#TSHISTORY FORMULA

#Purpose

This tshistory component provides a formula language to build computed series.

Formulas are defined using a simple lisp-like syntax, using a pre-defined function library.

Formulas are read-only series (you can't update or replace values).

They also have an history, which is built, time stamps wise, using the union of all constituent time stamps, and value wise, by applying the formula.

Because of this the staircase operator is available on formulae. Some staircase operations can have a very fast implementation if the formula obeys commutativity rules.

#Formula

#General Syntax

Formulas are expressed in a lisp-like syntax using operators, positional (mandatory) parameters and keyword (optional) parameters.

The general form is:

(<operator> <param1> ... <paramN> #:<keyword1> <value1> ... #:<keywordN> <valueN>)

Here are a couple examples:

• (add (series "wallonie") (series "bruxelles") (series "flandres"))

Here we see the two fundamental add and series operators at work.

This would form a new synthetic series out of three base series (which can be either raw series or formulas themselves).

Some notes:

• operator names can contain dashes or arbitrary caracters

• literal values can be: 3 (integer), 5.2 (float), "hello" (string) and #t or #f (true ot false)

#Pre-defined operators

#*

Performs a scalar product on a series.

Example: (* -1 (series "positive-things"))

#+

Add a constant quantity to a series.

Example: (+ 42 (series "i-feel-undervalued"))

#/

Perform a scalar division between numbers or a series and a scalar.

Example: (/ (series "div-me") (/ 3 2))

#add

Linear combination of two or more series. Takes a variable number of series as input.

Example: (add (series "wallonie") (series "bruxelles") (series "flandres"))

To specify the behaviour of the add operation in the face of missing data, the series can be built with the fill keyword. This option is only really applied when several series are combined. By default, if an input series has missing values for a given time stamp, the resulting series has no value for this timestamp (unless a fill rule is provided).

#clip

Set an upper/lower threashold for a series. Takes a series as positional parameter and accepts two optional keywords min and max which must be numbers (integers or floats).

Example: (clip (series "must-be-positive") #:min 0)

#date

Produces an utc timestamp from its input string date in iso format.

The tz keyword allows to specify an alternate time zone. The naive keyword forces production of a naive timestamp. Both tz and naive keywords are mutually exlcusive.

#div

Element wise division of two series.

Example: (div (series "$-to-€") (series "€-to-£"))

#min

Computes the row-wise minimum of its input series.

Example: (min (series "station0") (series "station1") (series "station2"))

#max

Computes the row-wise maximum of its input series.

Example: (max (series "station0") (series "station1") (series "station2"))

#mul

Element wise multiplication of series. Takes a variable number of series as input.

Example: (mul (series "banana-spot-price ($)") (series "$-to-€" #:fill 'ffill'))

This might convert a series priced in dollars to a series priced in euros, using a currency exchange rate series with a forward-fill option.

#naive

Allow demoting a series from a tz-aware index (strongly recommended) to a tz-naive index (unfortunately sometimes unavoidable for interop with other tz-naive series).

One must provide a country code and a target timezone.

Example: (naive (series "tz-aware-series-from-poland") "PL" "Europe/Warsaw")

#priority

The priority operator combines its input series as layers. For each timestamp in the union of all series time stamps, the value comes from the first series that provides a value.

Example: (priority (series "realized") (series "nominated") (series "forecasted"))

Here realized values show up first, and any missing values come from nominated first and then only from forecasted.

#resample

Resamples its input series using freq and the aggregation method method (as described in the pandas documentation).

Example: (resample (series "hourly") "D")

#row-mean

This operator computes the row-wise mean of its input series using the series weight option if present. The missing points are handled as if the whole series were absent.

Example: (row-mean (series "station0") (series "station1" #:weight 2) (series "station2"))

Weights are provided as a keyword to series. No weight is interpreted as 1.

#series

The series operator accepts several keywords:

• fill to specify a filling policy to avoid nans when the series will be added with others; accepted values are "ffill" (forward-fill), "bfill" (backward-fill) or any floating value.

For instance in (add (series "a" #:fill 0) (series "b") will make sure that series a, if shorter than series b will get zeroes instead of nans where b provides values.

#slice

This allows cutting a series at date points. It takes one positional parameter (the series) and two optional keywords fromdate and todate which must be strings in the iso8601 format.

Example: (slice (series "cut-me") #:fromdate "2018-01-01")

#std

Computes the standard deviation over its input series.

Example: (std (series "station0") (series "station1") (series "station2"))

#timedelta

Takes a timestamp and a number of years, months, weekds, days, hours, minutes (int) and computes a new date according to the asked delta elements.

Example: (timedelta (date "2020-1-1") #:weeks 1 #:hours 2)

#today

Produces a timezone-aware timestamp as of today

The tz keyword allows to specify an alternate time zone. The naive keyword forces production of a naive timestamp. Both tz and naive keywords are mutually exlcusive.

Example: (today)

#Series API

A few api calls are added to the tshistory base:

• .register_formula to define a formula

• .eval_formula to evaluate on-the-fly a formula (useful to check that it computes before registering it)

#register_formula

Exemple:

tsa.register_formula(
      'my-sweet-formula',
      '(* 3.14 (series "going-round"))'
  )

#eval_formula

Example:

>>> tsa.eval_formula('(* 3.14 (series "going-round"))')
 ...
 2020-01-01    3.14
 2020-01-02    6.28
 2020-01-03    9.42
 dtype: float64