Package functionality review

[sairus7]

Hi!
I have some experience working with time series (from medical sensors), and I was thinking of using TimeSeries.jl for my projects. For now I have some sort of review of this package, outlining choises that look strange to me, at least from docs, along with proposals from my point of view. Maybe authors will find it helpful.

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I. AbstractTimeSeries is absent from docs - is this some kind of common interface for different timeseries types? If so, you should add an example, which methods should I implement to support custom timeseries type.

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II. Heterogenous series (tables) are dropped, from docs:

"All the values inside the values array must be of the same type."

This is a huge limitation, if one needs timeseries with complex information, stored as vector of structures, or a namedtuple of columns of different types (see StructArrays.jl).

Maybe there should be a different TimeTable type with heterogenous columns (similar to DataFrame), and TimeArray for a single column type, sharing the same timestamps from parent table?

More than that, individual columns can be a custom AbstractVector with some metadata for exotic element types. For example, if elements are encoded and metadata is needed to decode them on getindex:

• from point to physical unit, or
• from number to a category name (CategoricalArrays.jl), or
• from 8-bit element to 8 binary values (each encoded by bit position).

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III. There is no separate implementation for timeseries with regular sample rate, that can be constrained to operations that produce a uniform sampling (similar to SampledSignals.jl). This type does not need to store materialized timestamps vector at all, since time can be calculated from index, startdate and samplerate (I call this a "time grid", which provides a index2time and time2index pair of functions). Timeseries remains uniform unless you want to take irregular / arbitraty samples from it - result is then converted to a common (non-uniform) timeseries with timestamps vector in it.

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IV. There are no timeseries with several timestamp columns. In my practive, I always have three different timeseries types:

1. series - regularly sampled timeseries
2. events - irregularly sampled timeseries with one timestamp value
3. segments - irregularly samples timeseries with two timestamp values (start, stop) for elements that have some extent in time.

There are several special cases for (3) with regard to indexing (what to do if I request time point inside the segment or time interval that partially overlap with segments on edges).

Maybe there can be even more exotic (or common) timeseries with more that two timestamps (each row is itself a repetition of some complex process in time with many "phases"), where you should explicitly choose, wich timestamp column you want to index by. But I would not complicate it that far.

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V. Row indexing. You can index rows by:

• single integer,
• integer range / with step
• single Date
• multiple Dates
• range of Date with step

What is missing:

• Multiple integers (at least from docs).
• Intervals of Date with no step (or step = 0, it should return all values within two boundaries, regardless of time step).
• Combined time and integer index. Sometimes you want to get, say, next ten elements relative to some timepoint: "get 10 elements after 2020-12-01", or even "get 5 elements before and 5 elements after 2020-12-01", or "get all elements between 2020-12-01 and 2020-12-31, including 1 previous and 1 next element" - so there can be a combination of two relative indexes, AND a time point / interval. In fact, indexing only by integer value is a special case, when your time point equals to first element timestamp. (I use getindex method with both time and index positional arguments for different combinations).

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VI. Splitting by condition section has two different sets of functions:

• special cases of where in tables, but for timeseries (when, findwhen, findall),
• other functions that duplicate indexing (from, to).

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VII. Maybe there should be some convention between functions that take and return timeseries, and functions that return standard vector types:

• findwhen vs findall;
• select column as a simple vector, or a timearray with a single column
• logical operators returning a timearray of Bool, or a bitvector

Also, there may be some methods to toggle between timeseries type - and underlying Table type, or standard array / vector of tuples. This is similar to Tables.columntable from DataFrames, they are using it to toggle between type-stable and compile-friendly cases.

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VIII. Operation on single columns - or whole timeseries

• Dot-wise operations:

only calculated on values that share a timestamp.

this is very tricky part, because there is implicit inner join, and all columns should be the same numeric type. So maybe it should be applied only on a single column, or a single column can be modified this way inplace? This is also about heterogenity, as in section II above.

• For Apply methods there are many standard or third-party package functions (from DSP, RollingFunctions, etc.) that apply on simple Vector types, so there is no need to rewrite them all, if you can provide one common syntax to "wrap" any function on individual column. Then you can replace diff, percentchange, moving, upto with similar functions from any other package.
• Also, basecall looks strange to me - what if I want to run function not from Base, and run it on a single column, or a set of selected columns?

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IX. Combine methods

• Why merge naming instead of more common join?
• collapse: AFAIK this is called decimation or resampling with another samplerate or time intervals - not only day, week, etc. Maybe even a vector of custom intervals. And there should be any arbitrary function, that can reduce all elements that fall within each time interval (for example, you can get time distribution, if you count number of elements over a fixed time intervals)

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X. Customize TimeArray printing
Can I choose a time string format to show, or is it chosen automatically based on - what? It would be nice to have examples for high-frequency timestamps in units of milliseconds.

[iblislin]

Hi @sairus7.
I appreciate you share this valuable review.
I agree with the main concepts and points from I ~ V, VII, IX, X.

• VI (Splitting methods), I want to consolidate them single filter function (some discussion can be found at Time series filtering #456) and add the integration of TableOperations.jl.
• VIII, I think the basecall is the method you want, if we can handle the case of heterogenous series. (And maybe we can work out a better name for basecall)
• IX (Combine methods), I also want to rename them :p. I'm not sure why the original creators of this package chose that terms. But now, we can refine/re-design it.

There are a many designs that I'm not sure about the original ideas (I guess most of them are for financial time series).
It's time for getting this package overhauled.

Let's work out each issue one-by-one,

I. The AbstractTimeSeries. I will divide this issue into two small pieces:
a. The type parameter of AbstractTimeSeries.
b. The function list of AbstractTimeSeries. We can listing them first, then define signature later. And consider which methods from Tables.jl/TableOperations.jl need to includes.

