Version: Python

# emstd_tick

emstd_tick creates a tick-based (row-based) EMSTD (exponential moving standard deviation) for an update_by table operation. The formula for the tick-based EMSTD of a column $X$ is:

$a = e^{\frac{-1}{\tau}}$

$s^2_0 = 0$

$s^2_i = a*(s^2_{i-1} + (1-a)*(x_i - \bar{x}_{i-1})^2)$

$s_i = \sqrt{s^2_i}$

Where:

• $\tau$ is decay_ticks, an input parameter to the method.
• $\bar{x}_i$ is the exponential moving average of $X$ at step $i$
• $s_i$ is the exponential moving standard deviation of $X$ at step $i$.
• $x_i$ is the current value.
• $i$ denotes the time step, ranging from $i=1$ to $i = n-1$, where $n$ is the number of elements in $X$.
note

In the above formula, $s^2_0 = 0$ yields the correct results for subsequent calculations. However, sample variance for fewer than two data points is undefined, so the first element of an EMSTD calculation will always be NaN.

## Syntax​

emstd_tick(    decay_ticks: int,    cols: list[str],    op_control: OperationControl = None,) -> UpdateByOperation

## Parameters​

ParameterTypeDescription
decay_ticksint

The decay rate in ticks (rows).

colslist[str]

The columns to be operated on. These can include expressions to rename the output (e.g., NewCol = Col). If None, EMSTD is calculated for all columns.

op_control optionalOperationControl

Defines how special cases should behave. The default value is None, which uses default OperationControl settings.

## Returns​

An UpdateByOperation to be used in an update_by table operation.

## Examples​

### One column, no groups​

The following example calculates the tick-based (row-based) EMSTD of the X column, renaming the resultant column to EmStdX. The decay rate, decay_ticks, is set to 2. No grouping columns are specified, so the EMSTD is calculated over all rows.

from deephaven.updateby import emstd_tickfrom deephaven import empty_tablesource = empty_table(10).update(["Letter = (i % 2 == 0) ? A : B", "X = i"])result = source.update_by(ops=emstd_tick(decay_ticks=2, cols=["EmStdX = X"]))

### One EMSTD column, one grouping column​

The following example builds on the previous by specifying Letter as the key column. Thus, the EMSTD is calculated on a per-letter basis.

from deephaven.updateby import emstd_tickfrom deephaven import empty_tablesource = empty_table(10).update(["Letter = (i % 2 == 0) ? A : B", "X = i"])result = source.update_by(    ops=emstd_tick(decay_ticks=2, cols=["EmStdX = X"]), by=["Letter"])

### Multiple EMSTD columns, multiple grouping columns​

The following example builds on the previous by calculating the EMSTD of multiple columns in the same UpdateByOperation. Also, the groups are defined by unique combinations of letter and boolean in the Letter and Truth columns, respectively.

from deephaven.updateby import emstd_tickfrom deephaven import empty_tablesource = empty_table(20).update(    [        "Letter = (i % 2 == 0) ? A : B",        "Truth = randomBool()",        "X = i",        "Y = randomInt(5, 10)",    ])result = source.update_by(    ops=emstd_tick(decay_ticks=2, cols=["EmStdX = X", "EmStdY = Y"]),    by=["Letter", "Truth"],)

### Multiple UpdateByOperations, multiple grouping columns​

The following example builds on the previous by calculating the EMSTD of multiple columns, each with its own UpdateByOperation. This allows each EMSTD to have its own decay rate. The different decay rates are reflected in the renamed resultant column names.

from deephaven.updateby import emstd_tickfrom deephaven import empty_tablesource = empty_table(20).update(    [        "Letter = (i % 2 == 0) ? A : B",        "Truth = randomBool()",        "X = i",        "Y = randomInt(5, 10)",    ])emstd_x = emstd_tick(decay_ticks=2, cols=["EmStdX2rows = X"])emstd_y = emstd_tick(decay_ticks=4, cols=["EmStdY5rows = Y"])result = source.update_by(ops=[emstd_x, emstd_y], by=["Letter", "Truth"])