# Time series manipulation in C#

In this section, we look at Deedle features that are useful when working with series data in C#. A series can be either ordered (e.g. time series) or unordered. Although we mainly look at operations on the Series type here, many of the operations can be applied to data frame Frame containing multiple series. Furthermore, data frame provides an elegant way for aligning and joining series.

You can also get the samples on this page as a C# source file from GitHub and run the samples.

## What is a series

• Key value mapping - a series is represented by a type Series<K, V> from the Deedle namespace. The type represents a data series mapping keys of type K to values of type V. There are no restriction on the types of keys and values, but some operations are only available for keys that can be ordered (implement the IComparable<K> interface).

• Typical uses - typical keys include int for ordinally indexed keys and DateTimeOffset when working with time series. The most common types of values are double or decimal for numeric data. Another common use of series is with keys of type string and values of type object to represent heterogeneous data set - typically a column in a data frame that stores multiple named properties of different types.

• Immutable - the type Series<K, V> is immutable. Once you create a series object, it cannot be changed. All operations that operate on series return a copy (and typically also copy the data of the series, although this is an internal aspect of the implementation). So, working with series is similar to workinig with .NET string type or with the IEnumerable<T> type using LINQ.

• Missing values - series is desinged to automatically support and handle missing data. This means that you can create a series where values are missing for some keys (e.g. when data is not available) and then handle missing values (provide defaults or fill with previous values). All series operations automatically propagate or handle missing data.

Once you referenced the Deedle NuGet package and opened the Deedle namespace, you can create series in a number of ways. The Deedle library implements the builder object pattern, so if you want to create a series explicitly, you can use the generic SeriesBuilder type.

### Using series builder

If you want to create a series with explicitly given list of key-value pairs, you can use the C# collection initializer syntax and SeriesBuilder<K, V>. The series builder exposes a property Series that returns (a cloned) series containing the values added so far:

 1: 2: 3:  var numNames = new SeriesBuilder() { { 1, "one" }, { 2, "two" }, { 3, "three" } }.Series; numNames.Print();

The SeriesBuilder<K, V> type implements the Add method, so you can also easily use it if you want to add elements one by one in a loop. The above snippet uses extension method Print to output the series to a console. In this case, the output will look as follows:

 1: 2: 3:  1 -> one 2 -> two 3 -> three 

Another feature supported by the series builder is the C# dynamic keyword. If you want to create a series that maps string keys to values (e.g. when building a row that you want to append to a data frame), you can do so as follows:

  1: 2: 3: 4: 5: 6: 7: 8: 9: 10:  // Create series builder and use it via 'dynamic' var nameNumsBuild = new SeriesBuilder(); dynamic nameNumsDyn = nameNumsBuild; nameNumsDyn.One = 1; nameNumsDyn.Two = 2; nameNumsDyn.Three = 3; // Build series and print it var nameNums = nameNumsBuild.Series; nameNums.Print();

Here, we assing SeriesBuilder<K, V> to a variable nameNumsDyn of type dynamic and use property setter syntax to add values for strng keys One, Two and Three. Then we convert the original series builder to a series and print it.

### Converting collections to series

Using the series builder is useful if you want to create series with some data explicitly from code. However, more commonly, you already have the data you want to use in some collection. In that case, you can use one of the extension methods exposed by Deedle.

If you only care about the values, you can use ToSeriesOrdinal which s defined for any IEnumerable<V> and automatically generates keys of type int. For example, here we create a series containing random double values:

 1: 2: 3: 4:  var rnd = new Random(); var randNums = Enumerable.Range(0, 100) .Select(_ => rnd.NextDouble()).ToOrdinalSeries(); randNums.Print();

If you want to create a series with specified keys and values, you can use extension method ToSeries on IEnumerable<KeyValuePair<K, V>>. The following snippet uses a helper method KeyValue.Create that is exposed by Deedle and makes it easier to create key value pairs:

 1: 2: 3: 4:  var sin = Enumerable.Range(0, 1000) .Select(x => KeyValue.Create(x, Math.Sin(x / 100.0))) .ToSeries(); sin.Print();

To create a series where values are missing for some keys, you need to use the type OptionalValue<K>. You can use two C#-friendly methods - to create an empty value, you can use OptionalValue.Empty<T>() and to convert a value value to optional, use OptionalValue.Create(value). Alternatively, you can also use OptionalValue.OfNullable:

 1: 2: 3: 4:  var opts = Enumerable.Range(0, 10) .Select(x => KeyValue.Create(x, OptionalValue.OfNullable(x))) .ToSparseSeries(); opts.Print();

Note that the sample uses extension method ToSparseSeries to indicate that we are creating series from a collection of key value pairs where the values may be missing. The resulting series has a type Series<int, int> (the fact that there are missing values has no effect on the type).

Finally, our last example uses the Frame type (you can find more about it in a separate data frame tutorial. We load data frame from a given CSV file, specify that we want to use the "Date" column as the index of type DateTime, order the rows and then get a time series representing the "Open" column:

 1: 2: 3: 4:  var frame = Frame.ReadCsv(Path.Combine(root, "../data/stocks/msft.csv")); var frameDate = frame.IndexRows("Date").SortRowsByKey(); var msftOpen = frameDate.GetColumn("Open"); msftOpen.Print();

The result is an ordered time series of type Series<DateTime, float> that we'll use in some of the later examples in this tutorial.

## Lookup and slicing

Given a series, the first thing that we might want to do is to access the data in the series. In this section, we look at lookup operations that can be used to retrieve values from series and slicing operations that give us a sub-series.

### Lookup by key and index

A series supports C# indexer that takes the series key as an argument. Given a series Series<K, V> and a key of type K, you can access the associated value using indexer. Series also supports random access using index, which can be done using the GetAt method:

 1: 2: 3: 4: 5: 6: 7:  // Get value for a specified int and string key var tenth = randNums[10]; var one = nameNums["One"]; // Get first and last value using index var fst = nameNums.GetAt(0); var lst = nameNums.GetAt(nameNums.KeyCount - 1);

Accessing an element may fail for two reasons. When the key is not present in the series, you get KeyNotFoundException. When the key is present, but the series does not contain any value for the key, the access operations throw MissingValueException (defined in Deedle namespace). To avoid handling exceptions, you can use TryGet and TryGetAt methods that return the result as OptionalValue<T>:

 1: 2: 3: 4: 5: 6: 7:  // Get value as OptionalValue and use it var opt = opts.TryGet(5); if (opt.HasValue) Console.Write(opt.Value); // For value types, we can convert to nullable type int? value1 = opts.TryGet(5).AsNullable(); int? value2 = opts.TryGetAt(0).AsNullable();

As the snippet shows, OptionalValue<T> can be processed easily using HasValue and Value properties. If the value contained in a series is a value type, then you can also turn the result into a more convenient nullable type using AsNullable extension method.

### Lookup and slicing for ordered series

The operations discussed so far work on any series. However, more is available if the series is ordered (e.g. time series representing MSFT stock prices that we loaded in the previous section).

First of all, if the value is not available for a specified key (say January 1, 2012) then we can ask the series to give us the value for nearest greater or smaller key that has a value. This is done using the Get method (which behaves as the indexer in the simple case):

  1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11:  // Get value exactly at the specified key var jan3 = msftOpen .Get(new DateTime(2012, 1, 3)); // Get value at a key or for the nearest previous date var beforeJan1 = msftOpen .Get(new DateTime(2012, 1, 1), Lookup.ExactOrSmaller); // Get value at a key or for the nearest later date var afterJan1 = msftOpen .Get(new DateTime(2012, 1, 1), Lookup.ExactOrGreater);

Even though no value is available for January 1, 2012 (because it was not a business day), the last two operations succeed and return a value.

The next set of operations that are available on ordered series perform slicing. Given a series representing the entire history of Microsoft stock prices (from 1975 to the present date), we can easily get a sub-series that represents values only for some sub-range of the original dates:

  1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13:  // Get a series starting/ending at // the specified date (inclusive) var msftStartIncl = msftOpen.StartAt(new DateTime(2012, 1, 1)); var msftEndIncl = msftOpen.EndAt(new DateTime(2012, 12, 31)); // Get a series starting/ending after/before // the specified date (exclusive) var msftStartExcl = msftOpen.After(new DateTime(2012, 1, 1)); var msftEndExcl = msftOpen.Before(new DateTime(2012, 12, 31)); // Get prices for 2012 (both keys are inclusive) var msft2012 = msftOpen.Between (new DateTime(2012, 1, 1), new DateTime(2012, 12, 31));

An important aspect of the slicing operations is that they can operate on lazily loaded series without evaluating it. For example, you can create a series that represents data from a database and then perform slicing without fetching the data. The fetching will only happen when other operations are performed and it will only fetch the data needed. For more information, see lazy data loading tutorial.

## Statistics and calculations

If a series contains numeric values (typically double) then we can perform various statistical operations and calculations with the series. The Deedle library supports standard numeric operators for series, basic statistical calculations (as extension methods) and it also gives you access to the underlying observations, in case you need to implement some calculation that is not directly supported.

The following example demonstrates the basic functionality by calculating the mean price of Microsoft stock prices over 2012 and then calculating the sum of squared differenc from the mean:

 1: 2: 3: 4: 5: 6: 7:  // Calculate median & mean price var msftMed = msft2012.Median(); var msftAvg = msft2012.Mean(); // Calculate sum of square differences var msftDiff = msft2012 - msftAvg; var msftSq = (msftDiff * msftDiff).Sum();

The snippet first uses extension method Mean (and also Median). Then it subtracts scalar value (number msftAvg) from a series (msft2012) to get a new series where each value is the result of subtracting the scalar from an original value.

The next line applies point-wise multiplication on two series - the result is a series where a value at each key is the multiplication of values at the same key in the two multiplied series. Finally, we use Sum to add all the differences.

Missing values. Note that all numerical operations on the Series<K, V> type carefuly handle missing data. If you have a series where value is not available for some dates, then the value is skipped when calculating statistics such as mean or sum. Point-wise and scalar operators automatically propagate missing data. When calculating s1 + s2 and one of the series does not contain data for a key k, then the resulting series will not contain data for k. For more about missing data, see the next section.

When calculating with time series, it is also useful to transform keys. For example, here is one possible approach to writing a calculation that calculates how the price changes between two days:

 1: 2: 3: 4: 5: 6: 7: 8: 9:   // Subtract previous day value from current day var msftChange = msft2012 - msft2012.Shift(1); // Use built-in Diff method to do the same var msftChangeAlt = msft2012.Diff(1); // Get biggest loss and biggest gain var minMsChange = msftChange.Min(); var maxMsChange = msftChange.Max();

The Shift operation creates a new series where the index is shifted by the specified offset. Using ser.Shift(1) creates a new series where element at index i is the element from index i - 1 in ser. In the above example, this means that the value in msft2012.Shift(1) for a certain day is the value for the previous day in msft2012. This means that the code takes prices at a specified day and subtracts yesterday's prices from them.

The operations available for series cover most of the standard operations, but if you need a more advanced functionality, you can always access the underlying data. For example, the Observations property gives you access to all key-value pairs of the series. The following calculates the price, divided by the number of days since the first day for which we have a value (this is just an example of an unusual calculation):

 1: 2:  var wackyStat = msft2012.Observations.Select(kvp => kvp.Value / (kvp.Key - msft2012.FirstKey()).TotalDays).Sum();

The following properties and methods are useful when writing custom calculations:

• Values - returns all values (skipping over missing data) in the series
• Observations - returns all observations (key-value pairs), skipping over missing data
• GetAllObservations() - returns all data, including keys with missing values
• FirstKey() - returns the first key (works only for ordered series)
• LastKey() - returns the last key (works only for ordered series)
• KeyCount - returns the number of keys in the series
• ValueCount - returns the number of values (may be smaller than KeyCount when the series contains missing values)

## Handling missing values

When discussing what is a series, we noted that series can contains missing values. This can happen when creating series from OptionalValue<T> values or, more frequently, when aligning data using data frames and then obtaining a series from a frame.

In this sample, we'll use an ordered series opts from earlier sample that contains keys from 0 to 9 and values only for even elements of the series - this means, the values are [0; NA; 2; NA; 4; NA; 6; NA; 8; NA].

For any series (oredered or unordered) we can drop the missing values or replace them with a constant:

 1: 2: 3: 4: 5: 6: 7:  // Fill missing data with constant var fillConst = opts.FillMissing(-1); fillConst.Print(); // Drop keys with no value from the series var drop = opts.DropMissing(); drop.Print();

The first operation returns a series with values [0; -1; 2; -1; 4; -1; 6; -1; 8; -1] and the second operation returns a series with keys [0; 2; 4; 6; 8].