What's your idea about the first issue? I'm studying Tables/TableOperations, I will post my blueprint here later.

[iblislin]

Here is my proposal:

I. AbstractTimeSeries Design

   a. The type parameter: AbstractTimeSeries{T} where T denotes the type of time index.
     a.1 if T <: Tuple, for instance: Tuple{Date,Time} <: Tuple, implies there are multiple columns forms the time index,.
     a.2 if !(T <: Tuple), implies there is only one column as the time index.

   b. The interface stuffs.
     b.1 Tables.jl integration

Function	Support	comment
Tables.istable	✔️	AbstractTimeSeries returns true by default.
Tables.columnaccess	✔️	true by default.
Tables.columns	✔️	just return the AbstractTimeSeries object by default.
Tables.rowaccess	✔️	true by default.
Tables.rows	✔️	Maybe we need a type to represent a row. What is the common terminology for a row of a time series?
Tables.schema	✔️	return the schema.
Tables.materializer	✔️	return the constructor of the concrete type.
Tables.getcolumn(table, i::Int)	✔️	It return the value vector. Setting i = 0 returns the time index vector.
Tables.getcolumn(table, nm::Symbol)	✔️	It return the value vector. Setting nm = :timestamp returns the time index vector.
Tables.columnnames(table)	✔️	Return the column names. And make the name :timestamp as a preserved one. Edit: I'm not sure about a fixed name of index is a good idea or not, maybe we can ask user to name the index.
Tables.getcolumn(table, ::Type{T}, i::Int, nm::Symbol)	Optional
Tables.partitions	TBD	Not sure about the use cases of this function
Tables.partitioner	TBD

     b.1 TableOperations.jl integration

Function	Support	comment
TableOperations.select	✔️	I think there are nothing to do for our pkg, once we got Tables.jl integration done. Just write some test cases to check the correctness.
TableOperations.transform	✔️	test cases only, like the select function
TableOperations.filter	✔️	test cases only
TableOperations.map	✔️	test cases only

@sairus7 could you review these ideas? and I can make a PR for this proposal.

[sairus7]

@iblis17
I.a.

AbstractTimeSeries{T} where T denotes the type of time index

Should there be any other compile-time information, except time type?
What are other specific methods and specific properties with this type, that are not covered by table interfaces?

a.1, a.2

multiple columns forms the time index

Do you mean that there can be two columns with different precision for time, like this link says https://docs.julialang.org/en/v1/stdlib/Dates/#Dates.Date ?

I think, it can be solved with "batching", where you have one timestamp type for a whole bunch of records (table of tables, or partitions), and a detailed relative timestamp for every element within that batch. So, I am not sure we should add it for a single table level. (But we can add reference time as a metadata field for a whole table object.)

What about other idea of having several timestamps (like a time interval t1:t2) for each row, I think it is similar to sparse arrays for highly duplicated data (since all rows between t1:t2 have the same values), and we should think of it after defining the main functionality.

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1.b About interface stuff.

I think, first, we should outline, what is the main difference between TimeSeries and table-data packages, like DataFrames.jl or IndexedTables.jl, otherwise there is no need in TimeSeries.jl itself. Expecially, if we decide to support heterogenous column types and stick to table interface. Or, if there are some minor differences, we can just rewrite TimeSeries.jl as a thin wrapper around those packages.

From my point of view, timeseries differ from simple arrays, because they have timestamps, and some specific operations. I think of timestamps like "position in time", or a timeindex, in addition to integer element index.

So, here is a list of questions, that should be answered first:

1. Heterogenous column types - yes or not? If we treat timeseries as any data, that is bound to a timestamp, then we should add columns of different types. On the other side, using matrix we have convenient matrix operations over homogenous channel groups. Although we can always wrap a whole matrix as a single column (at the cost of not operate with individual columns within matrix).

2. Static or dynamic columns? Can we add columns to an existing timeseries, or column number and types (schema) are known in parametric types at compile-time, like IndexedTables.jl does?

3. Tabular operations (link1, link2), what types they do return? For example, should getindex return a row object, or just a tuple? Should select return a single-column table, or some column object, or a vector?

4. Should we always store timestamps in sorted order? So, if we insert a new row, or change a timestamp, we should always re-sort rows? Should they be unique or not? Should we restrict join only by timestamp?

5. Should timestamps be always part of table data, or not? Like, should it always be the first column? Should it ever be in column list, or a "hidden" column like index, or both options?

6. Should we always add timestamp to any return type (subtable / row / column), even if it is not queried from table? What is a row, timestamp + row data? What is a column, timestamp + column data?

7. What if a table have many time columns, can we switch, what columns to use as timestamps?

[sairus7]

Maybe @bkamins can give us his opinion on this?

[bkamins]

Thank you for working on this. As there are many aspects of the issue (and probably I do not grasp everything you discussed) I would start with the question what is the main use case for TimeSeries.jl? and then design against this use case.

E.g. DataFrames.jl design objective is to be maximally flexible, possibly at the cost of performance (when used correctly it is fast though), i.e. to be used when no more specialized package exists.

I would assume that TimeSeries.jl would be a more specialized package which would provide functions that may be only made available if we have a notion of time index. There are many such use cases, that are currently hard with DataFrames.jl, e.g.:

1. lag by a period of time
2. interpolate
3. aggregate by some time periods
4. smooth data

So in summary. The question is: what features TimeSeries.jl should provide so that a user would want to switch from DataFrames.jl to TimeSeries.jl for some specific task. This will probably mean that TimeSeries.jl should provide by default more restrictions than DataFrames.jl at the benefit of doing things better (as currently you can do anything with DataFrames.jl but not always fast or conveniently).

