bsubst {timsac}R Documentation

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 : (polinomial type non-linear model, lag's read in),
3 : (polinomial type non-linear model, lag's automatically set) and
4 : (AR-model with polinomial mean value function).
5,6 and 7 are originaly 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)) * z(n-L2(i)) * 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).
i-th regressor is defined by z(n-L1(i)) * z(n-L2(i)) * z(n-L3(i)), where 0-lag term z(n-0) is replaced by the constant 1.
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 cross 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.
plot logical. If TRUE (default) daic, pre.err 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 (normalisedby 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, 0, 0, 2, 0, 0, 3, 0,  0, 4, 0,  0, 5, 0,  0, 6, 0, 0, 7,
                         0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 1, 1,
                         0, 2, 2, 0, 1, 2, 0, 3,  3, 0, 1,  1, 1, 2,  2, 2, 3, 3, 3 ), 3,19)
  z <- bsubst(Canadianlynx, mtype=2, lag=12, nreg=19, reg=Regressor, cstep=5 )
  z$arcoef.bay

[Package timsac version 1.2.1 Index]