arch.univariate.ARCHInMean¶

(G)ARCH-in-mean model and simulation

Parameters:¶

y: ndarray | DataFrame | Series | None = None¶: nobs element vector containing the dependent variable
x: ndarray | DataFrame | None = None¶: nobs by k element array containing exogenous regressors
lags: None | int | list[int] | ndarray = None¶: Description of lag structure of the HAR. Scalar included all lags between 1 and the value. A 1-d array includes the AR lags lags[0], lags[1], …
constant: bool = True¶: Flag whether the model should include a constant
hold_back: int | None = None¶: Number of observations at the start of the sample to exclude when estimating model parameters. Used when comparing models with different lag lengths to estimate on the common sample.
volatility: VolatilityProcess | None = None¶: Volatility process to use in the model. volatility.updateable must return True.
distribution: Distribution | None = None¶: Error distribution to use in the model
rescale: bool | None = None¶: Flag indicating whether to automatically rescale data if the scale of the data is likely to produce convergence issues when estimating model parameters. If False, the model is estimated on the data without transformation. If True, than y is rescaled and the new scale is reported in the estimation results.
form: int | float | 'log' | 'vol' | 'var' = 'vol'¶: The form of the conditional variance that appears in the mean equation. The string names use the log of the conditional variance (“log”), the square-root of the conditional variance (“vol”) or the conditional variance. When specified using a float, interpreted as \(\sigma_t^{form}\) so that 1 is equivalent to “vol” and 2 is equivalent to “var”. When using a number, must be different from 0.

Examples

>>> import numpy as np
>>> from arch.univariate import ARCHInMean, GARCH
>>> from arch.data.sp500 import load
>>> sp500 = load()
>>> rets = 100 * sp500["Adj Close"].pct_change().dropna()
>>> gim = ARCHInMean(rets, lags=[1, 2], volatility=GARCH())
>>> res = gim.fit()

Notes

The (G)arch-in-mean model with exogenous regressors (-X) is described by

\[y_t = \mu + \kappa f(\sigma^2_t)+ \sum_{i=1}^p \phi_{L_{i}} y_{t-L_{i}} + \gamma' x_t + \epsilon_t\]

where \(f(\cdot)\) is the function specified by form.

Methods

`bounds`()	Construct bounds for parameters to use in non-linear optimization
`compute_param_cov`(params[, backcast, robust])	Computes parameter covariances using numerical derivatives.
`constraints`()	Construct linear constraint arrays for use in non-linear optimization
`fit`([update_freq, disp, starting_values, ...])	Estimate model parameters
`fix`(params[, first_obs, last_obs])	Allows an ARCHModelFixedResult to be constructed from fixed parameters.
`forecast`(params[, horizon, start, align, ...])	Construct forecasts from estimated model
`parameter_names`()	List of parameters names
`resids`(params[, y, regressors])	Compute model residuals
`simulate`(params, nobs[, burn, ...])	Simulates data from a linear regression, AR or HAR models
`starting_values`()	Returns starting values for the mean model, often the same as the values returned from fit

Properties

`distribution`	Set or gets the error distribution
`form`	The form of the conditional variance in the mean
`name`	The name of the model.
`num_params`	Returns the number of parameters
`volatility`	Set or gets the volatility process
`x`	Gets the value of the exogenous regressors in the model
`y`	Returns the dependent variable