Signal Filtering and Generation of Synthetic Time-Series

Reference

• John F. Ehlers, "Cycle Analytics for Traders: Advanced Technical Trading Concepts".

• D. Prichard and J. Theiler, "Generating surrogate data for time series with several simultaneously measured variables".

• H. Vinod and J. Lopez-de-Lacalle, "Maximum entropy bootstrap for time series: the meboot R package".

Characteristics

• The code has been written and tested in Python 3.7.7.
• Implementation of several digital signal filters and functions for the generation of synthetic (surrogate) time-series.
• Filters (filters.py):
  • Generic Generic filter.
  • SMA Simple moving average.
  • EMA Exponential moving average.
  • WMA Weighted moving average.
  • MSMA Modified simple moving average.
  • MLSQ Modified least-squares quadratic.
  • ButterOrig Butterworth original filter.
  • ButterMod Butterworth modified filter.
  • SuperSmooth Supersmoother filter.
  • GaussLow Gauss low pass filter.
  • GaussHigh Gauss high pass filter.
  • BandPass Band-pass filter.
  • BandStop Band-stop filter.
  • ZEMA1 Zero-lag EMA (type 1).
  • ZEMA2 Zero-lag EMA (type 2).
  • InstTrend Instantaneous trendline.
  • SincFilter Sinc function filter.
  • Decycler De-cycler filter.
  • DecyclerOsc De-cycle oscillator.
  • ABG Alpha-beta-gamma filter.
  • Kalman One-dimensional steady-state Kalman filter.
• Synthetic time-series (synthetic.py):
  • synthetic_wave Generates multi-sine wave given periods, amplitudes, and phases.
  • synthetic_sampling Generates surrogates using randomized-sampling (bootstrap) with or without replacement.
  • synthetic_FFT Generates surrogates using the phase-randomized Fourier-transform algorithm.
  • synthetic_MEboot Generates surrogates using the maximum entropy bootstrap algorithm.
• File filters.py includes also functions to plot the filter signal, frequency response, and group delay.
• File synthetic.py includes also functions to differentiate, integrate, normalize, and scale the discrete time-series.
• Usage: python test.py example.

Main Parameters

example Name of the example to run (Filters, Kalman, FFT_boot, ME_boot, Response).

data_file File with the dataset (csv format). The extension is added automatically.

X Dataset to filter/time-series (input). It must be a 1D array, i.e. of shape (:, ), (:, 1), or (1, :).

b Transfer response coefficients (numerator).

a Transfer response coefficients (denominator).

Y Filtered dataset (output).

X_synt Surrogate/synthetic generated time-series (output).

n_reps Number of surrogates/synthetic time-series to generate.

Examples

There are five examples (all of them use the dataset in spx.csv). The results are shown here.

• Filter Example showing filtering using an EMA, a Butterworth modified filter, and a type 2 Zero-lag EMA.

• Kalman Example showing filtering using the three types of Kalman filter (alpha, alpha-beta, and alpha-beta-gamma).

• FFT_boot Example showing the generation of surrogates time-series using the Fourier-transform algorithm and discrete differences.

• ME_boot Example showing the generation of surrogates time-series using the maximum entropy bootstrap algorithm and discrete differences.

• Response Example showing the frequency response and lag/group delay for a band-pass filter.