/// <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>
/// 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;;
}
/// <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];
}
}
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;
}
}
