PDL::Stats::TS(3) 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);

## 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.

## 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.