3a9374c61a
- Belkin & Suchower (1998) credit cycle index (Zt) estimation via WLS - Vasicek single-factor conditional PD/TM model - Macro-Zt OLS regression with stepwise variable selection - 3-scenario (boom/neutral/recession) 50yr PD projection - Statistical validation suite (ADF, Ljung-Box, R2, ARCH) - BOK ECOS API integration with fallback data - Visualization module (7 chart types) - Detailed theoretical methodology docs/methodology.md
335 lines
11 KiB
Python
335 lines
11 KiB
Python
"""
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통계적 유의성 검증 모듈
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Zt 시계열 및 거시연계 회귀모형의 통계적 타당성을 엄밀하게 검증합니다.
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검증 항목:
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1. Zt 시계열: ADF 단위근 검정, Shapiro-Wilk 정규성 검정
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2. 회귀 모형: R², F-test, AIC/BIC, 잔차 진단
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3. 잔차: Durbin-Watson, Ljung-Box, ARCH-LM, Breusch-Pagan
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4. 구조적 안정성: CUSUM(추정 가능시)
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5. 다중공선성: VIF
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참고:
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- Greene, W.H. (2018). "Econometric Analysis" 8th ed.
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- Hamilton, J.D. (1994). "Time Series Analysis"
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"""
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import numpy as np
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import pandas as pd
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from scipy import stats
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from statsmodels.tsa.stattools import adfuller
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from statsmodels.stats.diagnostic import (
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het_breuschpagan, acorr_ljungbox, het_arch
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)
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from statsmodels.stats.stattools import durbin_watson
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from typing import Dict, Optional, List
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import logging
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logger = logging.getLogger(__name__)
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def test_stationarity(
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series: np.ndarray,
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name: str = "Zt",
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significance: float = 0.05
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) -> Dict:
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"""
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ADF (Augmented Dickey-Fuller) 단위근 검정
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H0: 단위근 존재 (비정상 시계열)
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H1: 정상 시계열
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Returns
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-------
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dict with test_statistic, p_value, critical_values, is_stationary
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"""
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result = adfuller(series, autolag="AIC")
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is_stationary = result[1] < significance
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output = {
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"test_name": "ADF (Augmented Dickey-Fuller)",
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"variable": name,
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"test_statistic": result[0],
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"p_value": result[1],
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"lags_used": result[2],
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"n_obs": result[3],
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"critical_values": result[4],
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"is_stationary": is_stationary,
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"conclusion": f"{'정상' if is_stationary else '비정상'} 시계열 "
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f"(p={result[1]:.4f}, α={significance})"
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}
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logger.info(f"ADF 검정 [{name}]: statistic={result[0]:.4f}, "
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f"p-value={result[1]:.4f} → {'Pass' if is_stationary else 'FAIL'}")
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return output
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def test_normality(
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series: np.ndarray,
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name: str = "Zt",
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significance: float = 0.05
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) -> Dict:
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"""
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Shapiro-Wilk 정규성 검정
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H0: 정규분포를 따름
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H1: 정규분포를 따르지 않음
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"""
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stat, p_value = stats.shapiro(series)
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is_normal = p_value > significance
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output = {
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"test_name": "Shapiro-Wilk Normality Test",
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"variable": name,
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"test_statistic": stat,
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"p_value": p_value,
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"is_normal": is_normal,
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"mean": float(np.mean(series)),
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"std": float(np.std(series)),
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"skewness": float(stats.skew(series)),
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"kurtosis": float(stats.kurtosis(series)),
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"conclusion": f"{'정규분포' if is_normal else '비정규분포'} "
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f"(p={p_value:.4f}, α={significance})"
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}
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logger.info(f"정규성 검정 [{name}]: W={stat:.4f}, "
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f"p-value={p_value:.4f} → {'Pass' if is_normal else 'FAIL'}")
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return output
