# Overview on extracted features¶

tsfresh calculates a comprehensive number of features. All feature calculators are contained in the submodule:

 `tsfresh.feature_extraction.feature_calculators` This module contains the feature calculators that take time series as input and calculate the values of the feature.

The following list contains all the feature calculations supported in the current version of tsfresh:

 `abs_energy`(x) Returns the absolute energy of the time series which is the sum over the squared values `absolute_maximum`(x) Calculates the highest absolute value of the time series x. `absolute_sum_of_changes`(x) Returns the sum over the absolute value of consecutive changes in the series x `agg_autocorrelation`(x, param) Descriptive statistics on the autocorrelation of the time series. `agg_linear_trend`(x, param) Calculates a linear least-squares regression for values of the time series that were aggregated over chunks versus the sequence from 0 up to the number of chunks minus one. `approximate_entropy`(x, m, r) Implements a vectorized Approximate entropy algorithm. `ar_coefficient`(x, param) This feature calculator fits the unconditional maximum likelihood of an autoregressive AR(k) process. `augmented_dickey_fuller`(x, param) Does the time series have a unit root? `autocorrelation`(x, lag) Calculates the autocorrelation of the specified lag, according to the formula [1] `benford_correlation`(x) Useful for anomaly detection applications [1][2]. `binned_entropy`(x, max_bins) First bins the values of x into max_bins equidistant bins. `c3`(x, lag) Uses c3 statistics to measure non linearity in the time series `change_quantiles`(x, ql, qh, isabs, f_agg) First fixes a corridor given by the quantiles ql and qh of the distribution of x. `cid_ce`(x, normalize) This function calculator is an estimate for a time series complexity [1] (A more complex time series has more peaks, valleys etc.). `count_above`(x, t) Returns the percentage of values in x that are higher than t `count_above_mean`(x) Returns the number of values in x that are higher than the mean of x `count_below`(x, t) Returns the percentage of values in x that are lower than t `count_below_mean`(x) Returns the number of values in x that are lower than the mean of x `cwt_coefficients`(x, param) Calculates a Continuous wavelet transform for the Ricker wavelet, also known as the “Mexican hat wavelet” which is `energy_ratio_by_chunks`(x, param) Calculates the sum of squares of chunk i out of N chunks expressed as a ratio with the sum of squares over the whole series. `fft_aggregated`(x, param) Returns the spectral centroid (mean), variance, skew, and kurtosis of the absolute fourier transform spectrum. `fft_coefficient`(x, param) Calculates the fourier coefficients of the one-dimensional discrete Fourier Transform for real input by fast `first_location_of_maximum`(x) Returns the first location of the maximum value of x. `first_location_of_minimum`(x) Returns the first location of the minimal value of x. `fourier_entropy`(x, bins) Calculate the binned entropy of the power spectral density of the time series (using the welch method). `friedrich_coefficients`(x, param) Coefficients of polynomial , which has been fitted to `has_duplicate`(x) Checks if any value in x occurs more than once `has_duplicate_max`(x) Checks if the maximum value of x is observed more than once `has_duplicate_min`(x) Checks if the minimal value of x is observed more than once `index_mass_quantile`(x, param) Calculates the relative index i of time series x where q% of the mass of x lies left of i. `kurtosis`(x) Returns the kurtosis of x (calculated with the adjusted Fisher-Pearson standardized moment coefficient G2). `large_standard_deviation`(x, r) Does time series have large standard deviation? `last_location_of_maximum`(x) Returns the relative last location of the maximum value of x. `last_location_of_minimum`(x) Returns the last location of the minimal value of x. `lempel_ziv_complexity`(x, bins) Calculate a complexity estimate based on the Lempel-Ziv compression algorithm. `length`(x) Returns the length of x `linear_trend`(x, param) Calculate a linear least-squares regression for the values of the time series versus the sequence from 0 to length of the time series minus one. `linear_trend_timewise`(x, param) Calculate a linear least-squares regression for the values of the time series versus the sequence from 0 to length of the time series minus one. `longest_strike_above_mean`(x) Returns the length of the longest consecutive subsequence in x that is bigger than the mean of x `longest_strike_below_mean`(x) Returns the length of the longest consecutive subsequence in x that is smaller than the mean of x `matrix_profile`(x, param) Calculates the 1-D Matrix Profile[1] and returns Tukey’s Five Number Set plus the mean of that Matrix Profile. `max_langevin_fixed_point`(x, r, m) Largest fixed point of dynamics :math:argmax_x {h(x)=0}` estimated from polynomial , `maximum`(x) Calculates the highest value of the time series x. `mean`(x) Returns the mean of x `mean_abs_change`(x) Average over first differences. `mean_change`(x) Average over time series differences. `mean_n_absolute_max`(x, number_of_maxima) Calculates the arithmetic mean of the n absolute maximum values of the time series. `mean_second_derivative_central`(x) Returns the mean value of a central approximation of the second derivative `median`(x) Returns the median of x `minimum`(x) Calculates the lowest value of the time series x. `number_crossing_m`(x, m) Calculates the number of crossings of x on m. `number_cwt_peaks`(x, n) Number of different peaks in x. `number_peaks`(x, n) Calculates the number of peaks of at least support n in the time series x. `partial_autocorrelation`(x, param) Calculates the value of the partial autocorrelation function at the given lag. `percentage_of_reoccurring_datapoints_to_all_datapoints`(x) Returns the percentage of non-unique data points. `percentage_of_reoccurring_values_to_all_values`(x) Returns the percentage of values that are present in the time series more than once. `permutation_entropy`(x, tau, dimension) Calculate the permutation entropy. `quantile`(x, q) Calculates the q quantile of x. `query_similarity_count`(x, param) This feature calculator accepts an input query subsequence parameter, compares the query (under z-normalized Euclidean distance) to all subsequences within the time series, and returns a count of the number of times the query was found in the time series (within some predefined maximum distance threshold). `range_count`(x, min, max) Count observed values within the interval [min, max). `ratio_beyond_r_sigma`(x, r) Ratio of values that are more than r * std(x) (so r times sigma) away from the mean of x. `ratio_value_number_to_time_series_length`(x) Returns a factor which is 1 if all values in the time series occur only once, and below one if this is not the case. `root_mean_square`(x) Returns the root mean square (rms) of the time series. `sample_entropy`(x) Calculate and return sample entropy of x. `set_property`(key, value) This method returns a decorator that sets the property key of the function to value `skewness`(x) Returns the sample skewness of x (calculated with the adjusted Fisher-Pearson standardized moment coefficient G1). `spkt_welch_density`(x, param) This feature calculator estimates the cross power spectral density of the time series x at different frequencies. `standard_deviation`(x) Returns the standard deviation of x `sum_of_reoccurring_data_points`(x) Returns the sum of all data points, that are present in the time series more than once. `sum_of_reoccurring_values`(x) Returns the sum of all values, that are present in the time series more than once. `sum_values`(x) Calculates the sum over the time series values `symmetry_looking`(x, param) Boolean variable denoting if the distribution of x looks symmetric. `time_reversal_asymmetry_statistic`(x, lag) Returns the time reversal asymmetry statistic. `value_count`(x, value) Count occurrences of value in time series x. `variance`(x) Returns the variance of x `variance_larger_than_standard_deviation`(x) Is variance higher than the standard deviation? `variation_coefficient`(x) Returns the variation coefficient (standard error / mean, give relative value of variation around mean) of x.