arch.univariate.christoffersen_conditional_coverage¶

arch.univariate.christoffersen_conditional_coverage(returns: ndarray[tuple[int], dtype[float64]] | Series | list[float], var: ndarray[tuple[int], dtype[float64]] | Series | list[float], p: float = 0.05) → WaldTestStatistic[source]¶

Christoffersen test of the conditional coverage of VaR.

Parameters:¶

returns: ndarray[tuple[int], dtype[float64]] | Series | list[float]¶: Realized returns, a 1-d array of finite numbers with at least 2 observations.
var: ndarray[tuple[int], dtype[float64]] | Series | list[float]¶: VaR forecasts as positive losses, a 1-d array of finite numbers. See var_exceptions for the sign convention and for how the inputs are aligned.
p: float = 0.05¶: The probability of an exception that the VaR is designed for, which is the size of the tail, in the interval (0, 0.5]. It is 0.05 for a 95% VaR and 0.01 for a 99% VaR. The default is 0.05, a 95% VaR.

Returns:¶

The likelihood-ratio statistic, which is asymptotically \(\chi^2_2\) under the null that exceptions are independent and have probability p, with its p-value.

Return type:¶

arch.utility.testing.WaldTestStatistic

Raises:¶

TypeError – If returns or var cannot be converted to numbers, or p is not a real number.
ValueError – If returns or var is not valid, as in var_exceptions, there are fewer than 2 observations, or p is not in (0, 0.5].