Keyword: 一変量, GJR, GARCH, 非対称, パラメータ推定
概要
本サンプルは一変量の非対称なGJR GARCHプロセスのパラメータ推定を行うC言語によるサンプルプログラムです。 本サンプルでは nag_rand_garchGJR (g05pfc)により生成される時系列を分析対象としています。
※本サンプルはnAG Cライブラリに含まれる関数 nag_estimate_garchGJR() のExampleコードです。本サンプル及び関数の詳細情報は nag_estimate_garchGJR のマニュアルページをご参照ください。
ご相談やお問い合わせはこちらまで
出力結果
（本関数の詳細はnag_estimate_garchGJR のマニュアルページを参照）| この出力例をダウンロード |
nag_estimate_garchGJR (g13fec) Example Program Results
Parameter estimates Standard errors Correct values
0.3852 (0.1074) 0.4000
0.0603 (0.0280) 0.1000
0.7207 (0.0568) 0.7000
0.1674 (0.0495) 0.1000
4.0146 (0.1709) 4.0000
1.4593 (0.1613) 1.5000
2.4538 (0.1006) 2.5000
6 step forecast = 1.7344
- ３〜１０行目にパラメータ推定値、標準誤差、正しい値が出力されています。
- １２行目には6ステップ先の予測値が出力されています。
ソースコード
（本関数の詳細はnag_estimate_garchGJR のマニュアルページを参照）
※本サンプルソースコードはnAG数値計算ライブラリ（Windows, Linux, MAC等に対応）の関数を呼び出します。
サンプルのコンパイル及び実行方法
| このソースコードをダウンロード |
/* nag_estimate_garchGJR (g13fec) Example Program.
*
* CLL6I261D/CLL6I261DL Version.
*
* Copyright 2017 Numerical Algorithms Group.
*
* nAG C Library
*
* Mark 26.1, 2017.
*
*/
#include <nag.h>
#include <nag_stdlib.h>
#include <stdio.h>
#include <ctype.h>
#include <math.h>
#include <nagg05.h>
#include <nagg13.h>
#define X(I, J) x[(I) *tdx + (J)]
int main(void)
{
/* Integer scalar and array declarations */
Integer exit_status = 0;
Integer i, j, k, npar, tdc, tdx, lr, lstate;
Integer *state = 0;
/* nAG structures and data types */
NagError fail;
Nag_Boolean fcall;
/* Double scalar and array declarations */
double fac1, hp, lgf, xterm;
double *covar = 0, *cvar = 0, *etm = 0, *ht = 0;
double *htm = 0, *r = 0, *sc = 0, *se = 0, *theta = 0;
double *x = 0, *yt = 0;
/* Choose the base generator */
Nag_BaseRNG genid = Nag_Basic;
Integer subid = 0;
/* Set the seed */
Integer seed[] = { 1762543 };
Integer lseed = 1;
/* Set parameters for the (randomly generated) time series ... */
/* Generate data assuming normally distributed errors */
Nag_ErrorDistn dist = Nag_NormalDistn;
double df = 0;
/* Size of the time series */
Integer num = 1000;
/* MA and AR parameters */
Integer ip = 1;
Integer iq = 1;
double param[] = { 0.4, 0.1, 0.7 };
/* Asymmetry parameter */
double gamma = 0.1;
/* Regression parameters */
Integer nreg = 2;
double mean = 4.0;
double bx[] = { 1.5, 2.5 };
/* ... end of parameters for (randomly generated) time series */
/* When fitting a model to the time series ... */
/* Include mean in the model */
Integer mn = 1;
/* Use the following maaximum number of iterations and tolerance */
Integer maxit = 50;
double tol = 1e-12;
/* Enforce stationary conditions */
Nag_Garch_Stationary_Type stat_opt = Nag_Garch_Stationary_True;
/* Estimate initial values for regression parameters */
Nag_Garch_Est_Initial_Type est_opt = Nag_Garch_Est_Initial_True;
/* Set the number of values to forecast from the fitted model */
Integer nt = 6;
/* ... end of model fitting options */
/* Initialize the error structure */
INIT_FAIL(fail);
printf("nag_estimate_garchGJR (g13fec) Example Program Results \n\n");
/* Get the length of the state array */
lstate = -1;
nag_rand_init_repeatable(genid, subid, seed, lseed, state, &lstate, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_init_repeatable (g05kfc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Derive various amounts */
npar = iq + ip + 1;
tdx = nreg;
tdc = npar + mn + nreg + 1;
/* Calculate the size of the reference vector */
lr = 2 * (iq + ip + 2);
if (!(covar = nAG_ALLOC((npar + mn + nreg + 1) * tdc, double))
