/// <summary>
/// Linear regression with Y and one or more independent variables
/// equation: y = b0 + b1x1 + b2x2 + ... + b(p-1)x(p-1) + e
/// equation in matrix form: Y = XB + E
/// </summary>
/// <param name="dependent">SeriesVariable. dependent variable</param>
/// <param name="independents">SeriesVariables. independent variable</param>
public LinearRegressionModel(SeriesVariable dependent, SeriesVariables independents)
{
//Vector vY = new Vector(dependent.SeriesValuesNoNaN.ToArray());
//int n = vY.Tuples;
//int p = independents.Count + 1;
//Matrix mX = new Matrix(n, p);
//for (int i = 0; i < p; i++) //kolom
//{
// for (int j = 0; j < n; j++) //baris
// {
// if (i == 0)
// mX[j, i] = 1.0;
// else
// mX[j, i] = independents[i - 1][j];
// }
//}
// changed to deal with missing values
Vector vY = new Vector(dependent.SeriesValuesNoNaN.ToArray());
int n = vY.Tuples;
int p = independents.Count + 1;
Matrix mX = new Matrix(n, p);
for (int i = 0; i < p; i++) //kolom
{
for (int j = 0; j < n; j++) //baris
{
if (i == 0)
mX[j, i] = 1.0;
else
mX[j, i] = independents[i - 1].SeriesValuesNoNaN[j];
}
}
this.lse = new LeastSquareEstimator(mX, vY);
this.f = this.lse.MSR / this.lse.MSE;
this.sigOfF = Distribution.F.PValue(this.f, p - 1, n - p);
double sumOfEtMinusEt_1Square = 0;
double sumOfESquare = this.lse.ESquare[0];
for (int i = 1; i < n; i++)
{
sumOfEtMinusEt_1Square += Math.Pow(this.lse.E[i] - this.lse.E[i - 1],2.0);
sumOfESquare += this.lse.ESquare[i];
}
this.durbinWatson = sumOfEtMinusEt_1Square / sumOfESquare;
this.stdErrorOfParameters = new double[p];
this.t = new double[p];
this.sigOfT = new double[p];
this.lbOfParameters = new double[p];
this.ubOfParameters = new double[p];
for (int i = 0; i < p; i++)
{
this.stdErrorOfParameters[i] = Math.Sqrt(this.lse.SbSquare[i, i]);
this.t[i] = this.lse.B[i] / this.stdErrorOfParameters[i];
this.sigOfT[i] = Distribution.T.PValue(this.t[i], n - p, Distribution.T.TestType.TwoSided);
double error = Distribution.T.InversCDF(0.975, n - p);
this.ubOfParameters[i] = this.lse.B[i] + error * this.stdErrorOfParameters[i];
this.lbOfParameters[i] = this.lse.B[i] - error * this.stdErrorOfParameters[i];
}
this.vifForPredictors = new double[p - 1];
this.partialCorr = new double[p - 1];
this.corr = new double[p - 1];
for (int i = 1; i < p; i++)
{
Vector y = new Vector(mX.GetColData(i));
Matrix x = new Matrix(n, p - 1);
int col = 0;
for (int j = 0; j < p; j++)
{
if (j != i)
{
for (int k = 0; k < n; k++)
{
x[k, col] = mX[k, j];
}
col++;
}
}
Matrix xtx = x.GetTranspose() * x;
Vector xty = x.GetTranspose() * y;
Vector b = xtx.Solve(xty);
Matrix mJ = new Matrix(n, n);
mJ.InitializeAllValue(1.0);
double yty = Vector.DoubleMultiply(y.GetTranspose(), y);
Vector jy = mJ * y;
double ssto = yty - Vector.DoubleMultiply(y.GetTranspose(), jy) / n;
double sse = yty - Vector.DoubleMultiply(b.GetTranspose(), xty);
double ssr = ssto - sse;
double rSquare = ssr / ssto;
this.vifForPredictors[i - 1] = 1 / (1 - rSquare);
this.corr[i - 1] = computePearsonCorr(vY,y);
Vector xty2 = x.GetTranspose() * vY;
Vector b2 = xtx.Solve(xty2);
double yty2 = Vector.DoubleMultiply(vY.GetTranspose(), vY);
double sse2 = yty2 - Vector.DoubleMultiply(b2.GetTranspose(), xty2);
double partDetermination = (sse2 - this.lse.SSE) / sse2;
this.partialCorr[i - 1] = Math.Sqrt(partDetermination);
}
this.expectedResidual = new double[n];
for (int k = 1; k <= n; k++)
{
this.expectedResidual[k - 1] = this.lse.StandardError * Distribution.Normal.InversCDF((k - 0.375) / (n + 0.25));
}
}
/// <summary>
/// Prosedur untuk menghitung inisialisasi nilai awal
/// Nilai awal ditentukan dengan menggunakan lse pada 6 observasi pertama
/// </summary>
private void Init()
{
Matrix x = new Matrix(this.n, 2);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
LeastSquareEstimator lse = new LeastSquareEstimator(x, y);
this.smoothing[0] = this.a * this.y[0] + ((1 - this.a) * (lse.B[0] + lse.B[1]));
this.trend[0] = this.g * (this.smoothing[0] - lse.B[0]) + (1 - this.g) * lse.B[1];
