Provided by: libpdl-stats-perl_0.75-2build1_amd64 bug

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

       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.