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.
dseason
Signature: (x(t); indx d(); [o]xd(t))
Deseasonalize data using moving average filter the size of period d.
dseason processes 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 );
filter_exp
Signature: (x(t); a(); [o]xf(t))
Filter, exponential smoothing. xf(t) = a * x(t) + (1-a) * xf(t-1)
filter_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.
filter_ma
Signature: (x(t); indx q(); [o]xf(t))
Filter, moving average. xf(t) = sum(x(t-q .. t+q)) / (2q + 1)
filter_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 processes 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 processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
wmape
Signature: (a(n); b(n); float+ [o]c())
Weighted mean absolute percent error. avg(abs(error)) / avg(abs(data)). Much more robust compared to mape with division by zero error (cf. Schütz, W., & Kolassa, 2006).
Usage:
$wmape = $y->wmape( $y_pred );
wmape processes 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]
season_m
Given length of season, returns seasonal mean and var for each period (returns seasonal mean only in scalar context).Default options (case insensitive):
START_POSITION => 0, # series starts at this position in season
MISSING => -999, # internal mark for missing points in season
PLOT => 1, # boolean
# see PDL::Graphics::PGPLOT::Window for next options
WIN => undef, # pass pgwin object for more plotting control
DEV => '/xs', # open and close dev for plotting if no WIN
# defaults to '/png' in Windows
COLOR => 1,
See PDL::Graphics::PGPLOT for detailed graphing options.
my ($m, $ms) = $data->season_m( 24, { START_POSITION=>2 } );
plot_dseason
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', # open and close dev for plotting if no WIN
# defaults to '/png' in Windows
COLOR => 1, # data point color
See PDL::Graphics::PGPLOT for detailed graphing options.
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', # open and close dev for plotting
# defaults to '/png' in Windows
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.Schütz, W., & Kolassa, S. (2006). Foresight: advantages of the MAD/Mean ratio over the MAPE. Retrieved Jan 28, 2010, from http://www.saf-ag.com/226+M5965d28cd19.html
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.