--- name: "PDL::Stats::TS" section: "3pm" platform: "linux" package: "libpdl-stats-perl" version: "0.82-3" release: "Debian 12 (Bookworm)" platforms: ["linux"] url: "https://new.carta.tech/PDL::Stats::TS" --- # PDL::Stats::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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 ndarrays if the flag is set for any of the input ndarrays. ### 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 => 0, # 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 \ 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.