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需Jama矩阵运算库.
java版源码:
包含自回归分析/线性回归分析/基金各项指标计算
import Jama.Matrix;
public class test {
public static void main(String[] args){
double rf = 1.0;
double[] rm = {1,2,3,4,3,2,5,6,8,8};
double[] rp = {2,2,3,4,4,3,5,6,9,8};
//线性回归
Linear l = linearRegression(rp,rm,rf);
System.out.println("线性回归");
System.out.println("alpha: "+l.alpha+"\nbeta: "+l.beta+"\nr2: "+l.rsquare);
//自回归
Autoregressive a = autoRegression(rp,2);
System.out.println("自回归");
//参数
for (double ci :a.ratios){
System.out.println("ratio: "+ci);
}
//拟合值
for (double ci :a.estimates){
System.out.println("estimates: "+ci);
}
//噪声
for (double ci :a.noises){
System.out.println("noises: "+ci);
}
//噪声均值
System.out.println("exp noises: "+exp(a.noises));
//噪声方差
System.out.println("dev noises: "+dev(a.noises));
}
//求均值
static double exp(double[] rp){
int len = rp.length;
if (len > 0){
double output = 0.0;
for (double p: rp){
output +=p;
}
output /= len;
return output;
}else {
return -9999;
}
}
//求标准差
static double dev(double[] rp){
int len = rp.length;
if (len > 0){
double output = 0.0;
double exp = exp(rp);
for (double p: rp){
output += Math.pow((p -exp),2);
}
output = Math.sqrt(output/(len -1));
return output;
}else {
return -9999;
}
}
//求下行风险标准差
static double downRisk(double[] rp, double rf){
int len = rp.length;
if (len > 0){
double output = 0.0;
int count = 0;
for (double p: rp){
if (p < rf){
count ++;
output += Math.pow((p - rf),2);
}
}
if (count > 1){
output = Math.sqrt(output/(count -1));
return output;
}else {
System.out.println("益率小于无风险利率的天数刚好为1");
return -9999;
}
}else {
return -9999;
}
}
//求索提诺比率
static double sortinoRatio(double exp, double rf, double dr){
if (dr != 0){
return (exp - rf)/dr;
}else {
System.out.println("下行风险标准差有误");
return -9999;
}
}
//求夏普比率
static double sharpRatio(double exp, double rf, double dp){
if (dp != 0){
return (exp - rf)/dp;
}else {
System.out.println("标准差为0");
return -9999;
}
}
//求线性回归 alpha beta R2
static Linear linearRegression(double[] rp,double[] rm,double rf){
Linear output = new Linear(-9999,-9999,-9999);
int len = rp.length;
int lenrm = rm.length;
if (len > 0){
if (len == lenrm){
double xexp = 0.0;
double yexp = 0.0;
double xsqura = 0.0;
double ysqura = 0.0;
double xy = 0.0;
for (int i = 0; i <len; i++){
double yi = rp[i] - rf;
double xi = rm[i] - rf;
xexp += xi;
yexp += yi;
xy += xi * yi;
xsqura += Math.pow(xi,2);
ysqura += Math.pow(yi,2);
}
xexp /= len;
yexp /= len;
double lxy = xy - len * xexp * yexp;
double lxx = xsqura - len * Math.pow(xexp,2);
double lyy = ysqura - len * Math.pow(yexp,2);
output.beta = lxy / lxx;
output.alpha = yexp - output.beta * xexp;
output.rsquare = Math.pow(lxy,2)/(lxx * lyy);
return output;
}else {
System.out.println("市场收益序列长度不匹配");
}
}else {
System.out.println("收益输入为空");
}
return output;
}
//求詹森系数
static double jensen(double eRp, double eRm, double rf, double beta){
return eRp - rf - beta *(eRm - rf);
}
//求特雷诺系数
static double treynorRatio(double exp, double rf, double beta){
if (beta != 0){
return (exp - rf)/beta;
}else {
System.out.println("系统风险beta为0");
return -9999;
}
}
//自回归分析 求系数 拟合值 噪声序列
static Autoregressive autoRegression(double[] rp, int p){
double[] op = {-9999};
Autoregressive output = new Autoregressive(op,op,op);
int len = rp.length;
if (len < 3 || p < 1 || len <= p +1){
System.out.println("输入有误");
}else {
int leny = len - p;
double[][] y = new double[leny][1];
for (int i = p; i <len; i ++){
y[i-p][0] = rp[i];
}
double[][] a = new double[leny][p];
for (int i = 0; i < leny ; i ++){
for (int j = 0 ; j < p; j ++){
a[i][j] = rp[p -1 - j + i];
}
}
Matrix mY = new Matrix(y);
Matrix mA = new Matrix(a);
Matrix mR = (mA.transpose().times(mA)).inverse().times(mA.transpose()).times(mY);
output.ratios = mR.getColumnPackedCopy();
Matrix mYhat = mA.times(mR);
output.estimates = mYhat.getColumnPackedCopy();
Matrix mNs = mY.minus(mYhat);
output.noises = mNs.getColumnPackedCopy();
}
return output;
}
}
class Linear {
double alpha;
double beta;
double rsquare;
public Linear(double alpha, double beta, double rsquare){
this.alpha = alpha;
this.beta = beta;
this.rsquare = rsquare;
}
}
class Autoregressive {
double[] ratios;
double[] estimates;
double[] noises;
public Autoregressive(double[] ratios, double[] estimates, double[] noises){
this.ratios = ratios;
this.noises = noises;
this.estimates = estimates;
}
}
结果示例:
=线性回归=
alpha: 0.5611510791366894
beta: 0.9496402877697845
r2: 0.9568894502718442
=自回归=
参数
ratio: 0.5716829919857536
ratio: 0.7043633125556548
估计值
estimates: 2.5520926090828167
estimates: 3.12377560106857
estimates: 4.399821905609978
estimates: 5.104185218165633
estimates: 4.532502226179879
estimates: 4.971504897595732
estimates: 6.951914514692795
estimates: 9.37132680320571
噪声
noises: 0.44790739091718335
noises: 0.8762243989314298
noises: -0.3998219056099783
noises: -2.1041852181656333
noises: 0.4674977738201207
noises: 1.0284951024042677
noises: 2.0480854853072046
noises: -1.3713268032057098
噪声均值
exp noises: 0.12410952804986058
噪声方差
dev noises: 1.3514101374682685
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