Keyword: 一変量時系列, GARCH, 非対称, パラメータ推定
概要
本サンプルは一変量の対称なGARCHプロセスもしくはAGARCH type1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_agarchI (g05pdc)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_agarchI() のExampleコードです。本サンプル及び関数の詳細情報は nag_estimate_agarchI 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_agarchI 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_agarchI (g13fac) Example Program Results
Parameter estimates Standard errors Correct values
0.1045 (0.0486) 0.1500
0.0884 (0.0235) 0.1000
0.8196 (0.0433) 0.8000
-0.7658 (0.2296) -0.3000
3.0051 (0.1309) 3.0000
1.4478 (0.0779) 1.5000
2.4681 (0.1229) 2.5000
3 step forecast = 1.1019
- 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_agarchI 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_agarchI (g13fac) Example Program.
*
* CLL6I261D/CLL6I261DL Version.
*
* Copyright 2017 Numerical Algorithms Group.
*
* 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, lstate, lr;
Integer *state = 0;
/* nAG structures and data types */
NagError fail;
Nag_Boolean fcall;
/* Double scalar and array declarations */
double *covar = 0, *cvar = 0, *et = 0, *ht = 0, *r = 0;
double *sc = 0, *se = 0, *theta = 0, *x = 0, *yt = 0;
double fac1, hp, lgf, xterm;
/* 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[] = { 0.15, 0.1, 0.8, 0.1 };
/* Asymmetry parameter */
double gamma = -0.3;
/* Regression parameters */
Integer nreg = 2;
double mean = 3.0;
double bx[] = { 1.5, 2.5 };
/* ... end of parameters for (randomly generated) time series */
/* When fitting a model to the time series ... */
/* Include asymmetry parameter in the model */
Integer isym = 1;
/* 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 = 3;
/* ... end of model fitting options */
/* Initialize the error structure */
INIT_FAIL(fail);
printf("nag_estimate_agarchI (g13fac) 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;
tdc = npar + mn + isym + nreg;
tdx = nreg;
/* Calculate the size of the reference vector */
lr = 2 * (iq + ip + 2);
/* Allocate arrays */
if (!(covar = nAG_ALLOC((npar + mn + isym + nreg) * tdc, double)) ||
!(et = nAG_ALLOC(num, double)) ||
!(ht = nAG_ALLOC(num, double)) ||
!(sc = nAG_ALLOC(npar + mn + isym + nreg, double)) ||
!(se = nAG_ALLOC(npar + mn + isym + nreg, double)) ||
!(theta = nAG_ALLOC(npar + mn + isym + nreg, double)) ||
!(state = nAG_ALLOC(lstate, Integer)) ||
!(r = nAG_ALLOC(lr, double)) ||
!(x = nAG_ALLOC(num * tdx, double)) ||
!(cvar = nAG_ALLOC(nt, 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, 0) = sin(fac1) * 0.7 + 0.01;
X(i, 1) = fac1 * 0.1 + 0.5;
}
/* Generate a realization of a random AGARCH I time series and discard it */
fcall = Nag_TRUE;
nag_rand_agarchI(dist, num, ip, iq, param, gamma, df, ht, yt, fcall, r, lr,
state, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_agarchI (g05pdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Generate a realization of a random AGARCH I time series to use */
fcall = Nag_FALSE;
nag_rand_agarchI(dist, num, ip, iq, param, gamma, df, ht, yt, fcall, r, lr,
state, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_agarchI (g05pdc).\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;
if (isym == 1)
theta[npar + isym - 1] = gamma * 0.5;
if (mn == 1)
theta[npar + isym] = mean * 0.5;
for (i = 0; i < nreg; ++i)
theta[npar + isym + mn + i] = bx[i] * 0.5;
/* nag_estimate_agarchI (g13fac).
* Univariate time series, parameter estimation for either a
* symmetric GARCH process or a GARCH process with asymmetry
* of the form (epsilon_(t-1)+gamma)^2
*/
nag_estimate_agarchI(yt, x, tdx, num, ip, iq, nreg, mn, isym, theta, se, sc,
covar, tdc, &hp, et, ht, &lgf, stat_opt, est_opt,
maxit, tol, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_estimate_agarchI (g13fac).\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]);
if (isym)
printf("%20.4f (%6.4f) %20.4f\n",
theta[npar + isym - 1], se[npar + isym - 1], gamma);
if (mn)
printf("%20.4f (%6.4f) %20.4f\n", theta[npar + isym],
se[npar + isym], mean);
for (j = 0; j < nreg; ++j)
printf("%20.4f (%6.4f) %20.4f\n",
theta[npar + isym + mn + j], se[npar + isym + mn + j], bx[j]);
/* Now forecast nt steps ahead */
if (isym) {
gamma = theta[npar + isym - 1];
}
else {
gamma = 0.0;
}
/* nag_forecast_agarchI (g13fbc).
* Univariate time series, forecast function for either a
* symmetric GARCH process or a GARCH process with asymmetry
* of the form (epsilon_(t-1)+gamma)^2
*/
nag_forecast_agarchI(num, nt, ip, iq, theta, gamma, cvar, ht, et, &fail);
printf("\n%ld step forecast = %8.4f\n", nt, cvar[nt - 1]);
END:
nAG_FREE(covar);
nAG_FREE(et);
nAG_FREE(ht);
nAG_FREE(sc);
nAG_FREE(se);
nAG_FREE(theta);
nAG_FREE(x);
nAG_FREE(cvar);
nAG_FREE(yt);
nAG_FREE(state);
nAG_FREE(r);
return exit_status;
}