# PAR Model¶

In this guide we will go through a series of steps that will let you discover functionalities of the PAR model for timeseries data.

## What is PAR?¶

The PAR class is an implementation of a Probabilistic AutoRegressive model that allows learning multi-type, multivariate timeseries data and later on generate new synthetic data that has the same format and properties as the learned one.

Additionally, the PAR model has the ability to generate new synthetic timeseries conditioned on the properties of the entity to which this timeseries data would be associated.

Note

The PAR model is under active development. Please use it, try it on your data and give us feedback on a github issue or our Slack workspace

## Quick Usage¶

We will start by loading one of our demo datasets, the nasdaq100_2019, which contains daily stock marked data from the NASDAQ 100 companies during the year 2019.

In [1]: from sdv.demo import load_timeseries_demo

In [2]: data = load_timeseries_demo()

Out[3]:
Symbol       Date       Open      Close     Volume     MarketCap      Sector                Industry
0   AAPL 2018-12-31  39.632500  39.435001  140014000  7.378734e+11  Technology  Computer Manufacturing
1   AAPL 2019-01-02  38.722500  39.480000  148158800  7.378734e+11  Technology  Computer Manufacturing
2   AAPL 2019-01-03  35.994999  35.547501  365248800  7.378734e+11  Technology  Computer Manufacturing
3   AAPL 2019-01-04  36.132500  37.064999  234428400  7.378734e+11  Technology  Computer Manufacturing
4   AAPL 2019-01-07  37.174999  36.982498  219111200  7.378734e+11  Technology  Computer Manufacturing


As you can see, this table contains information about multiple Tickers, including:

• Symbol of the Ticker.

• Date associated with the stock market values.

• The opening and closing prices for the day.

• The Volume of transactions of the day.

• The MarketCap of the company

• The Sector and the Industry in which the company operates.

This data format is a very common and well known format for timeseries data which includes 4 types of columns:

### Entity Columns¶

These are columns that indicate how the rows are associated with external, abstract, entities. The group of rows associated with each entity_id form a time series sequence, where order of the rows matters and where inter-row dependencies exist. However, the rows of different entities are completely independent from each other.

In this case, the external entity is the company, and the identifier of the company within our data is the Symbol column.

In [4]: entity_columns = ['Symbol']


Note

In some cases, the datsets do not contain any entity_columns because the rows are not associated with any external entity. In these cases, the entity_columns specification can be omitted and the complete dataset will be interpreted as a single timeseries sequence.

### Context¶

The timeseries datasets may have one or more context_columns. context_columns are variables that provide information about the entities associated with the timeseries in the form of attributes and which may condition how the timeseries variables evolve.

For example, in our stock market case, the MarketCap, the Sector and the Industry variables are all contextual attributes associated with each company and which have a great impact on what each timeseries look like.

In [5]: context_columns = ['MarketCap', 'Sector', 'Industry']


Note

The context_columns are attributes that are associated with the entities, and which do not change over time. For this reason, since each timeseries sequence has a single entity associated, the values of the context_columns are expected to remain constant alongside each combination of entity_columns values.

### Sequence Index¶

By definition, the timeseries datasets have inter-row dependencies for which the order of the rows matter. In most cases, this order will be indicated by a sequence_index column that will contain sortable values such as integers, floats or datetimes. In some other cases there may be no sequence_index, which means that the rows are assumed to be already given in the right order.

In this case, the column that indicates us the order of the rows within each sequence is the Date column:

In [6]: sequence_index = 'Date'


### Data Columns¶

Finally, the rest of the columns of the dataset are what we call the data_columns, and they are the columns that our PAR model will learn to generate synthetically conditioned on the values of the context_columns.

Let’s now see how to use the PAR class to learn this timeseries dataset and generate new synthetic timeseries that replicate its properties.

For this, you will need to:

• Import the sdv.timeseries.PAR class and create an instance of it passing the variables that we just created.

• Call its fit method passing the timeseries data.

• Call its sample method indicating the number of sequences that we want to generate.

In [7]: from sdv.timeseries import PAR

In [8]: model = PAR(
...:     entity_columns=entity_columns,
...:     context_columns=context_columns,
...:     sequence_index=sequence_index,
...: )
...:

In [9]: model.fit(data)


Note

Notice that the model fitting process took care of transforming the different fields using the appropriate Reversible Data Transforms to ensure that the data has a format that the underlying models can handle.

