Package 'mAr'

Eigendecomposition of m-variate AR(p) model

Description

Eigen-decomposition of the estimated matrix of autoregressive coefficients from an m-variate AR(p) model

Usage

mAr.eig(A, C = NULL, ...)

Arguments

A	matrix of estimated autoregression coefficients
C	noise covariance matrix
...	additional arguments for specific methods

Value

A list with components:

modes	periods and damping times associated to each eigenmode
eigv	m*p m-dimensional eigenvectors

Author(s)

S. M. Barbosa

References

Barbosa S.M., Silva M.E., Fernandes M.J. (2006), Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry. Nonlinear Processes in Geophysics, 13, 177-184.

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

Schneider, T. and Neumaier, A. (2001), A Matlab package fo the estimation of parameters and eigenmodes of multivariate autoregressive models, 27, 1, 58-65.

Examples

data(pinkham)
y=mAr.est(pinkham,2,5)
mAr.eig(y$AHat,y$CHat)

---

Estimation of multivariate AR(p) model

Description

Stepwise least-squares estimation of a multivariate AR(p) model based on the algorithm of Neumaier and Schneider (2001).

Usage

mAr.est(x, p, ...)

Arguments

x	matrix of multivariate time series
p	model order
...	additional arguments for specific methods

Details

Fits by stepwise least squares an m-variate AR(p) model given by

$X[t]=w + A1 X[t-1] +...+ Ap X[t-p] +e[t]$

where
X[t]=[X1(t)...Xm(t)]' is a vector of length m
w is a m-length vector of intercept terms
A=[A1 ... Ap] is a mp x m matrix of autoregressive coefficients
e(t) is a m-length uncorrelated noise vector with mean 0 and m x m covariance matrix C

Value

A list with components:

SBC	Schwartz Bayesian Criterion
wHat	vector of intercept terms
AHat	matrix of estimated autoregression coefficients for the fitted model
CHat	noise covariance matrix
resid	residuals from the fitted model

Author(s)

S. M. Barbosa

References

Barbosa S.M., Silva M.E., Fernandes M.J. (2006), Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry. Nonlinear Processes in Geophysics, 13, 177-184.

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

Schneider, T. and Neumaier, A. (2001), A Matlab package fo the estimation of parameters and eigenmodes of multivariate autoregressive models, 27, 1, 58-65.

Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.

Examples

data(pinkham)
y=mAr.est(pinkham,2,5)

---

Multivariate autoregressive analysis in PCA space

Description

Estimation of m-variate AR(p) model in reduced PCA space (for dimensionality reduction) and eigen-decomposition of augmented coefficient matrix

Usage

mAr.pca(x, p, k = dim(x)[2], ...)

Arguments

x	matrix of multivariate time series
p	model order
k	number of principal components to retain
...	additional arguments for specific methods

Value

A list with components:

p	model order
SBC	Schwartz Bayesian Criterion
fraction.variance	fraction of variance explained by the retained components
resid	residuals from the fitted model
eigv	m*p m-dimensional eigenvectors
modes	periods and damping times associated to each eigenmode

Author(s)

S. M. Barbosa

References

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

See Also

mAr.est

Examples

data(sparrows)
A=mAr.est(sparrows,1)$AHat
mAr.eig(A)$modes
mAr.pca(sparrows,1,k=4)$modes

---

Simulation from a multivariate AR(p) model

Description

Simulation from an m-variate AR(p) model

Usage

mAr.sim(w, A, C, N, ...)

Arguments

w	vector of intercept terms
A	matrix of AR coefficients
C	noise covariance matrix
N	length of output time series
...	additional arguments

Details

Simulation from an m-variate AR(p) model given by

$X[t]=w + A1 X[t-1] +...+ Ap X[t-p] +e[t]$

where
X[t]=[X1(t)...Xm(t)]' is a vector of length m
w is a m-length vector of intercept terms
A=[A1 ... Ap] is a m x mp matrix of autoregressive coefficients
e(t) is a m-length uncorrelated noise vector with mean 0 and m x m covariance matrix C

Value

returns a list containg the N simulated observations for each of the m time series

Author(s)

S. M. Barbosa

References

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

Schneider, T. and Neumaier, A. (2001), A Matlab package fo the estimation of parameters and eigenmodes of multivariate autoregressive models, 27, 1, 58-65.

Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.

Examples

w=c(0.25,0.1)
C=rbind(c(1,0.5),c(0.5,1.5))
A=rbind(c(0.4,1.2,0.35,-0.3),c(0.3,0.7,-0.4,-0.5))
x=mAr.sim(w,A,C,N=300)

---

Lydia Pinkham Annual Advertising and Sales data

Description

Annual domestic advertising and sales of Lydia E. Pinkham Medicine Company in thousands of dollars 1907-1960

Usage

data(pinkham)

Format

A data frame with 54 observations on the 2 variables.

Source

Pankratz, A. (1991) Forecasting With Dynamic Regression Models, Wiley.

References

Wei, W. (1994) Time series analysis - univariate and multivariate methods

---

Body measurements of sparrows

Description

Body measurements of 48 female sparrows.

Usage

data(sparrows)

Format

A data frame with 48 observations on 5 variables

Source

Manly, B. F. J. (1994). Multivariate Statistical Methods, second edition, Chapman and Hall.

---

Time series of ocean wave height measurements

Description

Ocean wave height measurements from an wire wave gauge and an infrared wave gauge

Usage

data(waves)

Format

A data frame with 4096 observations on the following 2 variables.

wire.gauge

height of ocean waves from wire wave gauge

ir.gauge

height of ocean waves from infrared wave gauge

Details

Time series of ocean wave height measurements (sampling = 1/ 30 seconds)

Source

Applied Physics Laboratory (Andy Jessup)

References

Jessup, A. T., Melville, W. K., Keller, W. C. (1991). Breaking Waves Affecting Microwave Backscatter: Detection and Verification (1991). Journal of Geophysical Research, 96, C11, 20,547–59.

Percival, D. B. (1993). Spectral Analysis of Univariate and Bivariate Time Series, Chapter 11 of "Statistical Methods for Physical Science," Stanford, J. L. and Vardeman, S. B. (Eds), Academic Press

---