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garchplot

Plot ARMAX/GARCH model responses

garchplot has been removed.

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 paths of each array simultaneously because garchplot color codes corresponding paths of each input array. However, the plots can become cluttered if you try to display more than a few paths 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 path 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 path of a univariate time series in which the first row contains the oldest observation of each path 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

  1. Load the Deutschmark/British pound foreign-exchange rate data and convert prices to returns:

    load Data_MarkPound
    dem2gbp = price2ret(Data);
    
  2. 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);
    rng('default')                % make output reproducible
    [e,s,y] = garchsim(coeff, 1000);
    
    ____________________________________________________________
       Diagnostic Information
    
    Number of variables: 4
    
    Functions 
    Objective:                            internal.econ.garchllfn
    Gradient:                             finite-differencing
    Hessian:                              finite-differencing (or Quasi-Newton)
    Nonlinear constraints:                armanlc
    Nonlinear constraints gradient:       finite-differencing
    
    Constraints
    Number of nonlinear inequality constraints: 0
    Number of nonlinear equality constraints:   0
     
    Number of linear inequality constraints:    1
    Number of linear equality constraints:      0
    Number of lower bound constraints:          4
    Number of upper bound constraints:          4
    
    Algorithm selected
       medium-scale: SQP, Quasi-Newton, line-search
    
    
    ____________________________________________________________
       End diagnostic information
    
                                    Max     Line search  Directional  First-order 
     Iter F-count        f(x)   constraint   steplength   derivative   optimality Procedure 
        0      5     -7915.72    -2.01e-06                                         
        1     27     -7916.01    -2.01e-06     7.63e-06    -7.68e+03     1.41e+05   
        2     34     -7959.65   -1.508e-06         0.25         -974     9.85e+07   
        3     42     -7964.03   -3.102e-06        0.125         -380      5.1e+06   
        4     48      -7965.9   -1.578e-06          0.5        -92.8     4.43e+07   
        5     60        -7967   -1.566e-06      0.00781         -520      1.6e+07   
        6     67     -7967.28   -2.407e-06         0.25         -231     2.23e+07   
        7     75     -7972.64   -2.711e-06        0.125         -177     8.62e+06   
        8     81     -7981.52   -1.356e-06          0.5         -150     1.33e+07   
        9     93     -7981.75   -1.473e-06      0.00781        -72.7     2.59e+06   
       10     99     -7982.65   -7.366e-07          0.5        -45.5     1.89e+07   
       11    107     -7983.07   -8.323e-07        0.125        -79.7     4.93e+06   
       12    116     -7983.11   -1.224e-06       0.0625        -20.5     7.44e+06   
       13    121      -7983.9   -7.633e-07            1        -32.5     1.42e+06   
       14    126     -7983.95   -7.983e-07            1        -7.62     6.66e+05   
       15    134     -7983.95   -7.972e-07        0.125          -13     5.73e+05   
    
    Local minimum possible. Constraints satisfied.
    
    fmincon stopped because the predicted change in the objective function
    is less than the selected value of the function tolerance and constraints 
    are satisfied to within the selected value of the constraint tolerance.
    
    
    
    No active inequalities.
    
  3. Plot the results:

    garchplot(e,s,y)
    

See Also

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