GARCH Toolbox™

garchplot

Plot matched univariate innovations, volatility, and return series

Syntax

garchplot(Innovations,Sigmas,Series)

Description

garchplot(Innovations,Sigmas,Series) lets you visually compare matched innovations, conditional standard deviations, and returns. It provides a convenient way to compare innovations series, simulated using garchsim or estimated using garchfit, with companion conditional standard deviations, or returns series. You can also use garchplot to plot forecasts, computed using garchpred, of conditional standard deviations and returns.

In general, garchplot produces a tiered plot of matched time series. garchplot does not display an empty or missing input array; it allocates no space to the array in the tiered figure window. garchplot displays valid (nonempty) Innovations, Sigmas, and Series arrays in the top, center, and bottom plots, respectively. Because garchplot assigns a title and label to each plot according to its position in the argument list, you can ensure correct plot annotation by using empty matrices ([]) as placeholders.

You can plot several realizations of each array simultaneously because garchplot color codes corresponding realizations of each input array. However, the plots can become cluttered if you try to display more than a few realizations of each input at one time.

Input Arguments

`Innovations`	Time-series column vector or matrix of innovations. As a column vector, `Innovations` represents a single realization of a univariate time series. The first element of this time series contains the oldest observation, and the last element the most recent. As a matrix, each column of `Innovations` represents a single realization of a univariate time series in which the first row contains the oldest observation of each realization and the last row the most recent. If `Innovations = []`, then `garchplot` does not display it.
`Sigmas`	Time-series column vector or matrix of conditional standard deviations. In general, `Innovations` and `Sigmas` are the same size, and form a matching pair of arrays. If `Sigmas = []`, then `garchplot` does not display it.
`Series`	Time-series column vector or matrix of asset returns. In general, `Series` is the same size as `Innovations` and `Sigmas`, and `garchplot` organizes it in the same way. If `Series = []` or is unspecified, then `garchplot` does not display it.

Examples

Example 1

Plot Innovations, Sigmas, and Series, assuming that they are not empty:

garchplot(Innovations)
garchplot(Innovations, [], Series)
garchplot([], Sigmas, Series) 
garchplot(Innovations, Sigmas, Series)
garchplot(Innovations, Sigmas, [])
garchplot(Innovations, Sigmas)

Example 2

Load the default GARCH(1,1) model to model the Deutschmark/British pound foreign-exchange series DEM2GBP:
```
load garchdata
dem2gbp = price2ret(DEM2GBP);
```
Use the estimated model to generate a single path of 1000 observations for return series, innovations, and conditional standard deviation processes:
```
[coeff, errors, LLF, innovations, sigmas] = garchfit(dem2gbp);
randn('state', 0);
rand('twister', 0);
[e, s, y] = garchsim(coeff, 1000);
```
Plot the results:
```
garchplot(e, s, y)
```