# formSmpl: Form the Posterior Sample In bayesGARCH: Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations

## Description

Form the joint posterior sampler from the MCMC output.

## Usage

 `1` ``` formSmpl(MCMC, l.bi = 0, batch.size = 1) ```

## Arguments

 `MCMC` object of the class `mcmc.list` (R package coda) or a list of matrices or a matrix. `l.bi` length of the burn-in phase. `batch.size` batching size used to diminish the autocorrelation within the chains.

## Value

The joint posterior sample as an `mcmc` object (R package coda).

## Note

Please cite the package in publications. Use `citation("bayesGARCH")`.

`bayesGARCH` for the Bayesian estimation of the GARCH(1,1) model with Student-t innovations.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` ## !!! INCREASE THE NUMBER OF MCMC ITERATIONS !!! ## LOAD DATA SET data(dem2gbp) y <- dem2gbp[1:750] ## RUN THE ESTIMATION MCMC <- bayesGARCH(y, control = list(n.chain = 2, l.chain = 100)) ## FORM THE SAMPLE FROM THE MCMC OUTPUT smpl <- formSmpl(MCMC, l.bi = 50, batch.size = 2) ## POSTERIOR STATISTICS summary(smpl) ```

### Example output

```chain:  1  iteration:  10  parameters:  0.0413 0.1873 0.6672 80.0681
chain:  1  iteration:  20  parameters:  0.0397 0.2532 0.6289 111.4176
chain:  1  iteration:  30  parameters:  0.0601 0.2385 0.5648 128.3438
chain:  1  iteration:  40  parameters:  0.0649 0.2043 0.5913 135.7295
chain:  1  iteration:  50  parameters:  0.0517 0.2186 0.6215 125.522
chain:  1  iteration:  60  parameters:  0.0401 0.2344 0.6546 106.9591
chain:  1  iteration:  70  parameters:  0.0472 0.16 0.6886 122.3733
chain:  1  iteration:  80  parameters:  0.0342 0.2067 0.6644 86.1813
chain:  1  iteration:  90  parameters:  0.0275 0.283 0.66 137.1891
chain:  1  iteration:  100  parameters:  0.0504 0.2691 0.5906 119.5155
chain:  2  iteration:  10  parameters:  0.0375 0.2163 0.7045 72.9043
chain:  2  iteration:  20  parameters:  0.0552 0.2582 0.6086 66.4738
chain:  2  iteration:  30  parameters:  0.0552 0.2401 0.5912 62.2921
chain:  2  iteration:  40  parameters:  0.0473 0.2028 0.6493 73.8324
chain:  2  iteration:  50  parameters:  0.0501 0.2306 0.6155 90.2817
chain:  2  iteration:  60  parameters:  0.0531 0.3456 0.5545 67.0353
chain:  2  iteration:  70  parameters:  0.0576 0.2832 0.5626 70.8458
chain:  2  iteration:  80  parameters:  0.0474 0.3112 0.5887 69.415
chain:  2  iteration:  90  parameters:  0.0509 0.2573 0.5957 116.0901
chain:  2  iteration:  100  parameters:  0.0384 0.2191 0.6504 72.6474

n.chain:  2
l.chain:  100
l.bi:  50
batch.size:  2
smpl size:  50

Iterations = 1:50
Thinning interval = 1
Number of chains = 1
Sample size per chain = 50

1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:

Mean        SD Naive SE Time-series SE
alpha0  0.04851  0.009319 0.001318       0.002593
alpha1  0.23908  0.042203 0.005968       0.009328
beta    0.62026  0.043774 0.006191       0.027919
nu     98.34994 22.751336 3.217525       7.330513

2. Quantiles for each variable:

2.5%      25%       50%       75%    97.5%
alpha0  0.03333  0.04279   0.04832   0.05371   0.0711
alpha1  0.18593  0.20436   0.23496   0.26137   0.3269
beta    0.55992  0.58864   0.60994   0.66428   0.6928
nu     67.02528 78.25008 101.10804 114.20171 140.7397
```

bayesGARCH documentation built on May 17, 2021, 1:09 a.m.