R: Bayesian Type All Subset Analysis

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 : | 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)) * 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).
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 ),
            3,19, byrow=TRUE)

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

      z$arcoef.bay

[Package timsac version 1.3.5 Index]