math
Class Stats

java.lang.Object
  math.Stats

public class Stats
extends java.lang.Object

User: lyon Date: Aug 27, 2007 Time: 7:15:31 AM Copyright DocJava, Inc. 2005.

Constructor Summary

Stats()

Method Summary

static double	avg(double[] source, int period, int startPoint)
static double	bestFit(double[] source, int period) Calculate the line of best fit of the data given by source.
static double[]	bestFitFunction(double[] source, int period) Return the equation of the line of best fit of the data given by source.
static double	bollingerLower(double[] source, int period, double standardDeviation) Calculate the lower band of the bollinger graph.
static double	bollingerUpper(double[] source, int period, double standardDeviation) Calculate the upper band of the bollinger graph.
double	corr(double[] x, double[] y, int period) Calculate the Pearson product-moment correlation between the two variables.
static double[]	cumProbability(double[] data, double[] x) This method calculates the cumulative probability curve of array data at locations x.
static double	cumulativeNormalDistributionFunction(double x)
static double	ema(double[] source, int period, double smoothingConstant) Calculate the Exponential Moving Average (EMA) value.
static double	ema(double[] source, int period, int startPoint, double smoothingConstant)
static double	getAverage(byte[] in)
static double	getAverage(double[] in)
static double	getAverage(short[] in)
static double	getAverageUnsigned(byte[] in)
static double[]	getAvg(double[] source, int period) Find the average of the given data.
static double	getCoefficientOfVariation(double[] doubles) Compute the coefficient of variation by dividing the standard deviation by the sample mean
static double[]	getEma(double[] source, int period, double smoothingConstant) Calculate the Exponential Moving Average (EMA) value.
static double	getMean(double[] source, int period) Find the average of the given quotes.
static double	getStandardDeviation(double[] d)
static double	getStandardDeviation(double[] source, int period) Find the standard deviation of the given values.
static double	getVariance(double[] data) This method calculates variance of a data set.
static double[]	getWindowedSums(double[] source, int period) Find the sum of the given data.
static double	getWindowSum(double[] source, int period, int startPoint) Add up the data from the start point for period data points
static double	interp1(double[] x, double[] y, double x0) This method linearly interpolates the (x,y) data at points x0.
static double	macd(double[] sourceSlow, double[] sourceFast) Calculate the Moving Average Convergence Divergence (MACD) value.
static double	median(double[] data) This method calculates the median of a data set.
static double	momentum(double[] source, int period) Calculate the Momentum value.
static int	obv(double[] sourceOpen, double[] sourceClose, double[] sourceVolume, int range, int initialValue) Calculate the On Balance Volume (OBV) value.
static double	powerMovingAverage(double[] sampleData, int startPoint, int period) startpoint < sampleData.length - period
static double	roundDouble(double d, int places)
static double	rsi(double[] source, int period) Calculate the Relative Strength Indicator (RSI) value.
static double	sma(double[] sampleData, int startPoint, int period)
static double	stdev(double[] source, int period, int startpoint) Find the standard deviation of the given values.
static void	testSma()

Methods inherited from class java.lang.Object

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

Constructor Detail

Stats

public Stats()

Method Detail

stdev

public static double stdev(double[] source,
                           int period,
                           int startpoint)

Find the standard deviation of the given values. This algorithm will calculate the standard deviation of the first period days. If a quote is missing on any of the days, then that day will be skipped and the function will find the average of the shorter period.

Parameters:

source - the source quotes

period - the number of days to average

Returns:

the standard deviation

avg

public static double avg(double[] source,
                         int period,
                         int startPoint)

getWindowSum

public static double getWindowSum(double[] source,
                                  int period,
                                  int startPoint)

Add up the data from the start point for period data points

Parameters:

source -

period -

startPoint -

Returns:

getAvg

public static double[] getAvg(double[] source,
                              int period)

Find the average of the given data. This function will calculate the average of the first period days. If a quote is missing on any of the days, then that day will be skipped and the function will find the average of the shorter period.

Parameters:

source - source of quotes to average

period - the number of days to average

Returns:

the average

getAverage

public static double getAverage(double[] in)

getAverage

public static double getAverage(short[] in)

getAverage

public static double getAverage(byte[] in)

getAverageUnsigned

public static double getAverageUnsigned(byte[] in)

getWindowedSums

public static double[] getWindowedSums(double[] source,
                                       int period)

Find the sum of the given data. This function will calculate the sum of the first period days. If a quote is missing on any of the days, then that day will be skipped and the function will find the sum of the shorter period.

