bsubst: Bayesian Type All Subset Analysis

In timsac: Time Series Analysis and Control Package

Bayesian Type All Subset Analysis

Description

Produce Bayesian estimates of time series models such as pure AR models, AR models with non-linear terms, AR models with polynomial type mean value functions, etc. The goodness of fit of a model is checked by the analysis of several steps ahead prediction errors.

Usage

bsubst(y, mtype, lag = NULL, nreg, reg = NULL, term.lag = NULL, cstep = 5,
       plot = TRUE)

Arguments

y	a univariate time series.
mtype	model type. Allowed values are 1 : autoregressive model, 2 : polynomial type non-linear model (lag's read in), 3 : polynomial type non-linear model (lag's automatically set), 4 : AR-model with polynomial mean value function, 5,6,7 : originally defined but omitted here.
lag	maximum time lag. Default is 2 \sqrt{n}, where n is the length of the time series y.
nreg	number of regressors.
reg	specification of regressor (mtype = 2). i-th regressor is defined by z(n-L1(i)) \times z(n-L2(i)) \times z(n-L3(i)), where L1(i) is reg(1,i), L2(i) is reg(2,i) and L3(i) is reg(3,i). 0-lag term z(n-0) is replaced by the constant 1.
term.lag	maximum time lag specify the regressors (L1(i),L2(i),L3(i)) (i=1,...,nreg) (mtype = 3). term.lag[1] : maximum time lag of linear term term.lag[2] : maximum time lag of squared term term.lag[3] : maximum time lag of quadratic crosses term term.lag[4] : maximum time lag of cubic term term.lag[5] : maximum time lag of cubic cross term.
cstep	prediction errors checking (up to cstep-steps ahead) is requested. (mtype = 1, 2, 3).
plot	logical. If TRUE (default), daic, perr and peautcor are plotted.

Details

The AR model is given by ( mtype = 2 )

y(t) = a(1)y(t-1) + ... + a(p)y(t-p) + u(t).

The non-linear model is given by ( mtype = 2, 3 )

y(t) = a(1)z(t,1) + a(2)z(t,2) + ... + a(p)z(t,p) + u(t).

Where p is AR order and u(t) is Gaussian white noise with mean 0 and variance v(p).

Value

ymean	mean of y.
yvar	variance of y.
v	innovation variance.
aic	AIC(m), (m=0, ... nreg).
aicmin	minimum AIC.
daic	AIC(m)-aicmin (m=0, ... nreg).
order.maice	order of minimum AIC.
v.maice	innovation variance attained at order.maice.
arcoef.maice	AR coefficients attained at order.maice.
v.bay	residual variance of Bayesian model.
aic.bay	AIC of Bayesian model.
np.bay	equivalent number of parameters.
arcoef.bay	AR coefficients of Bayesian model.
ind.c	index of parcor2 in order of increasing magnitude.
parcor2	square of partial correlations (normalized by multiplying N).
damp	binomial type damper.
bweight	final Bayesian weights of partial correlations.
parcor.bay	partial correlations of the Bayesian model.
eicmin	minimum EIC.
esum	whole subset regression models.
npmean	mean of number of parameter.
npmean.nreg	= npmean / nreg.
perr	prediction error.
mean	mean.
var	variance.
skew	skewness.
peak	peakedness.
peautcor	autocorrelation function of 1-step ahead prediction error.
pspec	power spectrum (mtype = 1).

References

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(Canadianlynx)
Regressor <- matrix(
     c( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 1, 3, 1, 2, 3,
        0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0, 1, 2, 2, 3, 1, 2, 3,
        0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0, 0, 0, 0, 0, 1, 2, 3 ),
     nrow = 3, ncol = 19, byrow = TRUE)
z <- bsubst(Canadianlynx, mtype = 2, lag = 12, nreg = 19, Regressor)
z$arcoef.bay

timsac documentation built on Sept. 30, 2023, 5:06 p.m.