this.predicted[0] = lse.B[0] + lse.B[1];
this.residual[0] = this.y[0] - this.predicted[0];
}
/// <summary>
/// Mengestimasi parameter
/// </summary>
private void estimateParameters()
{
if (this.linearRdb.Checked)
{
x = new Matrix(this.y.Tuples, 2);
for (int i = 0; i < this.y.Tuples; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
lse = new LeastSquareEstimator(x, this.y);
this.trendProperties.initialModel = 1;
this.trendProperties.includedObservations = this.y.Tuples;
this.trendProperties.parameters = lse.B.GetData();
this.trendProperties.sse = lse.SSE;
this.trendProperties.mse = lse.MSE;
this.trendProperties.r = lse.R;
this.trendProperties.rSquare = lse.RSquare;
this.trendProperties.rSquareAdjusted = 1 - (Math.Sqrt(lse.SSE) / lse.SSTO);
this.predicted = lse.YCap.GetData();
this.residual = lse.E.GetData();
}
else if (this.quadraticRdb.Checked)
{
x = new Matrix(this.y.Tuples, 3);
for (int i = 0; i < this.y.Tuples; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
x[i, 2] = Math.Pow(i + 1, 2);
}
lse = new LeastSquareEstimator(x, this.y);
this.trendProperties.initialModel = 2;
this.trendProperties.includedObservations = this.y.Tuples;
this.trendProperties.parameters = lse.B.GetData();
this.trendProperties.sse = lse.SSE;
this.trendProperties.mse = lse.MSE;
this.trendProperties.r = lse.R;
this.trendProperties.rSquare = lse.RSquare;
this.trendProperties.rSquareAdjusted = 1 - (Math.Sqrt(lse.SSE) / lse.SSTO);
this.predicted = lse.YCap.GetData();
this.residual = lse.E.GetData();
}
else if (this.expGrowthRdb.Checked)
{
x = new Matrix(this.y.Tuples, 2);
for (int i = 0; i < this.y.Tuples; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
Vector z = new Vector(this.y.Tuples);
for (int i = 0; i < this.y.Tuples; ++i)
z[i] = Math.Log10(this.y[i]);
lse = new LeastSquareEstimator(x, z);
this.trendProperties.parameters = lse.B.GetData();
this.trendProperties.includedObservations = this.y.Tuples;
this.trendProperties.initialModel = 4;
for (int i = 0; i < 2; ++i)
this.trendProperties.parameters[i] = Math.Pow(10, this.trendProperties.parameters[i]);
predicted = new double[this.y.Tuples];
residual = new double[this.y.Tuples];
for (int i = 0; i < this.y.Tuples; ++i)
{
this.predicted[i] = this.trendProperties.parameters[0] * Math.Pow(this.trendProperties.parameters[1], (i + 1));
this.residual[i] = this.y[i] - this.predicted[i];
}
this.trendProperties.sse = lse.SSE;
this.trendProperties.mse = lse.MSE;
this.trendProperties.r = lse.R;
this.trendProperties.rSquare = lse.RSquare;
this.trendProperties.rSquareAdjusted = 1 - (Math.Sqrt(lse.SSE) / lse.SSTO);
}
else if (this.cubicRdb.Checked)
{
x = new Matrix(this.y.Tuples, 4);
for (int i = 0; i < this.y.Tuples; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
x[i, 2] = Math.Pow(i + 1, 2);
x[i, 3] = Math.Pow(i + 1, 3);
}
lse = new LeastSquareEstimator(x, this.y);
this.trendProperties.initialModel = 3;
this.trendProperties.includedObservations = this.y.Tuples;
this.trendProperties.parameters = lse.B.GetData();
this.trendProperties.sse = lse.SSE;
this.trendProperties.mse = lse.MSE;
this.trendProperties.r = lse.R;
this.trendProperties.rSquare = lse.RSquare;
this.trendProperties.rSquareAdjusted = 1 - (Math.Sqrt(lse.SSE) / lse.SSTO);
this.predicted = lse.YCap.GetData();
this.residual = lse.E.GetData();
}
}
/// <summary>
/// Inisialisasi nilai awal untuk tipe model multiplikatif
/// Nilai awal musiman ditentukan dengan menggunakan Dummy Variabel dari data detrend
/// </summary>
private void InitMultiplicative()
{
//Menghitung nilai detrend
Matrix x = new Matrix(this.n, 2);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
LeastSquareEstimator lse1 = new LeastSquareEstimator(x, this.y);
Vector detrend = new Vector(this.n);
for (int i = 0; i < this.n; i++)
detrend[i] = this.y[i] / lse1.YCap[i];
//Mencari indeks musiman dengan Dummy Regresi
Matrix z = new Matrix(this.n, this.l);
for (int i = 0; i < this.n; i++)
{
for (int j = 0; j < this.l; j++)
{
if (j == this.term[i])
z[i, j] = 1;
else
z[i, j] = 0;
}