Parameters:

source - source of data to sum

period - the number of days to sum

Returns:

the sum

getStandardDeviation

public static double getStandardDeviation(double[] source,
                                          int period)

Find the standard deviation of the given values. This algorthim will calculate the standard deviation of the first period days. If a quote is missing on any of the days, then that day will be skipped and the function will find the average of the shorter period.

Parameters:

source - the source quottes

period - the number of days to average

Returns:

the standard deviation

getStandardDeviation

public static double getStandardDeviation(double[] d)

getMean

public static double getMean(double[] source,
                             int period)

Find the average of the given quotes. This function will calculate the average of the first period days.

Parameters:

source - source of quotes to average

period - the number of days to average

Returns:

the average

getEma

public static double[] getEma(double[] source,
                              int period,
                              double smoothingConstant)

Calculate the Exponential Moving Average (EMA) value. The Exponential Moving Average is a weighted moving average where the most recent values are weighted higher than the previous values.

The formula for the EMA is as follows:

EMA(current) = EMA(previous) + k * (day close - EMA(previous))

Where EMA(current) is the current EMA value you are calculating, EMA(previous) is the previous value and k is a smoothing constant.

Parameters:

source - the source of quotes to average

period - the number of days to analyse

smoothingConstant -

Returns:

the exponential moving average

ema

public static double ema(double[] source,
                         int period,
                         int startPoint,
                         double smoothingConstant)

corr

public double corr(double[] x,
                   double[] y,
                   int period)

Calculate the Pearson product-moment correlation between the two variables. This will return a correlation co-efficient which is in the range of -1 (negative correlation) through to (no correlation) through to 1 (perfect correlation.

The correlation co-efficient is calculated as follows:

 r = sum(Zx * Zy)
     ------------
         N - 1
 

 Where Zx = X - E(X)
            --------
              Sx
 

Where E(X) is the mean of X and Sx is the standard deviation of X.

Simillarly for Zy.

Parameters:

x - values to test against

y - values to detect correlation against x

period - number of days to analyse

Returns:

the correlation co-efficient

rsi

public static double rsi(double[] source,
                         int period)

Calculate the Relative Strength Indicator (RSI) value. Technical Analysis by Martin J. Pring describes the RSI as:

"It is a momentum indicator, or oscillator, that measures the relative internal strength of a security against itself....".

The formula for the RSI is as follows:

 

               100
 RSI = 100 - ------
             1 + RS
 

       average of x days' up closes
 RS = ------------------------------
      average of x days' down closes
 

 

To calculate an X day RSI you need X + 1 quote values. So make the period argument one more day that the period of the RSI.

Returns:

RSI

ema

public static double ema(double[] source,
                         int period,
                         double smoothingConstant)

Calculate the Exponential Moving Average (EMA) value. The Exponential Moving Average is a weighted moving average where the most recent values are weighted higher than the previous values.

The formula for the EMA is as follows:

EMA(current) = EMA(previous) + k * (day close - EMA(previous))

Where EMA(current) is the current EMA value you are calculating, EMA(previous) is the previous value and k is a smoothing constant.

Parameters:

source - the source of quotes to average

period - the number of days to analyse

smoothingConstant - a smoothing constant

Returns:

the exponential moving average

macd

public static double macd(double[] sourceSlow,
                          double[] sourceFast)

Calculate the Moving Average Convergence Divergence (MACD) value. The Moving Average Convergence Divergence is the remainder of the 26 days EMA and the 12 days EMA. The smoothing constant for the EMA functions is set to 0.1.

The formula for the MACD is as follows:

MACD = EMA(26) - EMA(12)

Where EMA(26) is the 26 days EMA and EMA(12) is the 12 days EMA.

Parameters:

sourceSlow - the source of quotes used by EMA to average (slow average)

sourceFast - the source of quotes used by EMA to average (fast average)

Returns:

the moving average convergence divergence

momentum

public static double momentum(double[] source,
                              int period)

Calculate the Momentum value. The Moving Average Convergence Divergence is the remainder of the today value and the period delayed value.

