Statistics and transforms

This page covers the 76 analysis methods that are not indicators or patterns. They fall into five classes: summary statistics of a range of candles, rolling statistic functions such as beta and linear regression, arithmetic between candle columns, mathematical transforms of one column, and the four price transforms that combine a candle's open, high, low and close into one figure.

The table below shows the five groups and how their results differ, which matters more here than on the other pages: the summary statistics return a single number, while the other four return the candles with a column added.

Group	Class	Methods	Returns
Price statistics	PriceStatistics	39	Mostly a single float for the whole range
Statistic functions	StatisticFunctions	8	The candles with a rolling column added
Math operators	MathOperators	10	The candles with a column added
Math transforms	MathTransforms	15	The candles with a column added
Price transforms	PriceTransforms	4	The candles with a column added

Every method on this page also takes the five range arguments of prices, which are interval, from_date, to_date, days and adjusted, and returns None when UBI has no candles for the range. Analysis describes those arguments, and the tables below leave them out.

Price statistics

PriceStatistics answers questions about a whole range at once, such as "what was the highest high this year" or "how skewed were the daily returns". Its 39 methods form three families, each built on the one before, as the diagram below shows.

flowchart LR
    P["prices()"] --> A["price_high, price_low<br/>price_mean ... price_histogram<br/>12 methods"]
    P --> V["volumes()"]
    V --> B["volume_total, volume_high<br/>... volume_histogram<br/>13 methods"]
    P --> R["returns(column)"]
    R --> C["returns_high, returns_low<br/>... returns_summary<br/>12 methods"]

volumes and returns are themselves methods, and they return a narrowed frame of exchange, segment, datetime, interval and one value column. returns uses pandas' pct_change, so its value is the fractional change from one candle to the next, 0.01 for a one per cent rise, and its first row is always empty. price_high and price_low always read the high and low columns and take no column argument.

The table below lists all 39 methods.

Method	What it does	Own arguments and defaults	Returns
price_high	Finds the highest high in the range	none	The highest high as a float
price_low	Finds the lowest low in the range	none	The lowest low as a float
price_mean	Finds the mean of one candle column in the range	column='close'	The mean as a float
price_median	Finds the median of one candle column in the range	column='close'	The median as a float
price_standard_deviation	Finds the standard deviation of one candle column in the range	column='close'	The standard deviation as a float
price_variance	Finds the variance of one candle column in the range	column='close'	The variance as a float
price_mean_absolute_deviation	Finds the mean absolute deviation of one candle column from its mean in the range	column='close'	The mean absolute deviation as a float
price_skewness	Finds the skewness of one candle column in the range	column='close'	The skewness as a float
price_kurtosis	Finds the kurtosis of one candle column in the range	column='close'	The kurtosis as a float
price_quantile	Finds a quantile of one candle column in the range	quantile=0.5, column='close'	The quantile as a float
price_summary	Summarises one candle column in the range with count, mean, spread and quartiles	column='close'	A pandas.Series of summary statistics
price_histogram	Draws a histogram of one candle column in the range with matplotlib	bins=50, column='close'	The matplotlib Axes the histogram was drawn on
volumes	Fetches the traded volume of each candle in the range	none	A pandas.DataFrame with exchange, segment, datetime, interval and volume columns
volume_total	Finds the total volume traded in the range	none	The total volume as a float
volume_high	Finds the highest volume of any candle in the range	none	The highest volume as a float
volume_low	Finds the lowest volume of any candle in the range	none	The lowest volume as a float
volume_mean	Finds the mean volume per candle in the range	none	The mean volume as a float
volume_median	Finds the median volume per candle in the range	none	The median volume as a float
volume_standard_deviation	Finds the standard deviation of volume per candle in the range	none	The standard deviation as a float
volume_variance	Finds the variance of volume per candle in the range	none	The variance as a float
volume_mean_absolute_deviation	Finds the mean absolute deviation of volume per candle from its mean in the range	none	The mean absolute deviation as a float
volume_kurtosis	Finds the kurtosis of volume per candle in the range	none	The kurtosis as a float
volume_skewness	Finds the skewness of volume per candle in the range	none	The skewness as a float
volume_quantile	Finds a quantile of volume per candle in the range	quantile=0.5	The quantile as a float
volume_summary	Summarises volume per candle in the range with count, mean, spread and quartiles	none	A pandas.Series of summary statistics
volume_histogram	Draws a histogram of volume per candle in the range with matplotlib	bins=50	The matplotlib Axes the histogram was drawn on
returns	Calculates the fractional change of one candle column from each candle to the next	column='close'	A pandas.DataFrame with exchange, segment, datetime, interval and returns columns
returns_high	Finds the highest return of one candle column in the range	column='close'	The highest return as a float
returns_low	Finds the lowest return of one candle column in the range	column='close'	The lowest return as a float
returns_mean	Finds the mean return of one candle column in the range	column='close'	The mean return as a float
returns_median	Finds the median return of one candle column in the range	column='close'	The median return as a float
returns_standard_deviation	Finds the standard deviation of returns of one candle column in the range	column='close'	The standard deviation as a float
returns_variance	Finds the variance of returns of one candle column in the range	column='close'	The variance as a float
returns_mean_absolute_deviation	Finds the mean absolute deviation of returns of one candle column from their mean in the range	column='close'	The mean absolute deviation as a float
returns_skewness	Finds the skewness of returns of one candle column in the range	column='close'	The skewness as a float
returns_kurtosis	Finds the kurtosis of returns of one candle column in the range	column='close'	The kurtosis as a float
returns_quantile	Finds a quantile of returns of one candle column in the range	quantile=0.5, column='close'	The quantile as a float
returns_histogram	Draws a histogram of returns of one candle column in the range with matplotlib	bins=50, column='close'	The matplotlib Axes the histogram was drawn on
returns_summary	Summarises returns of one candle column in the range with count, mean, spread and quartiles	column='close'	A pandas.Series of summary statistics