}
LeastSquareEstimator lse2 = new LeastSquareEstimator(z, detrend);
double[] seasonalIndex = lse2.B.GetData();
this.EstimateValue();
double smoothing0 = lse.B[0];
double trend0 = lse.B[1];
this.smoothing[0] = (this.alpha * this.y[0] / seasonalIndex[0]) + (1 - this.alpha) * (smoothing0 + trend0);
this.trend[0] = this.gamma * (this.smoothing[0] - smoothing0) + (1 - this.gamma) * trend0;
this.seasonal[0] = (this.beta * this.y[0] / this.smoothing[0]) + (1 - this.beta) * seasonalIndex[0];
this.predicted[0] = (smoothing0 + trend0) * seasonalIndex[0];
this.residual[0] = this.y[0] - this.predicted[0];
for (int i = 1; i < l; i++)
{
this.smoothing[i] = (this.alpha * this.y[i] / seasonalIndex[i]) + (1 - this.alpha) * (this.smoothing[i - 1] + this.trend[i - 1]);
this.trend[i] = this.gamma * (this.smoothing[i] - this.smoothing[i - 1]) + (1 - this.gamma) * this.trend[i - 1];
this.seasonal[i] = (this.beta * this.y[i] / this.smoothing[i]) + (1 - this.beta) * seasonalIndex[i];
this.predicted[i] = (this.smoothing[i - 1] + this.trend[i - 1]) * seasonalIndex[i];
this.residual[i] = this.y[i] - this.predicted[i];
}
}
/// <summary>
/// Prosedur untuk menghitung inisialisasi Pemulusan dan trend periode 0 (nol)
/// Dihitung lse untuk data sebanyak panjang musiman pertama
/// </summary>
private void EstimateValue()
{
//Menghitung nilai detrend
Matrix xL = new Matrix(this.l, 2);
for (int i = 0; i < this.l; ++i)
{
xL[i, 0] = 1;
xL[i, 1] = i + 1;
}
Vector yL = new Vector(this.l);
for (int i = 0; i < this.l; ++i)
yL[i] = this.y[i];
lse = new LeastSquareEstimator(xL, yL);
}
/// <summary>
/// Prosedur untuk menghitung inisialisasi nilai awal
/// nilai awal ditentukan dengan menggunakan lse
/// </summary>
private void Init()
{
Matrix x = new Matrix(this.n, 2);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
LeastSquareEstimator lse = new LeastSquareEstimator(x, y);
double[] parameters = lse.B.GetData();
double w = 1 - this.a;
double a0 = (double)(parameters[0] - ((w / this.a) * parameters[1]));
double b0 = (double)(parameters[0] - (2 * (w / this.a) * parameters[1]));
this.smoothing1[0] = this.a * this.y[0] + w * a0;
this.smoothing2[0] = this.a * this.smoothing1[0] + w * b0; ;
}
private void ComponentTrend()
{
switch (this.initialTrend)
{
case 1:
{
//Model tren linier
x = new Matrix(this.n, 2);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
Vector z = new Vector(this.deseasonal);
lse = new LeastSquareEstimator(x, z);
this.parameters = lse.B.GetData();
for (int i = 0; i < this.n; i++)
this.trend[i] = this.parameters[0] + this.parameters[1] * (i + 1);
break;
}
case 2:
{
//model tren kuadratik
x = new Matrix(this.n, 3);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
x[i, 2] = Math.Pow(i + 1, 2);
}
Vector z = new Vector(this.deseasonal);
lse = new LeastSquareEstimator(x, z);
this.parameters = lse.B.GetData();
for (int i = 0; i < this.n; i++)
this.trend[i] = this.parameters[0] + this.parameters[1] * (i + 1) + this.parameters[2] * Math.Pow(i + 1, 2);
break;
}
case 3:
{
//model tren kubik
x = new Matrix(this.n, 4);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
x[i, 2] = Math.Pow(i + 1, 2);
x[i, 3] = Math.Pow(i + 1, 3);
}
Vector z = new Vector(this.deseasonal);
lse = new LeastSquareEstimator(x, z);
this.parameters = lse.B.GetData();
for (int i = 0; i < this.n; i++)
this.trend[i] = this.parameters[0] + this.parameters[1] * (i + 1) + this.parameters[2] * Math.Pow(i + 1, 2)
+ this.parameters[3] * Math.Pow(i + 1, 3);
break;
}
case 4:
{
//model tren eksponensial
x = new Matrix(this.n, 2);
for (int i = 0; i < this.n; ++i)
{
x[i, 0] = 1;
x[i, 1] = i + 1;
}
Vector z = new Vector(this.n);
for (int i = 0; i < this.n; ++i)
z[i] = Math.Log10(this.deseasonal[i]);
lse = new LeastSquareEstimator(x, z);
this.parameters = lse.B.GetData();
for (int i = 0; i < 2; ++i)
this.parameters[i] = Math.Pow(10, this.parameters[i]);
for (int i = 0; i < this.n; i++)
this.trend[i] = this.parameters[0] * Math.Pow(this.parameters[1], (i + 1));
break;
}
default:
goto case 1;
}
}
