com.yahoo.egads.utilities

Class SpectralMethods

java.lang.Object

com.yahoo.egads.utilities.SpectralMethods

public class SpectralMethods
extends java.lang.Object

SpectralMethods implements utility functions for: 1. Computing the Hankel matrix of a given time-series, 2. Converting the Hankel matrix representation of the time-series to the regular time-series, 3. Computing te Singular Value Decomposition (SVD) of the time-series' Hankel matrix for the purpose of filtering and smoothing the time-series. The larger singular-values of the time-series' Hankel matrix correspond to the high-variance components of the time-series (i.e. trend and seasonality), while the smaller singular-values correspond to the low-variance components (i.e noise components). The filtering methods: 1. 'VARIANCE' keeps the 'methodParameter'% of the variance in the spectrum and filters out the rest. (Default 'methodParameter' = 0.99) 2. 'EXPLICIT' keeps the largest 'methodParameter' singular-values in the spectrum and filters out the rest. (Default 'methodParameter' = 10) 3. 'K_GAP' first finds the smallest singular-value whose eigen-gap is among the 'methodParameter' largest eigen-gaps in the spectrum, and then filters out all the singular-values smaller than that singular-value. (Default 'methodParameter' = 8) 4. 'SMOOTHNESS' keeps throwing away the lowest singular-values of the spectrum until the Smoothness value of the remainder is higher than or equal to the desired 'methodParameter' level. Note: the Smoothness is computed via computeSmoothness(). (Default 'methodParameter' = 0.97) 5. 'EIGEN_RATIO' first finds the largest singular value whose ration to the largest (first) singular value is greter than or equal 'methodParameter' and then filters out all the singular-values smaller than that singular-value. (Default 'methodParameter' = 0.1) 6. 'GAP_RATIO' is similar to 'EIGEN_RATIO' except that the eigen gap to the largest (first) singular value ratio is used instead of the direct ratio of each singular value to the largest (first) singular value. (Default 'methodParameter' = 0.01)

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SpectralMethods.FilteringMethod

Constructor Summary

Constructors

Constructor and Description
SpectralMethods()

Method Summary

Modifier and Type	Method and Description
static org.apache.commons.math3.linear.RealMatrix	averageHankelMatrix(org.apache.commons.math3.linear.RealMatrix hankelMat, int windowSize)
static org.apache.commons.math3.linear.RealMatrix	createHankelMatrix(org.apache.commons.math3.linear.RealMatrix data, int windowSize)
static org.apache.commons.math3.linear.RealMatrix	mFilter(org.apache.commons.math3.linear.RealMatrix data, int windowSize, SpectralMethods.FilteringMethod method, double methodParameter)
static TimeSeries.DataSequence	mFilter(TimeSeries.DataSequence data, int windowSize, SpectralMethods.FilteringMethod method, double methodParameter)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SpectralMethods

public SpectralMethods()

Method Detail

createHankelMatrix

public static org.apache.commons.math3.linear.RealMatrix createHankelMatrix(org.apache.commons.math3.linear.RealMatrix data,
                                                                            int windowSize)

averageHankelMatrix

public static org.apache.commons.math3.linear.RealMatrix averageHankelMatrix(org.apache.commons.math3.linear.RealMatrix hankelMat,
                                                                             int windowSize)

mFilter

public static org.apache.commons.math3.linear.RealMatrix mFilter(org.apache.commons.math3.linear.RealMatrix data,
                                                                 int windowSize,
                                                                 SpectralMethods.FilteringMethod method,
                                                                 double methodParameter)

mFilter

public static TimeSeries.DataSequence mFilter(TimeSeries.DataSequence data,
                                              int windowSize,
                                              SpectralMethods.FilteringMethod method,
                                              double methodParameter)