The formula for the Momentum is as follows:

Momentum = Quote(Today) - Quote(Today+1-period)

Where Quote is got from the input parameter: source.

Parameters:

source - the source of quotes

Returns:

the momentum

obv

public static int obv(double[] sourceOpen,
                      double[] sourceClose,
                      double[] sourceVolume,
                      int range,
                      int initialValue)

Calculate the On Balance Volume (OBV) value. The On Balance Volume is counted adding or subtracting the day volume from range until today, starting from an initial value.

The formula for the OBV is as follows:

if close(current)>open(current): OBV(current) = OBV(previous) + Volume(current) if close(current)

Parameters:

sourceOpen - the source of open quotes

sourceClose - the source of close quotes

sourceVolume - the source of volumes

range - the range which we calculate over

initialValue - the starting value of OBV

Returns:

the on balance volume value

bollingerUpper

public static double bollingerUpper(double[] source,
                                    int period,
                                    double standardDeviation)

Calculate the upper band of the bollinger graph. The upper band can be calculated by:

BollingerUpper = Average + 2 * SD

Where SD is the standard deviation.

Parameters:

source - the source of quotes

period - the number of days to analyse

Returns:

the upper bollinger band

bollingerLower

public static double bollingerLower(double[] source,
                                    int period,
                                    double standardDeviation)

Calculate the lower band of the bollinger graph. The lower band can be calculated by:

BollingerLower = Average - 2 * SD

Where SD is the standard deviation.

Parameters:

source - the source of quotes

period - the number of days to analyse

Returns:

the lower bollinger band

roundDouble

public static double roundDouble(double d,
                                 int places)

bestFit

public static double bestFit(double[] source,
                             int period)

Calculate the line of best fit of the data given by source.

using the formula: slope = period * Sum(xy) - Sum(x)Sum(y) / period * Sum(x^2) - (Sum(x))^2 intercept = ( Sum(y) - slope * Sum(x) ) / period

Parameters:

source - the source of quotes

period - the number of days to analyse

Returns:

the value of the trend at the end of period

bestFitFunction

public static double[] bestFitFunction(double[] source,
                                       int period)

Return the equation of the line of best fit of the data given by source. Uses the same formula as bestFit, but returns slope and intercept so that it can be used on charts.

Parameters:

source - the source of quotes

period - the number of days to analyse

Returns:

the value of the trend at the end of period

testSma

public static void testSma()

sma

public static double sma(double[] sampleData,
                         int startPoint,
                         int period)

Parameters:

sampleData -

startPoint - - offset into the sample data

period - - interval of the average

Returns:

powerMovingAverage

public static double powerMovingAverage(double[] sampleData,
                                        int startPoint,
                                        int period)

startpoint < sampleData.length - period

Parameters:

sampleData -

startPoint - - offset into the sample data

period - - interval of the average

Returns:

getCoefficientOfVariation

public static double getCoefficientOfVariation(double[] doubles)

Compute the coefficient of variation by dividing the standard deviation by the sample mean

Parameters:

doubles -

Returns:

a number that is multiplied by 100 to obtain percentage points

cumulativeNormalDistributionFunction

public static double cumulativeNormalDistributionFunction(double x)

median

public static double median(double[] data)

This method calculates the median of a data set.

Parameters:

data - The input data set

Returns:

the median of data.

getVariance

public static double getVariance(double[] data)

This method calculates variance of a data set. This method normalizes by n-1 where n is the sequence length, so it is the best unbiased estimate of variance if the data set is sampled from a normal distribution.

Parameters:

data - The input data set

Returns:

the variance of data.

cumProbability

public static double[] cumProbability(double[] data,
                                      double[] x)

This method calculates the cumulative probability curve of array data at locations x.

Parameters:

data - The input data set

x - The locations to calculate cumulative probability

Returns:

the cumulative probabilities

interp1

public static double interp1(double[] x,
                             double[] y,
                             double x0)

This method linearly interpolates the (x,y) data at points x0. In this method, if x0 < x[0], y0 = y[0], and if x0 > x[x.length-1], y0 = y[x.length-1].

Parameters:

x - Input x values

y - Input y values

x0 - Locations to interpolate

Returns:

the interpolated values