### Generate synthetic data from the model¶

Once the modeling has finished you are ready to generate new synthetic data by calling the sample method from your model passing the number of the sequences that we want to generate.

Let’s start by generating a single sequence.

In [10]: new_data = model.sample(1)


This will return a table identical to the one which the model was fitted on, but filled with new synthetic data which resembles the original one.

In [11]: new_data.head()
Out[11]:
Symbol       Date       Open       Close   Volume     MarketCap Sector Industry
0      a 2019-01-01 -71.884493  288.410820  6569659  5.108324e+10    NaN      NaN
1      a 2019-01-02  93.943953  146.852024  8035699  5.108324e+10    NaN      NaN
2      a 2019-01-04  59.918731  179.637401  6569659  5.108324e+10    NaN      NaN
3      a 2019-01-07  84.278194  104.172287  3853769  5.108324e+10    NaN      NaN
4      a 2019-01-07  65.236900   76.599564  4321088  5.108324e+10    NaN      NaN


Note

Note

Notice how the model generated a random string for the Symbol identifier which does not look like the regular Ticker symbols that we saw in the original data. This is because the model needs you to tell it how these symbols need to be generated by providing a regular expression that it can use. We will see how to do this in a later section.

### Save and Load the model¶

In many scenarios it will be convenient to generate synthetic versions of your data directly in systems that do not have access to the original data source. For example, if you may want to generate testing data on the fly inside a testing environment that does not have access to your production database. In these scenarios, fitting the model with real data every time that you need to generate new data is feasible, so you will need to fit a model in your production environment, save the fitted model into a file, send this file to the testing environment and then load it there to be able to sample from it.

Let’s see how this process works.

#### Save and share the model¶

Once you have fitted the model, all you need to do is call its save method passing the name of the file in which you want to save the model. Note that the extension of the filename is not relevant, but we will be using the .pkl extension to highlight that the serialization protocol used is pickle.

In [12]: model.save('my_model.pkl')


This will have created a file called my_model.pkl in the same directory in which you are running SDV.

Note

If you inspect the generated file you will notice that its size is much smaller than the size of the data that you used to generate it. This is because the serialized model contains no information about the original data, other than the parameters it needs to generate synthetic versions of it. This means that you can safely share this my_model.pkl file without the risk of disclosing any of your real data!

#### Load the model and generate new data¶

The file you just generated can be sent over to the system where the synthetic data will be generated. Once it is there, you can load it using the PAR.load method, and then you are ready to sample new data from the loaded instance:

In [13]: loaded = PAR.load('my_model.pkl')

Out[14]:
Symbol       Date        Open       Close   Volume     MarketCap       Sector Industry
0      a 2018-12-28  128.691390  167.067695 -4648538  8.075710e+10  Health Care      NaN
1      a 2019-01-01  151.974849  193.628866  6091985  8.075710e+10  Health Care      NaN
2      a 2019-01-03  148.042099  220.129512  5198613  8.075710e+10  Health Care      NaN
3      a 2019-01-02  145.789941  186.299063  4987714  8.075710e+10  Health Care      NaN
4      a 2019-01-06  161.697250  157.542294  2211275  8.075710e+10  Health Care      NaN


Warning

Notice that the system where the model is loaded needs to also have sdv installed, otherwise it will not be able to load the model and use it.

### Conditional Sampling¶

In the previous examples we had the model generate random values for use to populate the context_columns and the entity_columns. In order to do this, the model learned the context and entity values using a GaussianCopula, which later on was used to sample new realistic values for them. This is fine for cases in which we do not have any constraints regarding the type of data that we generate, but in some cases we might want to control the values of the contextual columns to force the model into generating data of a certain type.

In order to achieve this, we will first have to create a pandas.DataFrame with the expected values.

As an example, let’s generate values for two companies in the Technology and Health Care sectors.

In [15]: import pandas as pd

In [16]: context = pd.DataFrame([
....:     {
....:         'Symbol': 'AAAA',
....:         'MarketCap': 1.2345e+11,
....:         'Sector': 'Technology',
....:         'Industry': 'Electronic Components'
....:     },
....:     {
....:         'Symbol': 'BBBB',
....:         'MarketCap': 4.5678e+10,
....:         'Sector': 'Health Care',
....:         'Industry': 'Medical/Nursing Services'
....:     },
....: ])
....:

In [17]: context
Out[17]:
Symbol     MarketCap       Sector                  Industry
0   AAAA  1.234500e+11   Technology     Electronic Components
1   BBBB  4.567800e+10  Health Care  Medical/Nursing Services


Once you have created this, you can simply pass the dataframe as the context argument to the sample method.

In [18]: new_data = model.sample(context=context)


And we can now see the data generated for the two companies:

In [19]: new_data[new_data.Symbol == 'AAAA'].head()
Out[19]:
Symbol       Date        Open       Close    Volume     MarketCap      Sector               Industry
0   AAAA 2019-01-02  307.136884  329.584775   6569659  1.234500e+11  Technology  Electronic Components
1   AAAA 2019-01-02  287.600364  266.314908  17295459  1.234500e+11  Technology  Electronic Components
2   AAAA 2019-01-04  180.082566  294.810512   5573774  1.234500e+11  Technology  Electronic Components
3   AAAA 2019-01-07  247.106467  222.289814   3811807  1.234500e+11  Technology  Electronic Components
4   AAAA 2019-01-08  261.889996  285.043352   4355697  1.234500e+11  Technology  Electronic Components

In [20]: new_data[new_data.Symbol == 'BBBB'].head()
Out[20]:
Symbol       Date        Open       Close    Volume     MarketCap       Sector                  Industry
252   BBBB 2019-01-02  183.437196  224.662597   6569659  4.567800e+10  Health Care  Medical/Nursing Services
253   BBBB 2019-01-01  194.999228  239.718958  13585819  4.567800e+10  Health Care  Medical/Nursing Services
254   BBBB 2019-01-04  206.219318  181.995457   7593167  4.567800e+10  Health Care  Medical/Nursing Services
255   BBBB 2019-01-05  183.437196  199.526551   3873297  4.567800e+10  Health Care  Medical/Nursing Services
256   BBBB 2019-01-07  186.309442  187.886965   2124316  4.567800e+10  Health Care  Medical/Nursing Services


Now that we have discovered the basics, let’s go over a few more advanced usage examples and see the different arguments that we can pass to our PAR Model in order to customize it to our needs.

### How to customize the generated IDs?¶

In the previous examples we saw how the Symbol values were generated as random strings that do not look like those typically seen for Tickers, which usually are strings made of between 2 and 4 uppercase letters.

In order to fix this and force the model to generate values that are valid for the field, we can use the field_types argument to indicate the characteristics of each field by passing a dictionary that follows the Metadata field specification.

For this case in particular, we will indicate that the Symbol field needs to be generated using the regular expression [A-Z]{2,4}.

In [21]: field_types = {
....:     'Symbol': {
....:         'type': 'id',
....:         'subtype': 'string',
....:         'regex': '[A-Z]{2,4}'
....:     }
....: }
....:

In [22]: model = PAR(
....:     entity_columns=entity_columns,
....:     context_columns=context_columns,
....:     sequence_index=sequence_index,
....:     field_types=field_types
....: )
....:

In [23]: model.fit(data)


After this, we can observe how the new Symbols are generated as indicated.

In [24]: model.sample(num_sequences=1).head()
Out[24]:
Symbol       Date       Open      Close   Volume     MarketCap             Sector               Industry
0     AA 2019-01-02 -17.872941  76.415811  8997374  8.544824e+10  Consumer Services  Electronic Components
1     AA 2019-01-01 -68.648649  85.624796  9204070  8.544824e+10  Consumer Services  Electronic Components
2     AA 2019-01-06 -15.376359  21.809077  6569659  8.544824e+10  Consumer Services  Electronic Components
3     AA 2019-01-07 -21.263334   2.222860  8753115  8.544824e+10  Consumer Services  Electronic Components
4     AA 2019-01-07  -0.142471  -4.065077    78403  8.544824e+10  Consumer Services  Electronic Components


Note

Notice how in this case we only specified the properties of the Symbol field and the PAR model was able to handle the other fields appropriately without needing any indication from us.