|| !(etm = nAG_ALLOC(num, double))
|| !(ht = nAG_ALLOC(num, double))
|| !(htm = nAG_ALLOC(num, double))
|| !(r = nAG_ALLOC(lr, double))
|| !(state = nAG_ALLOC(lstate, Integer))
|| !(sc = nAG_ALLOC(npar + mn + nreg + 1, double))
|| !(se = nAG_ALLOC(npar + mn + nreg + 1, double))
|| !(theta = nAG_ALLOC(npar + mn + nreg + 1, double))
|| !(cvar = nAG_ALLOC(nt, double))
|| !(x = nAG_ALLOC(num * tdx, double))
|| !(yt = nAG_ALLOC(num, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Initialize the generator to a repeatable sequence */
nag_rand_init_repeatable(genid, subid, seed, lseed, state, &lstate, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_init_repeatable (g05kfc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Set up the time dependent exogenous matrix x */
for (i = 0; i < num; ++i) {
fac1 = (double) (i + 1) * 0.01;
X(i, 1) = sin(fac1) * 0.7 + 0.01;
X(i, 0) = fac1 * 0.1 + 0.5;
}
/* Generate a realization of a random GARCH GJR time series and discard it */
fcall = Nag_TRUE;
nag_rand_garchGJR(dist, num, ip, iq, param, gamma, df, ht, yt, fcall, r, lr,
state, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_garchGJR (g05pfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Generate a realization of a random GARCH GJR time series to use */
fcall = Nag_FALSE;
nag_rand_garchGJR(dist, num, ip, iq, param, gamma, df, ht, yt, fcall, r, lr,
state, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_garchGJR (g05pfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Adjust the randomly generated time series to take into account for the
exogenous matrix x */
for (i = 0; i < num; ++i) {
xterm = 0.0;
for (k = 0; k < nreg; ++k)
xterm += X(i, k) * bx[k];
if (mn == 1)
yt[i] = mean + xterm + yt[i];
else
yt[i] = xterm + yt[i];
}
/* Set initial estimates for the parameters */
for (i = 0; i < npar; ++i)
theta[i] = param[i] * 0.5;
theta[npar] = gamma * 0.5;
if (mn == 1)
theta[npar + 1] = mean * 0.5;
for (i = 0; i < nreg; ++i)
theta[npar + 1 + mn + i] = bx[i] * 0.5;
/* nag_estimate_garchGJR (g13fec).
* Univariate time series, parameter estimation for an
* asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH
* process
*/
nag_estimate_garchGJR(yt, x, tdx, num, ip, iq, nreg, mn,
theta, se, sc, covar, tdc, &hp,
etm, htm, &lgf, stat_opt, est_opt, maxit, tol, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_estimate_garchGJR (g13fec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Display the results */
printf(" Parameter estimates Standard errors "
"Correct values\n");
for (j = 0; j < npar; ++j)
printf("%20.4f (%6.4f) %20.4f\n", theta[j], se[j], param[j]);
printf("%20.4f (%6.4f) %20.4f\n", theta[npar], se[npar], gamma);
if (mn)
printf("%20.4f (%6.4f) %20.4f\n", theta[npar + 1],
se[npar + 1], mean);
for (j = 0; j < nreg; ++j)
printf("%20.4f (%6.4f) %20.4f\n",
theta[npar + 1 + mn + j], se[npar + 1 + mn + j], bx[j]);
/* Now forecast nt steps ahead */
gamma = theta[npar];
/* nag_forecast_garchGJR (g13ffc).
* Univariate time series, forecast function for an
* asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH
* process
*/
nag_forecast_garchGJR(num, nt, ip, iq, theta, gamma, cvar, htm, etm, &fail);
printf("\n%ld step forecast = %8.4f\n", nt, cvar[nt - 1]);
END:
nAG_FREE(covar);
nAG_FREE(etm);
nAG_FREE(ht);
nAG_FREE(htm);
nAG_FREE(sc);
nAG_FREE(se);
nAG_FREE(theta);
nAG_FREE(cvar);
nAG_FREE(x);
nAG_FREE(yt);
nAG_FREE(r);
nAG_FREE(state);
return exit_status;
}