X, l, r, k_Max = 3, k_Min = 0, n.sim = 500,
p.burnin = 0.3, n.thin = 1)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series {Z_t}. |
k_Max |
The minimum value for each autoregressive order. The default is 3. |
k_Min |
The maximum value for each autoregressive order. The default is 0. |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for burn-in |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The log-normal TAR model is given by
log X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}log X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for some j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The identified autoregressive orders with posterior probabilities
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
simu.tar.lognorm, ARorder.norm
Examples
set.seed(12345678)
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,0.5,-0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.3)
X <- simu.tar.lognorm(Z,l,r,K,theta,H)
#res <- ARorder.lognorm(Z,X,l,r)
#res$K.est
#res$K.prob
Identify the autoregressive orders for a Gaussian TAR model given the number of regimes and thresholds.
Description
This function identify the autoregressive orders for a TAR model with Gaussian noise process given the number of regimes and thresholds.
Usage
ARorder.norm(Z, X, l, r, k_Max = 3, k_Min = 0, n.sim = 500,
p.burnin = 0.3, n.thin = 1)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series {Z_t}. |
k_Max |
The minimum value for each autoregressive order. The default is 3. |
k_Min |
The maximum value for each autoregressive order. The default is 0. |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The identified autoregressive orders with posterior probabilities
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
set.seed(123456789)
Z<-arima.sim(n=300,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l)
H <- c(1, 1.5)
X <- simu.tar.norm(Z,l,r,K,theta,H)
#res <- ARorder.norm(Z,X,l,r)
#res$K.est
#res$K.prob
Estimate a log-normal TAR model using Least Square method given the structural parameters.
Description
This function estimate a log-normal TAR model using Least Square method given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.
Usage
LS.lognorm(Z, X, l, r, K)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the |
Details
The TAR model is given by
log X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}log X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights.
Value
The function returns the autoregressive coefficients matrix theta and variance weights H. Rows of the matrix theta represent regimes
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,0.5,-0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.3)
X <- simu.tar.lognorm(Z,l,r,K,theta,H)
ts.plot(X)
LS.lognorm(Z,X,l,r,K)
Estimate a Gaussian TAR model using Least Square method given the structural parameters.
Description
This function estimate a Gaussian TAR model using Least Square method given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.
Usage
LS.norm(Z, X, l, r, K)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights.
Value
The function returns the autoregressive coefficients matrix theta and variance weights H. Rows of the matrix theta represent regimes
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l)
H <- c(1, 1.5)
X <- simu.tar.norm(Z,l,r,K,theta,H)
LS.norm(Z,X,l,r,c(0,0))
Estimate a TAR model using Gibbs Sampler given the structural parameters.
Description
This function estimate a TAR model using Gibbs Sampler given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.
Usage
Param.lognorm(Z, X, l, r, K, n.sim = 500, p.burnin = 0.2, n.thin = 3)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the l regimes. |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for burn-in |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The function returns the autoregressive coefficients matrix theta and variance weights H. Rows of the matrix theta represent regimes
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
# Example 1, TAR model with 2 regimes
#' set.seed(12345678)
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,0.5,-0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.3)
X <- simu.tar.lognorm(Z,l,r,K,theta,H)
# res <- Param.lognorm(Z,X,l,r,K)
# Example 2, TAR model with 3 regimes
Z<-arima.sim(n=300, list(ar=c(0.5)))
l <- 3
r <- c(-0.6, 0.6)
K <- c(1, 2, 1)
theta <- matrix(c(1,0.5,-0.5,-0.5,0.2,-0.7,NA, 0.5,NA), nrow=l)
H <- c(1, 1.5, 2)
X <- simu.tar.lognorm(Z, l, r, K, theta, H)
# res <- Param.lognorm(Z,X,l,r,K)
Estimate a Gaussian TAR model using Gibbs Sampler given the structural parameters.
Description
This function estimate a Gaussian TAR model using Gibbs Sampler given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.