Below I say what I would find intuitive in answers to the 7 points you put:

Heterogenous column types - yes or not? If we treat timeseries as any data, that is bound to a timestamp, then we should add columns of different types. On the other side, using matrix we have convenient matrix operations over homogenous channel groups. Although we can always wrap a whole matrix as a single column (at the cost of not operate with individual columns within matrix).

I do not think it would be super useful (though sometimes it might be useful). So if you see big benefits of having homogeneous type I would go for homogeneous choice.

However, my intuition is that there will not be big benefits.

Static or dynamic columns? Can we add columns to an existing timeseries, or column number and types (schema) are known in parametric types at compile-time, like IndexedTables.jl does?

If you go for homogeneous type I think for sure dynamic is better (as you have type inference for free).

However, in general in DataFrames.jl although it is not type stable mostly you can easily switch to "type-stalbe" mode.

Actually I think that the crucial thing is if you want to allow to add rows to time series in place. I assume you want it (which e.g. means that you cannot use Matrix as internal representation).

Tabular operations (link1, link2), what types they do return? For example, should getindex return a row object, or just a tuple? Should select return a single-column table, or some column object, or a vector?

Do you see any uses for such a row-object? (like taking advantage that it would know its time stamp). If yes I think it is not a problem to have a custom type for it. Also do you want the row-object to be a view (like DataFrameRow) or a copy? (which eg. a Tuple) would be.

Should we always store timestamps in sorted order? So, if we insert a new row, or change a timestamp, we should always re-sort rows? Should they be unique or not? Should we restrict join only by timestamp?

I would find keeping them sorted intuitive. In what cases would you want to allow to change a timestamp? I would feel that it should be immutable? Also I feel timestamps should be unique and that join should be performed only on timestamp (at least by default).

Should timestamps be always part of table data, or not? Like, should it always be the first column? Should it ever be in column list, or a "hidden" column like index, or both options?

I would normally think that it should be a "hidden" column like index.

Should we always add timestamp to any return type (subtable / row / column), even if it is not queried from table? What is a row, timestamp + row data? What is a column, timestamp + column data?

For me timestamp would be an index only

What if a table have many time columns, can we switch, what columns to use as timestamps?

I think it should create a new table.

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Please treat these comments as loose first impressions of course.

[iblislin]

I.a.

Should there be any other compile-time information, except time type?

I think for AbstractTimeSeries, it is time type only and for the other subtypes, we can add other type parameter if needed.
So the time type is the minimal requirement.

What are other specific methods and specific properties with this type, that are not covered by table interfaces?

ah, right. I try to list some here, and maybe we can make it completed later, once we decide some key design.

Function	Return type	Comment
length(::AbstractTimeSeries)	Int
ndims(::AbstractTimeSeries)	Int
size(::AbstractTimeSeries, ::Int)	Int
axes(::AbstractTimeSeries)	Int
axes(::AbstractTimeSeries, ::Int)	Int
copy(::AbstractTimeSeries)	AbstractTimeSeries
deepcopy(::AbstractTimeSeries)	AbstractTimeSeries
similar(::AbstractTimeSeries)	AbstractTimeSeries
names(::AbstractTimeSeries)	Vector{Symbol}
rename(::AbstractTimeSeries, ::Pair...)	AbstractTimeSeries
rename!(::AbstractTimeSeries, ::Pair...)	AbstractTimeSeries
vcat(::AbstractTimeSeries, ::AbstractTimeSeries)	AbstractTimeSeries
hcat(::AbstractTimeSeries, ::AbstractTimeSeries)	AbstractTimeSeries
hvcat(::Tuple{Vararg{Int}}, ::AbstractTimeSeries...)	AbstractTimeSeries
view(::AbstractTimeSeries, dims...)	AbstractTimeSeries	Seems that we need to implement a Sub- type for each concrete type, like SubArray does
first(::AbstractTimeSeries)	(TBD)	Maybe a AbstractTimeSeriesRow ?
last(::AbstractTimeSeries)	(TBD)
stack and unstack		Are there any real use cases for time series data?
join(::AbstractTimeSeries, ::AbstractTimeSeries) family	AbstractTimeSeries
select(::AbstractTimeSeries, args...), select!, transform and transform!	AbstractTimeSeries	❓ Since user might need to create a new column from two (or more) original column, and the input type of custom callable f is critical. There are two design: (1) timestamp + value (2) value only. I can easily found a real case that use (2) for calculating a ratio of two columns, in this case, the timestamp is useless for f, user just write something like select(ats, [:a, :b] => /) and (2) will work perfectly. Are there any cases we need to adopt (1)?
filter(::Callable, ::AbstractTimeSeries) and filter!	AbstractTimeSeries	❓ Again the same story happened on filter and map, the issue of input type, (1) timestamp + value (2) value only. If we choose (2), we will got tons of function from Base or other package supported (like isnothing, iszero ... etc). Maybe we need to found cases that need (1) and investigate them. In my personal use, (2) is quite common. I need to get rid of NaN. Inf or 0 usually.
map(::Callable, ::AbstractTimeSeries)		❓ I think the functionality is replaced by select and transform. And we don't need it.
moving, reduce, foldl and foldr	AbstractTimeSeries	❓ We can handle the case of iterating over row value by select or similar. The another dimension is calculating again whole (or a subset) column. A classic example is running mean. The input type will be (2) for running mean. Also, lag, lead, or diff only need input type (2) to work. ❓ 2: the naming for this function. IIUC, pandas named it as rolling ?

a.1, a.2

multiple columns forms the time index

Do you mean that there can be two columns with different precision for time, like this link says https://docs.julialang.org/en/v1/stdlib/Dates/#Dates.Date ?

I want to cover both these cases (difference precision and multiple timestamp as interval) in the type parameter design.
And I think these two cases can also be distinguished without problem. Tuple{Date,Time} vs Tuple{DateTime,DateTime} for example.

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1.b Interface

I think, first, we should outline, what is the main difference between TimeSeries and table-data packages, like DataFrames.jl or IndexedTables.jl, otherwise there is no need in TimeSeries.jl itself. Expecially, if we decide to support heterogenous column types and stick to table interface. Or, if there are some minor differences, we can just rewrite TimeSeries.jl as a thin wrapper around those packages.

This is a hard question. Since the property of time index breaks all the rules and make wrapping around those pkgs not profitable I think. So in the beginning, I prefer not to depend on them. I keep opening mind to this issue. After we explored the enough use cases, maybe part of cases we can leverage those pkgs.

1. Heterogenous column types - yes or not? If we treat timeseries as any data, that is bound to a timestamp, then we should add columns of different types. On the other side, using matrix we have convenient matrix operations over homogenous channel groups. Although we can always wrap a whole matrix as a single column (at the cost of not operate with individual columns within matrix).

2. Static or dynamic columns? Can we add columns to an existing timeseries, or column number and types (schema) are known in parametric types at compile-time, like IndexedTables.jl does?

4. Should we always store timestamps in sorted order? So, if we insert a new row, or change a timestamp, we should always re-sort rows? Should they be unique or not? Should we restrict join only by timestamp?

Well, in short, my answer is that we can implement all styles if needed.
There are 8 combinations of these properties:

Combination	Unstored 🟢 / Sorted 🔴	Hetero 🟢 / Homo 🔴	Dynamic 🟢 / Static 🔴	Comment
1	🟢	🟢	🟢	I think this is fulfilled by DataFrames. It's the most flexible data structure. I think we don't need to create another DataFrame.
2	🔴	🟢	🟢	Since the timestamp got sorted, we can provide search/filter or more operations on it with better performance. And seem we have urgent need of it.
3	🟢	🔴	🟢
4	🔴	🔴	🟢
5	🟢	🟢	🔴	Is this just IndexedTable ?
6	🔴	🟢	🔴
7	🟢	🔴	🔴
8	🔴	🔴	🔴	Actually, this is the current struct TimeArray, we already implement it 😹

I cannot find cases that user need to manipulate an unsorted time series. So combination 4, 6, 8 are kept, and I think case 6 won't have enough performance benefit. Combination 4 and 8 might have benefit if the underlying structure is Matrix for row operation, but this claim needs evidence from real use cases.

So, I will vote for combination 2 as top priority then implementing combination 4 and 8 if we still have enough mental effort.

3. Tabular operations (link1, link2), what types they do return? For example, should getindex return a row object, or just a tuple? Should select return a single-column table, or some column object, or a vector?

I managed to list them in the table of part a.
For getindex, if user getindex a single row, a row object will be better, since the column information is useful. If user getindex a range of row, just return a time series object.
For select, transform or filter, I think they should return an object that same as the input type.

4. Should we always store timestamps in sorted order? So, if we insert a new row, or change a timestamp, we should always re-sort rows? Should they be unique or not? Should we restrict join only by timestamp?

I want timestamps sorted all the time. The timestamps isn't needed to be unique, and the order between these records which shares the same timestamps is defined by user. We should make sure function provide by this pkg not change that relative order. I have some sensor generated data that share same timestamp, since the timestamp precision isn't enough.

About join, I want that time index is required but also accept optional non-index columns.
I do have two dataset that need to be join with date and username. (I did it in DataFrames and convert it to TimeArray later.)

5. Should timestamps be always part of table data, or not? Like, should it always be the first column? Should it ever be in column list, or a "hidden" column like index, or both options?

I think a hidden column is fine for me. I want that user can always set/switch the index. Once set, the column will be the first column in the presentation (via print) and the Tables.jl integration will set that index as first column.

6. Should we always add timestamp to any return type (subtable / row / column), even if it is not queried from table? What is a row, timestamp + row data? What is a column, timestamp + column data?

Well, this is quite complex question since I encountered both situations in single project: (1) I want the raw row value without timestamp, so I can feed them into function from Base (2) I want row value + column info + timestamp, so I can easily get the specific column.
I think is the same dilemma as the part a function select described. The input type of custom function problem is same as your "return type problem".

I don't have an elegant approach at this moment. I still think about it. I write down some here.

(i) Determine which is the common use case, make the common case as default. Then provide a variant function to support another. For example: filter for raw row value as input type, filter_ts for feeding row object

(ii) Always return the row object. Then provide a convert/vec to make it turn into plain Array, but I suspect this will hurt the performance?

7. What if a table have many time columns, can we switch, what columns to use as timestamps?

Yes, the type with dynamic columns should support this funcitonality.

[sairus7]

I think we should divide our methods into three distinct parts, with increasing functionality:
A. Only timestamps vector with no data bound to it.
B. Timestamps + data vector (a single column).
C. Operations on tables.

Here are some (incomplete) considerations about theese three parts:

---

A. Timestamps

I agree that timeindex differ from integer index. One of the key difference - it has global "adress space". Integer index exist only within a specific collection, and can be changed or dropped when querying a subcollection or element. But timeindex refers to some "adress in time", not a certain collection, and cannot be dropped by default.

Also, while index is integer, timeindex is continuous, and it can have different precision levels (days, minutes and so on) with different rounding and comparison behaviour between two time values which have different precision.

A.1 Time types

What time types can be used:
a) DateTime instance - most accurate
b) Period - for time intervals, or time relative to some reference point
c) Sum of two different time Periods can produce another type, CompoundPeriod
d) a Number of seconds/minutes/etc…
e) a Unitful.jl time unit - is used in AxisArrays.jl, not quite sure if it works with built-in types and if we have to do something to support it.
f) Two values of above types?

Possible operations:

• Add, substract.
• Reduce precision (e.g. from days to months, from milliseconds to seconds).
• Compare two times, what should we do if they have different precision?
• Translate between absolute DateTime (a) and relative Period (b), from some reference point in time. Or maybe have different behaviour for them?

A.2. Vector of timestamps, some kind of "point process".

I agree that timestamps should be sorted and not unique.
But if they can repeat, we can get several elements instead of one, when requesting only one time value. Also, should join repeat rows if it joins one row of table 1 with several rows from table 2?

It can be:

1. Arbitrary
2. Discrete (ADC integrates some continuous amplitude within fixed timesteps)
   2a) Regular (with possible missing intervals)
   2b) Irregular

For discrete case, should we think that each timestamp has non-zero length equal to timestep?

I have some draft examples of how I use a combination of types from A.1 (a), (b), (d) as timestamps, and transformations between them: https://gist.github.com/sairus7/7a3f2ea6d3e0c34b4ea973d3b80105e8
Here I work both with absolute and relative times, but they are stored as relative indices. And for some operations I want to retrieve index itself, not a time type. There is a series of thansforms in both directions: integer index <-> number of milliseconds <-> Period <-> DateTime (sum of period and a starttime).

Possible operations:

• All vector operations (is it so?)
• Get index by time, returns index
• Get element by index, returns timestamp
• Get elements (or indices) within time range, returns timestamps subvector (or index range)
• Convert absolute time to relative (e.g. from first vector element?)
• Get a subvector of timestamps, AND:
  a) change timestamps relative to the first point of subvector?
  b) leave timestamps as is
• Calculate element number within some time interval (or any other reducing function).
• Same as above, but on a series of adjanced intervals (resample).
• Two "point process" timestamp vectors:
  • Merge two into one common (get all elements from both and re-sort them), with or without repetitions, or with priority of points from first vector.
  • Find indices of pairs with equal timestamps.
  • Find nearest neighbours (one-to-one).
  • Find nearest neighbours within time radius (one-to-one).
  • For previous three operations - also get all unmatched indices from first and second timestamp vector (to substract one from another)

---

B. Time vector / column

Here we have just two synced vectors - timestamp vector from A.2., and data vector. I will call it here a column.

Operations:

• All vector operations (is it so?)
• Make a subvector / view.
• Get index by time, returns index (same as above)
• Get time by index, returns timestamp (same as above)
• Get element by index, returns timestamp + value (?)
• Get element by time, return timestamp + value (or index + value?)
• Change time vector to another (or make a new column object) - and re-sort both vectors by timestamps vector.
• Change one timestamp element - and re-sort both vectors by timestamps vector (??)
• Compare two columns with each other, and:
  • All operations from A (two "point-process" vectors)
  • Make element-wise operations on two columns, synchronized (same as joined) by their timestamps. If their timestamp object is the same, this is a usual elementwise vector to vector operation.
  • Two columns with different timestamps, one have smaller timestep (higher frequency). Associate all elements from high-frequency column to elements of low-frequency columns (many-to-one), and vice-versa. Then reduce them with some function and get column-3 (or repeat them).
  • Find all timestamps from column-2 inside a time radius around each timestamp of column-1, and reduce them to some new value (results into a column-3 with the same timestamps as column-1)

---

C. Table - seems like this is just a set of columns from B, which have the same timestamps vector?

What about table of combinations, IndexedTable have sorted primary key, so they are in option 6 too.
Also, we missed AxisArrays.jl for option 8 (https://github.com/mbauman/Signals.jl was deprecated in favor of AxisArrays.jl), seems like it is similar to TimeSeries. AxisArrays has interesting functionality with indervals:

using AxisArrays, Dates
t = Dates.now()
timerange = t : Millisecond(5) : t + Millisecond(45)
data = reshape(1:20, :, 2) |> collect

a = AxisArray(data; time = (timerange), chan = ([:c1, :c2]))

a[time = t, chan = :c1]
a[time = t..t+Millisecond(10), chan = :c2]

I agree that we can start with option 2 from the table.

I agree we should return time series objects on getindex, select, transform or filter, and a single row object on getindex. For a row object, maybe we can transform row to data like this: data = row[]. Or it can be wrapped, similar to CategoricalValue. Type of data can be a named tuple, but only if we add static tables, or some function barriers for them.
What about issues with transform or filter, somewhat similar enumerate operator comes to mind:
for (i, v) in enumerate(x) ... end
We can start without time in returned result and see what happen then.

I agree on joins on non-index columns. Should join work with other table types (e.g. join TimeSeries with DataFrame and produce TimeSeries)?

In general, I don't see any disagreements with your proposals.

[iblislin]

The next step is completing the interface specs. I think the naming issue is the most difficult part. Feel free to correct me if my naming is confused.

A. Timestamps

A.1. Time types

I only want to discuss about (b) Period and (d), and others are fine for me. About the relative time to some reference point:
I think the only information that Period can hold about this is the 'offset' value, the information of reference point cannot be hold in this type. So let me clarify it, I want this:

(b) Period: for time intervals, or time offset value (time relative to some reference point).
(d) This is just a Period:

julia> Minute <: Period
true

Do we need a type for holding both reference point + offset value? Maybe no, at least I cannot find such type in Cartesian coordinate or in C/Cpp pointer, there isn't a type contains both info. So I think Period is enough.

The general policy of adding a operations:

• If the operation follows Base interface, just implement it in the specific package.
• If not, define a new interface in TimeSeries, and make all types supported.

