Plot ARMAX/GARCH model responses
garchplot has been removed.
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.
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.
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.
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.
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)
Load the Deutschmark/British pound foreign-exchange rate data and convert prices to returns:
load Data_MarkPound dem2gbp = price2ret(Data);
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.
Plot the results: