nautilus-analysis 0.62.0

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//
//  Licensed under the GNU Lesser General Public License Version 3.0 (the "License");
//  You may not use this file except in compliance with the License.
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// -------------------------------------------------------------------------------------------------

//! Returns Kurtosis statistic.

use nautilus_model::position::Position;

use crate::{Returns, statistic::PortfolioStatistic};

/// Calculates the excess kurtosis of portfolio returns.
///
/// Kurtosis measures the heaviness of the tails of the return distribution
/// relative to a normal distribution. A positive value indicates fatter tails
/// (more outliers); a negative value indicates thinner tails.
///
/// Uses the bias-corrected sample excess kurtosis (adjusted Fisher-Pearson),
/// matching `pandas.Series.kurt` and Excel `KURT`. A normal distribution yields 0:
///
/// `G2 = n(n + 1) / ((n - 1)(n - 2)(n - 3)) * sum(((x - mean) / s)^4)
///       - 3(n - 1)^2 / ((n - 2)(n - 3))`
///
/// where `s` is the sample standard deviation (Bessel's correction, ddof=1).
/// Returns `NaN` for fewer than four returns or zero dispersion.
///
/// # References
///
/// - Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness
///   and kurtosis. *Journal of the Royal Statistical Society: Series D*, 47(1), 183-189.
#[repr(C)]
#[derive(Debug, Clone, Default)]
#[cfg_attr(
    feature = "python",
    pyo3::pyclass(module = "nautilus_trader.analysis", from_py_object)
)]
#[cfg_attr(
    feature = "python",
    pyo3_stub_gen::derive::gen_stub_pyclass(module = "nautilus_trader.analysis")
)]
pub struct ReturnsKurtosis {}

impl ReturnsKurtosis {
    /// Creates a new [`ReturnsKurtosis`] instance.
    #[must_use]
    pub fn new() -> Self {
        Self {}
    }
}

impl PortfolioStatistic for ReturnsKurtosis {
    type Item = f64;

    fn name(&self) -> String {
        "Returns Kurtosis".to_string()
    }

    fn calculate_from_returns(&self, raw_returns: &Returns) -> Option<Self::Item> {
        if !self.check_valid_returns(raw_returns) {
            return Some(f64::NAN);
        }

        let returns = self.downsample_to_daily_bins(raw_returns);
        let n = returns.len();
        if n < 4 {
            return Some(f64::NAN);
        }

        let n_f = n as f64;
        let mean = returns.values().sum::<f64>() / n_f;
        let std = self.calculate_std(&returns);
        if std == 0.0 || !std.is_finite() {
            return Some(f64::NAN);
        }

        let sum_quartic = returns
            .values()
            .map(|x| ((x - mean) / std).powi(4))
            .sum::<f64>();
        let kurtosis = (n_f * (n_f + 1.0)) / ((n_f - 1.0) * (n_f - 2.0) * (n_f - 3.0))
            * sum_quartic
            - 3.0 * (n_f - 1.0).powi(2) / ((n_f - 2.0) * (n_f - 3.0));

        Some(kurtosis)
    }

    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
        None
    }

    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
        None
    }
}

#[cfg(test)]
mod tests {
    use std::collections::BTreeMap;

    use nautilus_core::{UnixNanos, approx_eq};
    use rstest::rstest;

    use super::*;

    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
        let mut new_return = BTreeMap::new();
        let one_day_in_nanos = 86_400_000_000_000;
        let start_time = 1_600_000_000_000_000_000;

        for (i, &value) in values.iter().enumerate() {
            let timestamp = start_time + i as u64 * one_day_in_nanos;
            new_return.insert(UnixNanos::from(timestamp), value);
        }

        new_return
    }

    #[rstest]
    fn test_name() {
        let kurtosis = ReturnsKurtosis::new();
        assert_eq!(kurtosis.name(), "Returns Kurtosis");
    }

    #[rstest]
    fn test_empty_returns() {
        let kurtosis = ReturnsKurtosis::new();
        let returns = create_returns(&[]);
        let result = kurtosis.calculate_from_returns(&returns);
        assert!(result.is_some());
        assert!(result.unwrap().is_nan());
    }

    #[rstest]
    fn test_insufficient_data() {
        let kurtosis = ReturnsKurtosis::new();
        let returns = create_returns(&[0.01, -0.02, 0.03]);
        let result = kurtosis.calculate_from_returns(&returns);
        assert!(result.is_some());
        assert!(result.unwrap().is_nan());
    }

    #[rstest]
    fn test_zero_dispersion() {
        let kurtosis = ReturnsKurtosis::new();
        let returns = create_returns(&[0.01, 0.01, 0.01, 0.01]);
        let result = kurtosis.calculate_from_returns(&returns);
        assert!(result.is_some());
        assert!(result.unwrap().is_nan());
    }

    #[rstest]
    fn test_kurtosis_calculation() {
        // Reference value from pandas Series.kurt() (excess, adjusted Fisher-Pearson).
        let kurtosis = ReturnsKurtosis::new();
        let returns = create_returns(&[
            0.01, -0.02, 0.03, -0.01, 0.02, 0.04, -0.03, 0.05, -0.04, 0.02,
        ]);
        let result = kurtosis.calculate_from_returns(&returns);
        assert!(result.is_some());
        assert!(approx_eq!(
            f64,
            result.unwrap(),
            -1.2622443251995028,
            epsilon = 1e-12
        ));
    }
}