### Can I control the length of the sequences?¶

When learning the data, the PAR model also learned the distribution of the lengths of the sequences, so each generated sequence may have a different length:

In [25]: model.sample(num_sequences=5).groupby('Symbol').size()
Out[25]:
Symbol
AA    237
AB    252
AC    252
AE    252
dtype: int64


If we want to force a specific length to the generated sequences we can pass the sequence_length argument to the sample method:

In [26]: model.sample(num_sequences=5, sequence_length=100).groupby('Symbol').size()
Out[26]:
Symbol
AA    100
AB    100
AC    100
AE    100
dtype: int64


### Can I use timeseries without context?¶

Sometimes the timeseries datasets do not provide any additional properties from the entities associated with each sequence, other than the unique identifier of the entity.

Let’s simulate this situation by dropping the context columns from our data.

In [27]: no_context = data[['Symbol', 'Date', 'Open', 'Close', 'Volume']].copy()

Out[28]:
Symbol       Date       Open      Close     Volume
0   AAPL 2018-12-31  39.632500  39.435001  140014000
1   AAPL 2019-01-02  38.722500  39.480000  148158800
2   AAPL 2019-01-03  35.994999  35.547501  365248800
3   AAPL 2019-01-04  36.132500  37.064999  234428400
4   AAPL 2019-01-07  37.174999  36.982498  219111200


In this case, we can simply skip the context columns when creating the model, and PAR will be able to learn the timeseries without imposing any conditions to them.

In [29]: model = PAR(
....:     entity_columns=entity_columns,
....:     sequence_index=sequence_index,
....:     field_types=field_types,
....: )
....:

In [30]: model.fit(no_context)

Out[31]:
Symbol       Date        Open       Close    Volume
0     AA 2019-01-02  271.870294  183.531971  17555765
1     AA 2019-01-04  154.734828  165.688874   6569659
2     AA 2019-01-05  155.601747  152.540718   8734688
3     AA 2019-01-06  150.953032  183.531971  10771765
4     AA 2019-01-09  151.138982  140.814244   6117260


In this case, of course, we are not able to sample new sequences conditioned on any value, but we are still able to force the symbols that we want on the generated data by passing them in a pandas.DataFrame

In [32]: symbols = pd.DataFrame({
....:     'Symbol': ['TSLA']
....: })
....:

Out[33]:
Symbol       Date        Open       Close   Volume
0   TSLA 2019-01-07  210.315891  183.531971  6569659
1   TSLA 2019-01-03  183.437196  183.531971  9444219
2   TSLA 2019-01-06   43.354136   30.762127  5289528
3   TSLA 2019-01-04   35.306009   35.165767   457407
4   TSLA 2019-01-06   30.035686  183.531971  2049217


### What happens if there are no entity_columns either?¶

In some cases the timeseries datasets are made of a single timeseries sequence with no identifiers of external entities. For example, suppose we only had the data from one company:

In [34]: tsla = no_context[no_context.Symbol == 'TSLA'].copy()

In [35]: del tsla['Symbol']

Out[36]:
Date       Open      Close    Volume
1008 2018-12-31  67.557999  66.559998  31511500
1009 2019-01-02  61.220001  62.023998  58293000
1010 2019-01-03  61.400002  60.071999  34826000
1011 2019-01-04  61.200001  63.537998  36970500
1012 2019-01-07  64.344002  66.991997  37756000


In this case, we can simply omit the entity_columns argument when creating our PAR instance:

In [37]: model = PAR(
....:     sequence_index=sequence_index,
....: )
....:

In [38]: model.fit(tsla)

In [39]: model.sample()
Out[39]:
Date       Open      Close    Volume
0   2018-12-31  54.552286  51.873922  45715575
1   2018-12-31  58.558843  51.649230  78316980
2   2019-01-01  55.603399  55.005639  26436050
3   2019-01-02  55.277031  55.239350   6430053
4   2019-01-03  56.076203  58.568528  81543390
..         ...        ...        ...       ...
247 2019-12-13  59.431436  57.675351  58604330
248 2019-12-15  56.069973  57.830136  40572842
249 2019-12-16  59.474082  56.990021  29029974
250 2019-12-16  56.877771  54.898882  73402590
251 2019-12-19  57.661725  54.828524  62042644

[252 rows x 4 columns]