Operations

Operations	interface	comment
Arithmetic	Base.:+, Base.:-, ...etc	> Add, substract. These should be provided by Base or the type package. TimeSeries won't change their behavior.
Reduce precision	❓ Base.round, Base.ceil, Base.floor	https://docs.julialang.org/en/v1/stdlib/Dates/#Rounding so I think this one is defined by each package.
Comparison	Base.:>, Base.:<	> what should we do if they have different precision? Just let packages define their own behavior.

A.2. Vector of timestamps

(well, I know nothing about the point process before you mention it, any resource that I can consult are appreciated)

But if they can repeat, we can get several elements instead of one, when requesting only one time value. Also, should join repeat rows if it joins one row of table 1 with several rows from table 2?

Allowing repeat does introduce some API design issues, I'm not sure about which one is the good design, just write down my thought here.

a) secondary index: By automatically building the secondary index that represent the given order, the join (or other) operations can be done via the compound key of timestamp + secondary index. For instance:

timestamp	secondary index	value
10:00:00	1	foo
10:00:00	2	bar
10:00:00	3	qwe
10:30:00	1	baz
...

But if they can repeat, we can get several elements instead of one, when requesting only one time value.

We can provide two set of APIs. The first set will use 'secondary index=1' as default, then return the Row object when querying.
The second set can accept the secondary index as a argument, then return a AbstractTimeSeries object when querying.

b) parametric type

By adding a boolean parameter in type that denotes that the existence of repeated timestamps, dispatch the AbstractTimeSeries instance to the different methods.

• If the boolean param is true, implies there are some repeated timestamps. Then all the related operations, like querying, returns a complete AbstractTimeSeries.
• If false. The behaviour of related operations is to return a Row object.

I have some draft examples of how I use a combination of types from A.1 (a), (b), (d) as timestamps, and transformations between them: https://gist.github.com/sairus7/7a3f2ea6d3e0c34b4ea973d3b80105e8

This example is a good starting point.

A.2.i Types

So, assume that we have an abstract type AbstractTimeAxis that represent a vector of timestamp.
(or, is there a type maintained by JuliaData suitable?)

abstract type AbstractTimeAxis{T} <: AbstractVector{T} end

where T can be any of types mentioned in section A.

I think the naming is still need more discussion and aims to not confuse users.

• TimeGrid: It stores the starting time, frequency (or period) and optional ending time. (I consider RegularTimestamps from @sairus7's example as a special case of this type).
• IrregularTimeGrid: just rename the IrregularTImestamps in example.
• SparseTimeGrid: rename the SparseTimestamps in example.

A.2.ii Operations

a. Support the iterator protocol

Some types in @sairus7's example are lazy (calculate the timestamp while needed). I will make it support the iterator protocol, so user can materialize it if desire.

b. Indexing related operations

Function	Return Type	Comment
getindex(::AbstractTimeAxis, i::Int)	TimeType or KeyError	Integer index -> TimeType
getindex(::AbstractTimeAxis, t::TimeType)	Integer or KeyError	Integer index <- TimeType
findfirst(::Base.Fix2{typeof(>=),<:TimeType}, ::AbstractTimeAxis), findlast, findnext and findprev	Integer or Nothing	integer index <- TimeType. Where the typeof(>=(Dates.now())) is Base.Fix2{typeof(==),DateTime}.
and other comparison function >, ==, !=, <, <= with find* family	Integer or Nothing	Integer index <- TimeType
findfirst(::typeof(nss), ::AbstractTimeAxis) and findlast	Integer or Nothing	Integer index <- TimeType. Where the nss function is defined in the section A.2.ii.h, the keyword argument c should be set.

c. Relative time calculation

The signature getindex(::TimeGrid, ::Period) in @sairus7's example is used for the relative time calculation.
I think a common notation is in the form of T+n (e.g. T+42). Maybe we can have the + and - for this purpose?

Function	Return Type	Comment
getindex(::AbstractTimeAxis, ::typeof(+), n::Int)	Nanosecond	Step forward n timesteps. An example implementation could be here.
getindex(::AbstractTimeAxis, ::typeof(-), n::Int)	Nanosecond	Step backward.
getindex(::AbstractTimeAxis, ::typeof(+), p::Period)	Int	Index of relative time.
Base.:+(iter::AbstractTimeAxis, i::Union{Integer, Period})	AbstractTimeAxis	Return a new iterator with both of starting and ending reference point changed
Base.:-(iter::AbstractTimeAxis, i::Union{Integer, Period})	AbstractTimeAxis

Example:

julia> g = TimeGrid(DateTime(2020, 1, 1), 60)
TimeGrid(DateTime("2020-01-01T00:00:00"), 60.0)

julia> g[+, 0]
0 milliseconds

julia> g[+, 42]
700 milliseconds

julia> g[+, Minute(1)]
3601

d. Get a subvector of timestamps

Support view to return a new iterator. like the RegularTimestamps in the example code.

Function	Return Type	Comment
view(iter::AbstractTimeAxis, i::ClosedInterval{Int64})	AbstractTimeAxis	Return a new iterator starting from iter + i to j timesteps. The interval type is provided by IntervalSets.jl.
getindex(iter::AbstractTimeAxis, i::ClosedInterval{Int64})	AbstractTimeAxis	behaves same as view
collect(iter::AbstractTimeAxis)	Vector	Materialize the vector of timestamps

changes timestamp relative to the first point of subvector?