If the series is ordered, we have one more option. We can fill missing values with the first previous available value, or with the first subsequent available value. This is done using an overlaod that takes Direction:

 1: 2: 3: 4: 5: 6: 7:  // Fill with previous available value var fillFwd = opts.FillMissing(Direction.Forward); fillFwd.Print(); // Fill with the next available value var fillBwd = opts.FillMissing(Direction.Backward); fillBwd.Print();

It is worth noting that this does not always fill all missing values in the series. If you use Direction.Forward and the input series contains [NA; 0; NA; 1] then the result is [NA; 0; 0; 1] - the first value is still missing, because there is no preceeding available value. However, you can be sure that the only missing values are at the beginning (or the end) of the series.

## LINQ to series

The Series<K, V> type implements some of the methods supported by the C# LINQ pattern, which means that you can process series in a familiar way and, to some extent, you can also use the C# query syntax.

The following example shows how to count the number of days when the Microsoft stock price was below the average (which we calculated earlier, using the msft2012.Mean() extension method). First, let's look at using the LINQ methods directly:

 1: 2: 3:  var overMean = msft2012 .Select(kvp => kvp.Value - msftAvg) .Where(kvp => kvp.Value > 0.0).KeyCount;

Both of the methods are defined on the Series<K, V> type - this means that the result is also a series and we can get the number of keys on the resulting series using the KeyCount property (the Where method drops the keys for which the condition does not hold).

Efficiency. Note that both Select and Where copy the series and so long method chaining will be less efficient. In that case, it is more desirable to use series.Values and operate on IEnumerable<T> before converting the result back to a series.

The same code can be also written using the C# query syntax as follows (this time, we get the number of days when the price was below the average):

 1: 2: 3: 4:  var underMean = ( from kvp in msft2012 where kvp.Value - msftAvg < 0.0 select kvp ).KeyCount;

The Series<K, V> type does not support all query operations, but you can certainly use from, where and select to transform and filter series. One tricky aspect is that the variable bound in the from clause is key value pair containing the key (index) and value (the value in the series) to allow projection/filtering based on both the key and the value.

## Grouping, windowing and chunking

Deedle supports a number of operations that can be used to group or aggregate data. There are two operations - for any (possibly unordered) series, grouping works by obtaining a new key for each observation and then grouping the input by such keys; aggregation works only on ordered series. It aggregates consecutive elements (possibly with overlap) of the series - a typical use of aggregation is getting floating windows of certain length.

### Grouping series

The grouping operation is similar to GroupBy from LINQ. It takes a key selector that produces a new key and a value selector that produces new value for a group of values with the same key. The following example uses randNums which is a series of 100 randomly generated values between 0 and 1. We group them by the first digit and count number of elements in each group to get the distribution of the random number generator:

 1: 2: 3: 4: 5:  // Group random numbers by the first digit & get distribution var buckets = randNums .GroupBy(kvp => (int)(kvp.Value * 10)) .Select(kvp => OptionalValue.Create(kvp.Value.KeyCount)); buckets.Print();

Note that the aggregation function needs to return OptionalValue<T>. This makes it possible to write aggregation that returns series with missing values for some key (e.g. when the group does not contain any valid value).

### Floating windows and chunking

When working with time series (e.g. stock prices), floating windows can be used to take the average value over certain number of previous values. The following example takes 5 last values for each day and averages them (skipping over the first 4 items in the series where there is not enough past values available):

 1: 2: 3: 4: 5: 6: 7:  // Average over 25 element floating window var monthlyWinMean = msft2012.WindowInto(25, win => win.Mean()); // Get floating window over 5 elements as series of series // and then apply average on each series individually var weeklyWinMean = msft2012.Window(5).Select(kvp => kvp.Value.Mean());

The chunking operation is similar to windowing, but it builds chunks that do not overlap. For example, given [1; 2; 3; 4] a floating window of size two returns [[1; 2]; [2; 3]; [3; 4]] while chunks of size two return [[1; 2]; [3; 4]]. The chunking operations look very similar to windowing operations:

 1: 2: 3: 4: 5: 6:  // Get chunks of size 25 and mean each (disjoint) chunk var monthlyChunkMean = msft2012.ChunkInto(25, win => win.Mean()); // Get series containing individual chunks (as series) var weeklyChunkMean = msft2012.Chunk(5).Select(kvp => kvp.Value.Mean());