Usage
Param.norm(Z, X, l, r, K, n.sim = 500, p.burnin = 0.2, n.thin = 3)
Arguments
Z |
The threshold series |
X |
The series of interest |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for burn-in |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The function returns the autoregressive coefficients matrix theta and variance weights H. Rows of the matrix theta represent regimes
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
# Example 1, TAR model with 2 regimes
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l)
H <- c(1, 1.5)
X <- simu.tar.norm(Z,l,r,K,theta,H)
# res <- Param.norm(Z,X,l,r,K)
# Example 2, TAR model with 3 regimes
Z<-arima.sim(n=300, list(ar=c(0.5)))
l <- 3
r <- c(-0.6, 0.6)
K <- c(1, 2, 1)
theta <- matrix(c(1,0.5,-0.5,-0.5,0.2,-0.7,NA, 0.5,NA), nrow=l)
H <- c(1, 1.5, 2)
X <- simu.tar.norm(Z, l, r, K, theta, H)
# res <- Param.norm(Z,X,l,r,K)
Identify the number of regimes and the corresponding thresholds for a log-normal TAR model.
Description
This function identify the number of regimes and the corresponding thresholds for a log-normal TAR model.
Usage
reg.thr.lognorm(Z, X, n.sim = 500, p.burnin = 0.2, n.thin = 1)
Arguments
Z |
The threshold series |
X |
The series of interest |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for Burn-in |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The TAR model is given by
log X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}log X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The function returns the identified number of regimes with posterior probabilities and the thresholds with credible intervals.
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
set.seed(12345678)
# Example 1, log-normal TAR model with 2 regimes
Z<-arima.sim(n=400,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(-1,0.5,0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.5)
#X <- simu.tar.lognorm(Z,l,r,K,theta,H)
#res <- reg.thr.lognorm(Z,X)
#res$L.est
#res$L.prob
#res$R.est
#res$R.CI
Identify the number of regimes and the corresponding thresholds for a Gaussian TAR model.
Description
This function identify the number of regimes and the corresponding thresholds for a TAR model with Gaussian noise process.
Usage
reg.thr.norm(Z, X, n.sim = 500, p.burnin = 0.2, n.thin = 1)
Arguments
Z |
The threshold series |
X |
The series of interest |
n.sim |
Number of iteration for the Gibbs Sampler |
p.burnin |
Percentage of iterations used for Burn-in |
n.thin |
Thinnin factor for the Gibbs Sampler |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The function returns the identified number of regimes with posterior probabilities and the thresholds with credible intervals.
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
set.seed(12345678)
# Example 1, TAR model with 2 regimes
Z<-arima.sim(n=300,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l)
H <- c(1, 1.5)
X <- simu.tar.norm(Z,l,r,K,theta,H)
#res <- reg.thr.norm(Z,X)
#res$L.est
#res$L.prob
#res$R.est
#res$R.CI
Simulate a series from a log-normal TAR model with Gaussian distributed error for positive valued time series.
Description
This function simulates a serie from a log-normal TAR model with Gaussian distributed error given the parameters of the model from a given threshold process \{Z_t\}
Usage
simu.tar.lognorm(Z, l, r, K, theta, H)
Arguments
Z |
The threshold series |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the |
theta |
The matrix of autoregressive coefficients of dimension |
H |
The vector containing the variance weights of the |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The time series \{X_t\}.
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
set.seed(12345678)
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,0.5,-0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.3)
X <- simu.tar.lognorm(Z,l,r,K,theta,H)
ts.plot(X)
Simulate a series from a TAR model with Gaussian distributed error.
Description
This function simulates a serie from a TAR model with Gaussian distributed error given the parameters of the model from a given threshold process \{Z_t\}
Usage
simu.tar.norm(Z, l, r, K, theta, H)
Arguments
Z |
The threshold series |
l |
The number of regimes. |
r |
The vector of thresholds for the series |
K |
The vector containing the autoregressive orders of the l regimes. |
theta |
The matrix of autoregressive coefficients of dimension |
H |
The vector containing the variance weights of the |
Details
The TAR model is given by
X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t
when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l).
the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).
Value
The time series \{X_t\}.
Author(s)
Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
References
Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930
See Also
Examples
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA),nrow=l)
H <- c(1, 1.5)
X <- simu.tar.norm(Z,l,r,K,theta,H)
ts.plot(X)