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.

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

To install PDL::Stats, copy and paste the appropriate command in to your terminal.

cpanm

cpanm PDL::Stats

CPAN shell

perl -MCPAN -e shell
install PDL::Stats

For more information on module installation, please visit the detailed CPAN module installation guide.

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NAME

DESCRIPTION

SYNOPSIS

FUNCTIONS

acf

acvf

diff

inte

dseason

fill_ma

filter_exp

filter_ma

mae

mape

wmape

portmanteau

pred_ar

season_m

plot_dseason

METHODS

plot_acf

REFERENCES

AUTHOR

Module Install Instructions