---
title: emstd_time
---

`emstd_time` creates a time-based EMSTD (exponential moving standard deviation) for an [`update_by`](./updateBy.md) table operation. The formula for the time-based EMSTD of a column $X$ is:

$a_i = e^{\frac{-dt_i}{\tau}}$

$s^2_0 = 0$

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

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

Where:

- $dt_i$ is the difference between time $t_i$ and $t_{i-1}$ in nanoseconds.
- $\tau$ is `decay_time` in nanoseconds, an [input parameter](#parameters) to the method.
- $\bar{x}_i$ is the [exponential moving average](./ema-time.md) of $X$ at step $i$
- $s_i$ is the exponential moving standard deviation of $X$ at time 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

```python syntax
emstd_time(
    ts_col: str,
    decay_time: Union[str, int],
    cols: list[str],
    op_control: OperationControl = None,
) -> UpdateByOperation
```

## Parameters

<ParamTable>
<Param name="ts_col" type="str">

The name of the column containing timestamps.

</Param>
<Param name="decay_time" type="Union[str,int]">

The decay rate. This can be expressed as an integer in nanoseconds or a string [duration](../../query-language/types/durations.md); e.g., `"PT00:00:00.001"` or `"PTnHnMnS"`, where `H` is hour, `M` is minute, and `S` is second.

</Param>
<Param name="cols" type="list[str]">

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

</Param>
<Param name="op_control" optional type="OperationControl">

Defines how special cases should behave. The default value is `None`, which uses default [`OperationControl`](./OperationControl.md) settings.

</Param>
</ParamTable>

## Returns

An [`UpdateByOperation`](./updateBy.md#parameters) to be used in an [`update_by`](./updateBy.md) table operation.

## Examples

### One column, no group

The following example calculates the time-based EMSTD of the `X` column, renaming the resultant column to `EmStdX`. The decay rate, `decay_time`, is set to 5 seconds. No grouping columns are specified, so the EMSTD is calculated for all rows.

```python order=result,source
from deephaven.updateby import emstd_time
from deephaven import empty_table

source = empty_table(60).update(
    [
        "Timestamp = '2023-05-01T00:00:00 ET' + i * SECOND",
        "Letter = (i % 2 == 0) ? `A` : `B`",
        "X = randomInt(0, 25)",
    ]
)

result = source.update_by(
    ops=[emstd_time(ts_col="Timestamp", decay_time="PT00:00:05", cols=["EmStdX = X"])]
)
```

### One EMSTD column, one grouping column

The following example builds on the previous by specifying a single grouping column, `Letter`. Thus, the time-based EMSTD is calculated separately for each unique letter in `Letter`.

```python order=result,source
from deephaven.updateby import emstd_time
from deephaven import empty_table

source = empty_table(60).update(
    [
        "Timestamp = '2023-05-01T00:00:00 ET' + i * SECOND",
        "Letter = (i % 2 == 0) ? `A` : `B`",
        "X = randomInt(0, 25)",
    ]
)

result = source.update_by(
    ops=[emstd_time(ts_col="Timestamp", decay_time="PT00:00:05", cols=["EmStdX = X"])],
    by=["Letter"],
)
```

### Multiple EMSTD columns, multiple grouping columns

The following example builds on the previous by specifying multiple columns in a single EMSTD and renaming both appropriately. Additionally, groups are created from both the `Letter` and `Truth` columns, so groups are defined by unique combinations of letter and boolean, respectively.

```python order=result,source
from deephaven.updateby import emstd_time
from deephaven import empty_table

source = empty_table(60).update(
    [
        "Timestamp = '2023-05-01T00:00:00 ET' + i * SECOND",
        "Letter = (i % 2 == 0) ? `A` : `B`",
        "Truth = randomBool()",
        "X = randomInt(0, 25)",
        "Y = i",
    ]
)

result = source.update_by(
    ops=[
        emstd_time(
            ts_col="Timestamp",
            decay_time="PT00:00:05",
            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`](./updateBy.md#parameters). This allows each EMSTD to have its own decay rate. The different decay rates are reflected in the renamed resultant column names.

```python order=result,source
from deephaven.updateby import emstd_time
from deephaven import empty_table

source = empty_table(60).update(
    [
        "Timestamp = '2023-05-01T00:00:00 ET' + i * SECOND",
        "Letter = (i % 2 == 0) ? `A` : `B`",
        "Truth = randomBool()",
        "X = randomInt(0, 25)",
        "Y = i",
    ]
)

emstd_x = emstd_time(ts_col="Timestamp", decay_time="PT5S", cols=["EmStdX5sec = X"])
emstd_y = emstd_time(ts_col="Timestamp", decay_time="PT3S", cols=["EmStdY3sec = Y"])

result = source.update_by(ops=[emstd_x, emstd_y], by=["Letter", "Truth"])
```

## Related documentation

- [How to use `update_by`](../../../how-to-guides/rolling-aggregations.md)
- [Time-based exponential moving average in UpdateBy](./ema-time.md)
- [Create an empty table](../../../how-to-guides/new-and-empty-table.md#empty_table)
- [`update`](../select/update.md)
- [`update_by`](./updateBy.md)
- [Javadoc](https://deephaven.io/core/javadoc/io/deephaven/api/updateby/UpdateByOperation.html#EmStd(java.lang.String,java.time.Duration,java.lang.String...))
- [Pydoc](/core/pydoc/code/deephaven.updateby.html#deephaven.updateby.emstd_time)