Finally, it is very common to use windows of size two, which gives us the current value together with the previous value. In Deedle, this is available via the Pairwise operation which turns a series of values into a series of tuples (type Tuple<V, V>). Here we take the average of the current and previous value:

 1: 2: 3:  // For each key, get the previous value and average them var twoDayAvgs = msft2012.Pairwise().Select(kvp => (kvp.Value.Item1 + kvp.Value.Item2) / 2.0);

### General (ordered) aggregation

For chunking and windowing, previous examples always used a fixed number of elements to specify when a window/chunk ends. However, you might want to use more advanced conditions. This can be done using the fully general Aggregate operation. The Aggregation type in the following example provides methods for specifying additional conditions.

The options include windowing and chunking of fixed size where boundaries are handled differently, and windowing/chunking where each window/chunk ends when a certain property holds between the keys. For example, the following sample creates chunks such that the year and month are equal for each chunk:

  1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11:  msft2012.Aggregate ( // Get chunks while the month & year of the keys are the same Aggregation.ChunkWhile((k1, k2) => k1.Month == k2.Month && k2.Year == k1.Year ), // For each chunk, return the first key as the key and // either average value or missing value if it was empty chunk => KeyValue.Create ( chunk.Data.FirstKey(), chunk.Data.ValueCount > 0 ? OptionalValue.Create(chunk.Data.Mean()) : OptionalValue.Empty() ) );

The result of the operation is a series that has at most one value for each year/month which represents the average value in that month. When building the chunks, the aggregation calls the provided function (argument of ChunkWhile) on the first and the last key of the chunk until the function returns false and then it starts a new chunk.

## Indexing and sampling

In the last section of the series overview, we look at a number of operations that can be performed with the index of the series such as transformations and sampling. Index transformation is particularly important when working with multiple series in data frames (you might need to transform the keys so that you can align multiple series). Sampling is useful when you have a series with higher resolution of data than necessary, or when you need to transform data to uniform observations.

### Transforming the index

The first operation on the index is similar to Select, but instead of selecting new values, we select new keys. For example, given our msft2012 series which has DateTime values as keys, we might want to transform the keys to DateTimeOffset. Another useful operation drops the index and replaces it with ordinal numbers:

 1: 2: 3: 4: 5: 6:  // Turn DateTime keys into DateTimeOffset keys var byOffs = msft2012.SelectKeys(kvp => new DateTimeOffset(kvp.Key)); // Replace keys with ordinal numbers 0 .. KeyCount-1 var byInt = msft2012.IndexOrdinally();

Both of the operations in the snippet return series of a different type. Here, the type of byOffs is Series<DateTimeOffset, double> because the type of keys has changed from DateTime to DateTimeOffset (this is all inferred by the C# compiler, so we do not need to write the type explicitly). In the second example, the resulting type is Series<int, double>, because the keys are dropped and replaced with numbers in range 0 .. KeyCount-1.

Finally, if we want to replace an existing series of keys with a new series of keys (of the same length), we can use the IndexWith method. Here, we replace the index of a series numNames which has three observations with three dates:

 1: 2: 3: 4: 5:  // Replace keys with explictly specified new keys var byDays = numNames.IndexWith(new[] { DateTime.Today, DateTime.Today.AddDays(1.0), DateTime.Today.AddDays(2.0) });

Just like the two previous operations, IndexWith also changes the type of the series. It can also change whether the series is ordered or not (here, the resulting series has DateTime keys and is ordered).

### Time series sampling

When a series is ordered and the keys represent (typically) dates or times, we can use a number of sampling operations. There are two kinds of sampling operations:

• Resampling means that we aggregate values values into chunks based on a specified collection of keys (e.g. explicitly provided times), or based on some relation between keys (e.g. date times having the same date).

• Uniform resampling is similar to resampling, but we specify keys by providing functions that generate a uniform sequence of keys (e.g. days), the operation also fills value for days that have no corresponding observations in the input sequence.

Given a series ts, the sampling operations are available via the extension methods ts.Sample(..), ts.SampleInto(..), and ts.ResampleUniform(..). For more information about these methods, see the API reference and also the F# samples which are written using corresponding F# functions in the Series module.