quantpylib.simulator.models

quantpylib.simulator.models house powerful features for statistical analysis involving market and non-market variables. It features quantpylib.simulator.models.GeneticRegression class that is an abstraction layer written on top of the quantpylib.simulator.gene.Gene class and statsmodels.formula.api to perform no-code regression analysis using simple string specifications.

An example scenario for quantitative analysis is a momentum study on the impact of standardized returns on forward returns. We may specify such a regression study by the following regression formula:

forward_1(logret_1()) ~ div(logret_25(),volatility_25()) + tsargmax_16(close)

The GeneticRegression enables this in multiple steps:

• Parse the formula into blocks:
  • b0: forward_1(logret_1())
  • b1: div(logret_25(),volatility_25())
  • b2: tsargmax_16(close)
• Construct the equivalent regression specification: b0 ~ b1 + b2
• Evaluate each block using our evaluator-parser in the Gene class.
• Pass the evaluated blocks and regression specification into statsmodels for regression analysis.

This allows the user to both leverage on the well-tested and familiar statistical package developed under statsmodels, while enhancing the expressive capabilities of the formulaic language specialized for trading analysis. The full list of primitives (constants and functions) are documented here.

We also provide additional convenience methods for data binning and aggregation, diagnostics and plotting. The specifications are to be referred below.

The following notations apply in the documentation:

- y, b0 : response variable
- x[*], b[1..] : independent variable(s)
- y^ : fitted response
- uCI : upper confidence interval
- lCI : lower confidence interval
- res : residuals
- res# : (z-score) normalized residuals
- res+ : internally studentized residuals
- res* : externally studentized residuals
- PRP : partial regression plot
- CCPR : component-component plus residual plot

Bin

Bases: Enum

Enumeration representing different binning methods.

Attributes:

Name	Type	Description
WIDTH		Binning method where each bin has an equal interval length.
OBSERVATIONS		Binning method where each bin contains an equal number of observations.

GeneticRegression

__init__(formula='forward_1(logret_1()) ~ div(logret_25(),volatility_25())', start=None, end=None, dfs={}, instruments=[], granularity=Period.DAILY, build=True)

Initializes a GeneticRegression object.

Parameters:

Name	Type	Description	Default
formula	str	The regression formula. The formula describes the statistical model being analysed, and is closely inspired by the formula mini-language used in R and S. The model formula should consist of valid string representations of Gene formula blocks as dependent and independent variables delimited by the operators [ ~ + * : ] of the patsy language.	'forward_1(logret_1()) ~ div(logret_25(),volatility_25())'
start	datetime	Start period for regression analysis. If not tz-aware, assumed UTC. If not given, assume min of dataset in dfs.	None
end	datetime	End period for regression analysis. If not tz-aware, assumed UTC. If not given, assume max of dataset in dfs.	None
dfs	dict	inst : OHLCV/other Dataframes used for computations. Default is an empty dictionary.	{}
instruments	list	List of instruments used in the regression analysis.	[]
granularity	Period	The granularity of the regression analysis. Datapoints of lower granularity than specified are ignored. Last known datapoint of multiple entries in the same granularity interval is taken. Default is Period.DAILY.	DAILY
build	bool	Whether to evaluate the formulaic blocks upon initialization. Default is True.	True

build()

Evaluates the formulaic (dependent and independent) blocks to be used as regression variables using the initialized formula and dataframes provided. If build=False at initialization, then build() needs to be called before any of the regression methods, such as ols, are called.

diagnose()

Diagnoses the regression model for multicollinearity and other issues.

Returns:

Type	Description
dict	A dictionary containing the following: "cond_num": Condition number of the derived design matrix "vif b[1..]" : variance inflation factor for the relevant regressor variable.

ols(axis='flatten', bins=0, binned_by=Bin.OBSERVATIONS, bin_block='b0', selector=None, aggregator=lambda x: np.mean(winsorize(x, limits=(0.05, 0.05))))

Performs Ordinary Least Squares (OLS) regression analysis.

Parameters:

Name	Type	Description	Default
axis	str	The axis along which the regression analysis is performed. Possible values are flatten, xs, or ts. flatten uses all of the available data as regression input. xs uses cross sectional data on a particular date as regression input. ts uses time series data for a particular instrument as regression input.	'flatten'
bins	int	The number of bins for grouping the data. If 0, no binning is performed. Defaults to 0.	0
binned_by	Bin	The method used for binning the data. Possible values are Bin.OBSERVATIONS or Bin.WIDTH, corresponding to equal number of observations in each bin and equal interval length in each bin respectiely.	OBSERVATIONS
bin_block	str	The block used for binning the data. Defaults to b0, the dependent variable.	'b0'
selector	str or datetime	str instrument when axis=ts and datetime index when axis=xs to perform regression on. Ignored when axis=flatten.	None
aggregator	callable or dict	Used for aggregating data within each bin. If callable is provided, then all of the blocks are aggregated using this function. Different aggregators can be provided for different blocks, by providing dictionary containing block : aggregator such as {"b0" : np.mean, "b1" : np.median}. Defaults to lambda x:np.mean(winsorize(x, limits=(0.05, 0.05))).	lambda x: mean(winsorize(x, limits=(0.05, 0.05)))

Returns:

Type	Description
RegressionResults	The statsmodels results of the OLS regression analysis.

parse_formula(formula) staticmethod

Obtains the block-formula mapping and the derived patsy formula describing the regression model.

Parameters:

Name	Type	Description	Default
formula	str	The regression formula. The formula describes the statistical model being analyzed and follows the syntax of the patsy formula. Supports [ ~ + * : ] operators.	required

Returns:

Name	Type	Description
tuple		A tuple containing dict: Mapping of block names to their respective formula blocks. str: The derived patsy formula representing the regression model.

Examples:

>>> GeneticRegression.parse_formula("forward_1(logret_1()) ~ div(logret_25(),volatility_25()) + tsargmax_16(close)")
({'b0': 'forward_1(logret_1())', 'b1': 'div(logret_25(),volatility_25())', 'b2': 'tsargmax_16(close)'}, 'b0~b1+b2')

plot(fit=True, diagnostics=True, influence=True, leverage=True)

Plots various diagnostic plots for the regression model.

Parameters:

Name	Type	Description	Default
fit	bool	If True, plots, for each regressor x, uCI ~ x lCI ~ x y ~ x y^ ~ x	True
diagnostics	bool	If True, plots, for each regressor, y ~ x, y^ ~ x, uCI ~ x, lCI ~ x res ~ x PRP CCPR	True
influence	bool	If True, plots res* ~ leverage	True
leverage	bool	If True, plots leverage ~ (res#)**2	True