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|README.md||3 years ago|
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Signal Filtering and Generation of Synthetic Time-Series
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".
- 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.
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
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.
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.