The histogram methods need matplotlib

price_histogram, volume_histogram and returns_histogram draw with matplotlib through pandas and return the matplotlib Axes. matplotlib is not one of the library's declared dependencies, so install it yourself before calling them, and choose a backend, such as Agg, when there is no display.

The example below, which was not run for this page, summarises a year of RELIANCE's daily returns.

from tradingmachine.assets import equities

reliance = equities.Equity(exchange="nse", symbol="RELIANCE")
print(reliance.returns_standard_deviation(days=365))
print(reliance.returns_summary(days=365))

Statistic functions

StatisticFunctions holds TA-Lib's eight rolling statistic functions. Each works over a moving window and adds a column with one value per candle. The table below lists them.

Method	What it adds	Own arguments and defaults	TA-Lib function	Columns added
beta	Adds the rolling beta of the instrument against a benchmark, such as an index	benchmark, window=14, column='close'	BETA	benchmark_<column>, beta_<window>
correlation_coefficient	Adds the rolling Pearson correlation of the instrument's returns with a benchmark's returns	benchmark, window=14, column='close'	CORREL	benchmark_<column>, corr_<window>
linear_regression	Adds the end value of a rolling linear regression line through one candle column	window=14, column='close'	LINEARREG	lin_regr_<window>
linear_regression_slope	Adds the slope of a rolling linear regression line through one candle column	window=14, column='close'	LINEARREG_SLOPE	lin_regr_slope_<window>
linear_regression_intercept	Adds the intercept of a rolling linear regression line through one candle column	window=14, column='close'	LINEARREG_INTERCEPT	lin_regr_int_<window>
linear_regression_angle	Adds the angle in degrees of a rolling linear regression line through one candle column	window=14, column='close'	LINEARREG_ANGLE	lin_regr_angle_<window>
standard_deviation	Adds the rolling standard deviation of one candle column	window=14, standard_deviations=1, column='close'	STDDEV	std_dev_<window>
variance	Adds the rolling variance of one candle column	window=14, standard_deviations=1, column='close'	VAR	var_<window>

variance passes standard_deviations to TA-Lib as it always has, but TA-Lib's variance does not use it, so the argument has no effect there.

Beta and correlation against a benchmark

beta and correlation_coefficient compare the instrument with a second one, the benchmark, which is their first and required argument. The benchmark is usually an index, such as an EquityIndex for NIFTY, but any object with a prices method works. The sequence below shows how the two sets of candles are matched.

sequenceDiagram
    autonumber
    participant Y as Your code
    participant S as share.beta
    participant U as UBI
    participant T as TA-Lib
    Y->>S: benchmark=nifty, window=60, days=365
    S->>U: the share's candles
    S->>U: the benchmark's candles, same range
    U-->>S: two frames
    S->>S: join on datetime, keep only candles both have
    S->>T: BETA(benchmark close, share close, timeperiod=60)
    T-->>S: one beta per candle
    S-->>Y: candles with benchmark_close and beta_60

A candle that only one side has, such as a day the stock was suspended while the index traded, is left out rather than filled in. The benchmark's column is kept as benchmark_<column>, so you can see what was compared.

Two details make the numbers right. TA-Lib's BETA(x, y) returns the beta of y measured against x, which is the reverse of what its documentation suggests, so the method passes the benchmark first; a check on 2026-09-14 found 2.171 for INFY against NIFTY this way, matching a hand calculation, against 0.167 the other way round. And correlation_coefficient correlates returns rather than price levels, because two unrelated prices that both rise would otherwise look highly correlated.

