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libpdl-stats-perl - collection of statistics modules in Perl Data Language…  more info»

PDL::Stats::TS.3pm.gz

TS(3pm)          User Contributed Perl Documentation         TS(3pm)



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); int d(); [o]xd(t))

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

       dseason 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 );

   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); int 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 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.

   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. SchA~Xtz, W., & Kolassa, 2006).

       Usage:

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

       wmape 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]

   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.

       SchA~Xtz, 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.



perl v5.14.2                 2012-06-07                      TS(3pm)
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