/ 
PDL-Stats-0.3.2
River stage one • 3 direct dependents • 4 total dependents
/ PDL::Stats::TS

NAME

PDL::Stats::TS -- basic time series functions

DESCRIPTION

The terms FUNCTIONS and METHODS are arbitrarily used to refer to methods that are threadable and methods that are NOT threadable, respectively. Plots require PDL::Graphics::PGPLOT.

***EXPERIMENTAL!*** In particular, bad value support is spotty and may be shaky. USE WITH DISCRETION!

SYNOPSIS

use PDL::LiteF;
use PDL::NiceSlice;
use PDL::Stats::TS;

my $r = $data->acf(5);

FUNCTIONS

acf

Signature: (x(t); int h(); [o]r(h+1))

Autocorrelation function for up to lag h. If h is not specified it's set to t-1 by default.

acf does not process bad values.

usage:

perldl> $a = sequence 10

# lags 0 .. 5

perldl> p $a->acf(5)
[1 0.7 0.41212121 0.14848485 -0.078787879 -0.25757576]

acvf

Signature: (x(t); int h(); [o]v(h+1))

Autocovariance function for up to lag h. If h is not specified it's set to t-1 by default.

acvf does not process bad values.

usage:

perldl> $a = sequence 10

# lags 0 .. 5

perldl> p $a->acvf(5)
[82.5 57.75 34 12.25 -6.5 -21.25]

# autocorrelation

perldl> p $a->acvf(5) / $a->acvf(0)
[1 0.7 0.41212121 0.14848485 -0.078787879 -0.25757576]

diff

Signature: (x(t); [o]dx(t))

Differencing. DX(t) = X(t) - X(t-1), DX(0) = X(0). Can be done inplace.

diff does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

inte

Signature: (x(n); [o]ix(n))

Integration. Opposite of differencing. IX(t) = X(t) + X(t-1), IX(0) = X(0). Can be done inplace.

inte does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

dsea

Signature: (x(t); int d(); [o]xd(t))

Deseasonalize data using moving average filter the size of period d.

dsea does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

fill_ma

Signature: (x(t); int q(); [o]xf(t))

Fill missing value with moving average. xf(t) = sum(x(t-q .. t-1, t+1 .. t+q)) / 2q.

fill_ma does handle bad values. Output pdl bad flag is cleared unless the specified window size q is too small and there are still bad values.

my $x_filled = $x->fill_ma( $q );

filt_exp

Signature: (x(t); a(); [o]xf(t))

Filter, exponential smoothing. xf(t) = a * x(t) + (1-a) * xf(t-1)

filt_exp does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

filt_ma

Signature: (x(t); int q(); [o]xf(t))

Filter, moving average. xf(t) = sum(x(t-q .. t+q)) / (2q + 1)

filt_ma does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

mae

Signature: (a(n); b(n); float+ [o]c())

Mean absolute error. MAE = 1/n * sum( abs(y - y_pred) )

Usage:

$mae = $y->mae( $y_pred );

mae does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

mape

Signature: (a(n); b(n); float+ [o]c())

Mean absolute percent error. MAPE = 1/n * sum(abs((y - y_pred) / y))

Usage:

$mape = $y->mape( $y_pred );

mape does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

portmanteau

Signature: (r(h); longlong t(); [o]Q())

Portmanteau significance test (Ljung-Box) for autocorrelations.

Usage:

  perldl> $a = sequence 10

  # acf for lags 0-5
  # lag 0 excluded from portmanteau
  
  perldl> p $chisq = $a->acf(5)->portmanteau( $a->nelem )
  11.1753902662994
 
  # get p-value from chisq distr

  perldl> use PDL::GSL::CDF
  perldl> p 1 - gsl_cdf_chisq_P( $chisq, 5 )
  0.0480112934306748

portmanteau does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

pred_ar

Signature: (x(d); b(p|p+1); int t(); [o]pred(t))

Calculates predicted values up to period t (extend current series up to period t) for autoregressive series, with or without constant. If there is constant, it is the last element in b, as would be returned by ols or ols_t.

pred_ar does not process bad values.

CONST  => 1,

Usage:

   perldl> $x = sequence 2

     # last element is constant
   perldl> $b = pdl(.8, -.2, .3)

   perldl> p $x->pred_ar($b, 7)
   [0       1     1.1    0.74   0.492  0.3656 0.31408]

     # no constant
   perldl> p $x->pred_ar($b(0:1), 7, {const=>0})
   [0       1     0.8    0.44   0.192  0.0656 0.01408]

plot_dsea

Plots deseasonalized data and original data points. Opens and closes default window for plotting unless a pgwin object is passed in options. Returns deseasonalized data.

Default options (case insensitive):

WIN   => undef,
DEV   => "/xs",
COLOR => 1,       # data point color

See PDL::Graphics::PGPLOT for detailed graphing options.

plot_season

Seasonal subseries plot. Given length of season, plots mean and returns sample mean and sample var for each period.

$data should be pdl dim (period) or (period x series). $data must start from period 0. If actual data starts later into the season, set previous periods to bad.

Default options (case insensitive):

WIN   => undef,
DEV   => "/xs",
COLOR => 1,

See PDL::Graphics::PGPLOT for detailed graphing options.

$data->plot_season( 24, { DEV=>'/png' } );

METHODS

plot_acf

Plots and returns autocorrelations for a time series.

Default options (case insensitive):

SIG => 0.05,    # can specify .10, .05, .01, or .001
DEV => "/xs",   # see PDL::Graphics::PGPLOT

Usage:

perldl> $a = sequence 10

perldl> p $r = $a->plot_acf(5)
[1 0.7 0.41212121 0.14848485 -0.078787879 -0.25757576]

REFERENCES

Brockwell, P.J., & Davis, R.A. (2002). Introcution to Time Series and Forecasting (2nd ed.). New York, NY: Springer.

AUTHOR

Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>

All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file COPYING in the PDL distribution.