The example below, which was not run for this page, measures RELIANCE's 60-day rolling beta against NIFTY.

from tradingmachine.assets import equities

reliance = equities.Equity(exchange="nse", symbol="RELIANCE")
nifty = equities.EquityIndex(exchange="nse", symbol="NIFTY")

frame = reliance.beta(benchmark=nifty, window=60, days=365)
print(frame[["datetime", "close", "benchmark_close", "beta_60"]].tail())

Math operators

MathOperators holds TA-Lib's ten math operators: arithmetic between two candle columns, and the highest and lowest values of one column over a rolling window. The table below lists them.

Method	What it adds	Own arguments and defaults	TA-Lib function	Columns added
add	Adds the sum of two candle columns	first_column='high', second_column='low'	ADD	sum
subtract	Adds the second candle column subtracted from the first	first_column='high', second_column='low'	SUB	difference
multiply	Adds the product of two candle columns	first_column='high', second_column='low'	MULT	product
divide	Adds the first candle column divided by the second	first_column='high', second_column='low'	DIV	quotient
maximum	Adds the highest value of one candle column over each window	column='close', window=10	MAX	max
minimum	Adds the lowest value of one candle column over each window	column='close', window=10	MIN	min
maximum_index	Adds the row position of the highest value of one candle column over each window	column='close', window=10	MAXINDEX	maxindex
minimum_index	Adds the row position of the lowest value of one candle column over each window	column='close', window=10	MININDEX	minindex
minimum_maximum	Adds the lowest and highest values of one candle column over each window	column='close', window=10	MINMAX	min, max
minimum_maximum_index	Adds the row positions of the lowest and highest values of one candle column over each window	column='close', window=10	MINMAXINDEX	minindex, maxindex

Three details are worth knowing. The two-column methods default to high and low, so subtract() with no arguments gives each candle's range. The rolling methods take column before window, the reverse of most analysis methods, so call them by keyword. And the index methods give row positions counted from the first candle of the fetched range, not labels from the frame's index. minimum_maximum writes the same min and max columns as minimum and maximum, which only matters if you combine their frames by hand.

Math transforms

MathTransforms holds TA-Lib's fifteen mathematical transforms of a single column. The table below lists them.

Method	What it adds	Own arguments and defaults	TA-Lib function	Columns added
arc_cosine	Adds the arc cosine of one candle column	column='close'	ACOS	acos
arc_sine	Adds the arc sine of one candle column	column='close'	ASIN	asin
arc_tangent	Adds the arc tangent of one candle column	column='close'	ATAN	atan
ceiling	Adds the ceiling of one candle column	column='close'	CEIL	ceil
cosine	Adds the cosine of one candle column	column='close'	COS	cos
hyperbolic_cosine	Adds the hyperbolic cosine of one candle column	column='close'	COSH	cosh
exponential	Adds the exponential of one candle column	column='close'	EXP	exp
floor	Adds the floor of one candle column	column='close'	FLOOR	floor
natural_logarithm	Adds the natural logarithm of one candle column	column='close'	LN	ln
logarithm_base_10	Adds the base 10 logarithm of one candle column	column='close'	LOG10	log10
sine	Adds the sine of one candle column	column='close'	SIN	sin
hyperbolic_sine	Adds the hyperbolic sine of one candle column	column='close'	SINH	sinh
square_root	Adds the square root of one candle column	column='close'	SQRT	sqrt
tangent	Adds the tangent of one candle column	column='close'	TAN	tan
hyperbolic_tangent	Adds the hyperbolic tangent of one candle column	column='close'	TANH	tanh

Most of these are meaningless on raw prices

Arc cosine and arc sine are defined only between -1 and 1, so on a price of about a thousand rupees their columns are entirely empty. exponential, hyperbolic_cosine and hyperbolic_sine overflow to infinity for any value above about 710: over ten years of INFY's adjusted closes, 1,586 of 1,654 rows were infinite. The transforms are meant for columns that are already small. Note that column must name a column of the candles themselves, so a transform of returns needs the returns added to the frame first.

Price transforms

PriceTransforms holds TA-Lib's four price transforms, each of which combines a candle's prices into one representative figure. They take no arguments of their own. The table below lists them.

Method	What it adds	Own arguments and defaults	TA-Lib function	Columns added
average_price	Adds the average of each candle's open, high, low and close	none	AVGPRICE	avg_price
median_price	Adds the midpoint of each candle's high and low	none	MEDPRICE	med_price
typical_price	Adds the average of each candle's high, low and close	none	TYPPRICE	typ_price
weighted_close	Adds each candle's weighted close, which counts the close twice alongside the high and low	none	WCLPRICE	wght_close

average_price here is TA-Lib's average of each candle's open, high, low and close. It is unrelated to the average_price field in UBI's quote, which is the day's volume weighted average price and is read through TradeableInstrument.volume_weighted_average_price. On 2026-09-26 that property returned 1220.44 for RELIANCE.