# # Synthetic time series

Combine multiple time series, constants, and operators to create new synthetic time series.

For example, use the expression `3.6 * TS{externalId='wind-speed'}`

to convert units from m/s to k/h.

Also, you can **combine** time series: `TS{id=123} + TS{externalId='my_external_id'}`

, use **functions** with time series `sin(pow(TS{id=123}, 2))`

, and **aggregate** time series `TS{id=123, aggregate='average', granularity='1h'}+TS{id=456}`

. See below for a list of supported functions and aggregates.

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See the synthetic time series API documentation for more information about how to work with synthetic time series.

**In this article:**

## # Functions

Synthetic time series support these functions:

- Inputs with internal or external ID. The external ID must be surrounded by quotes (single or double).
- Mathematical operators +,-,*,/.
- Grouping with brackets ().
- Trigonometrics. sin(x), cos(x) and pi().
- ln(x), pow(base, exponent), sqrt(x), exp(x), abs(x).
- Variable length functions. max(x1, x2, ...), min(...), avg(...).
- round(x, decimals) (-10<decimals<10).
`on_error(expression, default)`

, for handling errors like overflow or division by zero.`map(expression, [list of strings to map from], [list of values to map to], default)`

.

### # Convert string time series to doubles

The `map()`

function can handle time series of type *string* and convert strings to doubles. If, for example, a time series for a valve can have the values `"OPEN"`

or `"CLOSED"`

, you can convert it to a number with:

```
map(TS{externalId='stringstate'}, ['OPEN', 'CLOSED'], [1, 0], -1)
```

`"OPEN"`

is mapped to 1, `"CLOSED"`

to 0, and everything else to -1.

Aggregates on string time series are currently not supported. All string time series are considered to be stepped time series.

### # Error handling - on_error()

There are three possible errors:

- TYPE_ERROR: You're using an invalid type as input. For example, a string time series with the division operator.
- BAD_DOMAIN: You're using invalid input ranges. For example, division by zero, or sqrt of a negative number.
- OVERFLOW: The result is more than 10^100 in absolute value.

Instead of returning a value for these cases, CDF returns an error field with an error message. To avoid these, you can wrap the (sub)expression in the `on_error()`

function, for example. `on_error(1/TS{externalId='canBeZero'}, 0)`

. Note that, because of interpolation, this can happen even if none of the raw data points are zero.

## # Aggregation

You define aggregates similar to time series inputs, but aggregates have extra parameters: `aggregate`

, `granularity`

, and (optionally) `alignment`

. Aggregate must be one of **interpolation**, **stepinterpolation**, or **average**.

You must enclose the value of aggregate and granularity in quotes.

```
ts{id=12356, aggregate="average", granularity="2h", alignment=3600000}
```

See also: Aggregating time series data.

### # Granularity

The granularity decides the length of the intervals CDF takes the aggregate over. They are specified as a number plus a granularity unit, like `120s`

, `15m`

, `48h`

, or `365d`

.

Intervals are half-open, including the start time and excluding the end time. `[start, start+granularity)`

Granularity must be on the form NG where N is a number, and G is *s*, *m*, *h*, or *d*. (second, minute, hour, day). The maximum number you can specify is 120, 120, 48, and 100.000 for seconds, minutes, hour, and days, respectively.

### # Output granularity

We return data points at any point in time where:

- Any input time series has an input.
- All time series are defined (between the first and last data point, inclusive)

For example, if time series A has data at time 15, 30, 45, 60, and time series B has data at times 30, 40, 50, A+B will have data at 30, 40, 45, and 50.

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Aggregates have data at every *granularity* time, rounded to multiples of *granularity* since epoch. For example, `60m`

aggregates have data points at `00.00`

, `01.00`

, and so on, even if the start time is `00.15`

. This **differs from retrieving aggregate data points from the non-synthetic endpoint**, where CDF rounds to multiples of the granularity *unit* and uses an arbitrary offset.

### # Interpolation

If there is no input data, CDF interpolates. As a general rule, CDF uses **linear** interpolation: finds the previous and next data point and draws a straight line between these. The other case is **step** interpolation: CDF uses the value of the previous data point.

CDF interpolates *any* interval. If there are data points in 1971 and 2050, CDF defines the time series for all timestamps in between.

Most aggregates are constant for the whole duration of *granularity*. The only exception is the *interpolation* aggregate on non-step time series.

### # Alignment

The alignment decides the start of the intervals and is specified in milliseconds.

The `alignment`

parameter allows you to align weekly aggregates to start on specific days of the week, for example Saturday, or Monday. By default, aggregation with synthetic time series is aligned to *Thursday 00:00:00 UTC, 1 January 1970* e.g., `alignment=0`

.

You can also use alignment to create aggregates that are aligned to different time zones. For example, the chart below shows the daily average chlorine indicator for city water (opens new window) aligned to two different time zones: GMT+0 and GMT+3.

To align to UTC/GMT+0 (aligned to: Sep 09 2020 00:00:00 UTC)

`ts{externalId='houston.ro.REMOTE_AI[34]', alignment=1599609600000, aggregate='average', granularity='24h'}`

To align to UTC/GMT+3 (aligned to: Sep 09 2020 03:00:00 UTC)

`ts{externalId='houston.ro.REMOTE_AI[34]', alignment=1599620400000, aggregate='average', granularity='24h'}`

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The alignment must be a multiple of the granularity unit. In the example above, the alignment needs to be a multiple of a whole hour, since the granularity is 24h.

All intervals are on the form `(N*granularity + alignment, (N+1)*granularity + alignment)`

, where `N`

is an integer.

## # Limits

In a single request, you can ask for:

- 10 expressions (10 synthetic time series).
- 10.000 data points, summed over all expressions.
- 100 input time series referrals, summed over all expressions.
- 2000 tokens in each expression. Similar to 2000 characters, except that words and numbers are counted as a single character.

If you use time series aggregates as inputs, and you get slow responses or a 503 error code, try again or reduce the limit. This is the expected behavior when you have recently updated the data points, and CDF needs to recalculate aggregates.