I think this can be simply achieved by cumsum(diff(iter)), we can just add a shorthand method for it, what's the best naming?

e. Reduction operations

Function	Return Type	Comment
count(::AbstractRange, ::AbstractTimeAxis)	Integer	Count the discrete time point in the time interval
reduce(::Base.Callable, ::AbstractTimeAxis; init)	Any	The associativity of the reduction is determined by the iterator via the iteration protocol.
foldl(::Base.Callable, ::AbstractTimeAxis; init)	Any	The associativity is small-to-big of timestamps
foldr(::Base.Callable, ::AbstractTimeAxis; init)	Any	The associativity is big-to-small of timestamps

f. Resampling operations

• The resampling operations can perform both downsampling and upsampling
• Maybe we can merge the code from https://github.com/femtotrader/TimeSeriesResampler.jl

Function	Return Type	Comment
resample(::AbstractTimeAxis, ::Period) and resample!	AbstractTimeAxis	Change the frequency of the iterators
resample(::AbstractTimeAxis, ::Real) and resample!	AbstractTimeAxis	Change the frequency by the scale of origin freq

g. Consolidate two vector of timestamps: merge and intersect

This is a quite complex case dealing with the AbstractTimeAxis. Let discuss this issue with the type TimeGrid and IrregularTimestamps. I will consider RegularTimestamps as a special case of TimeGrid.

• case 1: given two TimeGrid with period (or freq) p and q, and the ratio p/q is a rational number. The output type is TimeGrid.
• case 2: similar to case 1, but the ratio p/q is a irrational number. The output type is IrregularTimestamps.
• case 3: any one of input type is a IrrgularTimestmps, the output is IrregularTimestamps.

About the case 1 and 2, I reduce the problem as the product (or sum) of periodic function problem. The product (or sum) of two periodic functions may or may not be a periodic function. It depends on the period ratio. But in case of implementation, I want to treat a normal Float64 as rational number unless user use the type Irrational (e.g. Irrational{:π}) explicitly.

Function	Return Type	Comment
merge(::AbstractTimeAxis, ::AbstractTimeAxis) or :*(...)	AbstractTimeAxis	similar to product of two periodic function
intersect(::AbstractTimeAxis, ::AbstractTimeAxis) or :+(...)	AbstractTimeAxis	similar to sum of two periodic function

h. Search the point with given criteria, like equal or nearest neighbours

For two point process

• Find indices of pairs with equal timestamps.

• Find nearest neighbours (one-to-one).

• Find nearest neighbours within time radius (one-to-one).

• For previous three operations - also get all unmatched indices from first and second timestamp vector (to substract one from another)

I propose implementing findall with extra functions/helper types representing criteria:

Function	Return Type	Comment
findall(::typeof(==), ::AbstractTimeAxis, ::AbstractTimeAxis)	Vector{Tupe{Int,Union{Int,Missing}}}	the indices of pairs. If unmatched, it will be filled with missing.
findall(::NearestNeighbours, ::AbstractTimeAxis, ::AbstractTimeAxis)	Vector{Tupe{Int,Union{Int,Missing}}}
nns(; k::Int=1, c=nothing, radius::Period, direction=:both)	NearestNeighbours type	nns stands for nearest neighbour search. direction can be :forward, :backward or :both. c is the centroid and not used in this case.

• I found that AxisKeys.jl use the naming Near for nearest neighbours search. Which is the better naming, nns, Near or ≈ (\approx)?

i. Common vector operations

Here I only list some operations being notable for discussion.

Function	Return Type	Comment
diff(::AbstractTimeAxis)	AbstractTimeAxis	Use the lazy representation if possible.

B. Time vector / column

Here we have just two synced vectors - timestamp vector from A.2., and data vector. I will call it here a column.

And I will consider the time vector is a AbstractTimeSeries.

B.1 Operations

a. Indexing

Function	Return Type	Comment
getindex(::AbstractTimeSeries, ::TimeType)	Row type or KeyError	Timestamp -> Row type. Row type will hold index + timestamp + value
getindex(::AbstractTimeSeries, ::Int)	Row type	Integer index -> Row type
getindex(::AbstractTimeSeries, ::TimeType, ::Symbol)	Any	If the ::Symbol refers to the timestamp vector, this function returns index. For other cases, it returns the value from data vector.
getidnex(::AbstractTimeSeries, ::Int, ::Symbol)	Any	If the ::Symbol refers to the timestamp vector, this function returns timestamp. For other cases, it returns the value from data vector.
setindex!(::AbstractTimeSeries, ::AbstractTimeAxis, ::Symbol)	AbstractTimeSeries	Change the timestamp vector and resort. e.g. ts[:time] = TimeGrid(...)
setindex!(::AbstractTimeSeries, ::TimeType, ::Symbol, ::Union{Int, TimeType}	AbstractTimeSeries	Update a specific timestamp and resort data. e.g. ts[:time, 42] = DateTime(...). or ts[:time, DateTime(...)] = DateTime(...) (?: is there a better API design? or this is acceptable.)
findfirst(::Base.Fix2{typeof(==),<:TimeType}, ::AbstractTimeSeries) and other comparison operators	Integer or Nothing	Timestamp -> integer index.
findfirst(::typeof(nss), ::AbstractTimeSeries)	Integer or Nothing	Timestamp -> integer index. Where the nss function is defined in section A.2.ii.h.
findlast, findnext and findprev	Integer or Nothing	Timestamp -> integer index.

b. Element-wise binary operations with two `AbstractTimeSeries`

• The two AbstractTimeSeriess should have the same number of columns.
• Determine the new timestamp.
  • First, determine the output type from the merge algorithm of two timestamp vectors from the section B.
  • If the new timestamp vector is still a TimeGrid (or RegularTimestamp), then check the frequency issue. And execute the higher-freq to lower-freq (many-to-one) mapping
  • If user want to change/reduce the output freq, one can use the resample function later.
• The empty data value will be filled with missing.

