timsac (version 1.3.0)

bsubst: 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 rl{ 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 f

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).

term.lag

maximum time lag specify the regressors ($L1(i),L2(i),L3(i)$) (i=1,...,nreg) (mtype = 3). rl{ term.lag(1) : maximum time lag of linear term term.lag(2) : maximum time lag of squared term term.lag(

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.

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).

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 $v(p)$.

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 ),
        3,19, byrow=TRUE)

  z <- bsubst(Canadianlynx, 2, 12, 19, Regressor)

  z$arcoef.bay