  Function	Return Type	Comment
  .+, .-, .*, ./ and other arithmetic operations	AbstractTimeSeries

c. Get a sub-table or view

Function	Return Type	Comment
view(::AbstractTimeSeries, ::Union{Int, UnitRange{<:Int}, Colon, TimeType, AbstractTimeAxis}, ::Union{Int, UnitRange{<:Int}, Colon, Symbol, Vector{Symbol}} )	Sub-table type	should not copy the data
getindex with the same arguments as view	AbstractTimeSeries	It will copy
filter(::typeof(nss), ::AbstractTimeSeries) and filter!	AbstractTimeSeries	filter! is optionally supported.
filter(::Base.Callable, ::AbstractTimeSeries) and filter!	AbstractTimeSeries	If the number of col is 1, the input of the custom function is the scalar value. If # of column is more than 2, the input of custom function is a named tuple. filter! is optionally supported.
select(::AbstractTimeSeries, ::Symbol...) and select!	AbstractTimeSeries	select! is optionally supported.

d. `join` operations

• The method naming issue: (Reconsider overloading Base.join? JuliaData/DataFrames.jl#2092). One of the point is to be consistent with SQL and dplyr.
• Include DataAPI to extend the interface. (Add join family without default definition JuliaData/DataAPI.jl#36)
• corssjoin won't be supported.
• In all join operations, the time axis is the required join key.
• if the nearest neighbour search is needed for join condition, pass its output to on. e.g. on = nns(...).
• The on kwarg can be passed a vector of column names to create a compound join key.

Function	Return Type	Comment
innerjoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries	One-to-one comparison only. No extra handling for high-to-low or low-to-high frequency cases.
outerjoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries	One-to-one comparison only.
leftjoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries
rightjoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries
semijoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries
antijoin(::AbstractTimeSeries, ::AbstractTimeSeries; on = nothing)	AbstractTimeSeries

e. Change the time vector

Function	Return Type	Comment
lag(::AbstractTimeSeries, n::Integer)	AbstractTimeSeries	lag! is optionally supported
lead(::AbstractTimeSeries, n::Integer)	AbstractTimeSeries	lead! is optionally supported
reindex(::AbstractTimeSeries, AbstractTimeAxis; pad = :const, padvalue = missing)	AbstractTimeSeries	Change the time axis. Are there other naming options? the term reindex exists in Pandas. The inplace method reindex! is optionally supported. The padding method for missing value is controlled by the keywrod arg pad. pading method can be :const, :forward, :backward, :nearest.

f. Reduction operations on values for single table

Function	Return Type	Comment
maximum(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	The kwarg dims is required. If dims=1, it returns a table with the latest timestamp.
minimum(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	The kwarg dims is required. If dims=1, it returns a table with the first timestamp.
findmax(::AbstractTimeSeries; dims::Integer)	Tuple{AbstractTimeAxis,Vector{Int}}	dims is required.
findmin(::AbstractTimeSeries; dims::Integer)	Tuple{AbstractTimeAxis,Vector{Int}}	dims is required.
cumsum(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	dims is required. If dims=1, it returns a table with the first timestamp.
cumprod(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	dims is required. If dims=1, it returns a table with the first timestamp.
argmax(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	The kwarg dims is required. If dims=1, it returns a table with the latest timestamp.
argmin(::AbstractTimeSeries; dims::Integer)	AbstractTimeSeries	The kwarg dims is required. If dims=1, it returns a table with the first timestamp.

g. Resampling operations

Function	Return Type	Comment
resample(f::Base.Callable, ::AbstractTimeSeries, ::Period) and resample!	AbstractTimeSeries	The input of function f is a view of AbstractTimeSeries, the output should be a AbstractTimeSeries (or maybe support NameTuple ?). resample! is optionally supported.
resample(f::Base.Callable, ::AbstractTimeSeries, ::Real) and resample!	AbstractTimeSeries	The input of function f is a view of AbstractTimeSeries, the output should be a AbstractTimeSeries. resample! is optionally supported.

C. Table

seems like this is just a set of columns from B, which have the same timestamps vector?

Yes, so how about the treat the section B and C as the same?
I think there aren't different operations between B and C.

Also, we missed AxisArrays.jl for option 8 (https://github.com/mbauman/Signals.jl was deprecated in favor of AxisArrays.jl), seems like it is similar to TimeSeries. AxisArrays has interesting functionality with indervals:

The interval feature looks great. If I understand correctly, that interval data type is provided by IntervalSets.jl, and we can support it.

[sairus7]

A side note about precision and rounding, which is closely related to the question from A.2: "should we think that each timestamp has non-zero length equal to timestep?"

Why would we need it? I think of how to represent time segments (intervals) as timestamps, and the main difference is that intervals have additional "time length" attribute. Which makes me think that any timestamp is not a point with zero length, but a time interval with "unit" length. This is similar to the inner representation of timestamp itself as integer value (UTInstant) of either nanoseconds, minutes, days, moths, etc., so any floating-point value is trucnated to the nearest previous integer.

But AFAIK there are no methods to check that higher-resolution timestamp lies within a lower-resolution timestamp. More than that, we even don't know the actual resolution, right?

using Dates
t_month = floor(Dates.now(), Dates.Month)
t_sec = floor(Dates.now(), Dates.Second)
t_sec in t_month == true # method error

From this example t_sec should start with current second it points to and end just before the next second.
t_month should start with first day of the current month and end before the first day of the next month. With this knowledge we can more naturally join, groupby (or resample) two timestamp vectors with different known resolutions.

I'm not sure if we should leave this to user knowledge of his data, or decide to make some additional time-interval operations and check for (or dispatch on) known and unknown time-length. But if we do, then we should add some additional timestamp vector types with metadata.