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def test_serial_correlation(
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residuals: np.ndarray,
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lags: int = 5,
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significance: float = 0.05
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) -> Dict:
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"""
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잔차 자기상관 검정
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1) Durbin-Watson: d ≈ 2이면 자기상관 없음
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2) Ljung-Box Q-test: H0 = 자기상관 없음
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"""
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# Durbin-Watson
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dw = durbin_watson(residuals)
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# Ljung-Box
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lb_result = acorr_ljungbox(residuals, lags=[lags], return_df=True)
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lb_stat = lb_result["lb_stat"].values[0]
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lb_pvalue = lb_result["lb_pvalue"].values[0]
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no_autocorr = lb_pvalue > significance
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output = {
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"test_name": "Serial Correlation Tests",
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"durbin_watson": float(dw),
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"dw_interpretation": (
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"양의 자기상관" if dw < 1.5 else
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"음의 자기상관" if dw > 2.5 else
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"자기상관 없음"
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),
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"ljung_box_statistic": float(lb_stat),
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"ljung_box_pvalue": float(lb_pvalue),
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"ljung_box_lags": lags,
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"no_autocorrelation": no_autocorr,
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"conclusion": f"{'자기상관 없음' if no_autocorr else '자기상관 존재'} "
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f"(DW={dw:.3f}, LB p={lb_pvalue:.4f})"
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}
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logger.info(f"자기상관 검정: DW={dw:.3f}, LB p-value={lb_pvalue:.4f} "
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f"→ {'Pass' if no_autocorr else 'FAIL'}")
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return output
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def test_heteroscedasticity(
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residuals: np.ndarray,
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exog: np.ndarray,
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significance: float = 0.05
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) -> Dict:
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"""
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이분산 검정
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1) Breusch-Pagan: H0 = 등분산
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2) ARCH-LM: H0 = ARCH 효과 없음
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"""
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# Breusch-Pagan
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try:
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bp_stat, bp_pvalue, _, _ = het_breuschpagan(residuals, exog)
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except Exception:
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bp_stat, bp_pvalue = np.nan, np.nan
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# ARCH-LM
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try:
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arch_result = het_arch(residuals, nlags=3)
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arch_stat = arch_result[0]
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arch_pvalue = arch_result[1]
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except Exception:
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arch_stat, arch_pvalue = np.nan, np.nan
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homoscedastic = (
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(np.isnan(bp_pvalue) or bp_pvalue > significance) and
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(np.isnan(arch_pvalue) or arch_pvalue > significance)
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)
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output = {
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"test_name": "Heteroscedasticity Tests",
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"breusch_pagan_stat": float(bp_stat) if not np.isnan(bp_stat) else None,
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"breusch_pagan_pvalue": float(bp_pvalue) if not np.isnan(bp_pvalue) else None,
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"arch_lm_stat": float(arch_stat) if not np.isnan(arch_stat) else None,
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"arch_lm_pvalue": float(arch_pvalue) if not np.isnan(arch_pvalue) else None,
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"is_homoscedastic": homoscedastic,
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"conclusion": f"{'등분산' if homoscedastic else '이분산'} "
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f"(BP p={bp_pvalue:.4f}, ARCH p={arch_pvalue:.4f})"
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}
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logger.info(f"이분산 검정: BP p={bp_pvalue:.4f}, ARCH p={arch_pvalue:.4f} "
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f"→ {'Pass' if homoscedastic else 'FAIL'}")
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return output
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def validate_pd_properties(
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cumulative_pds: np.ndarray,
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grade_names: List[str] = None
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) -> Dict:
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"""
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PD 결과의 수학적 성질 검증
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1) 0 ≤ PD ≤ 1
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2) 누적 PD 단조증가
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3) 등급간 순서 유지 (낮은 등급 PD > 높은 등급 PD)
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"""
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issues = []
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# 1) 범위 검증
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if np.any(cumulative_pds < 0) or np.any(cumulative_pds > 1.0001):
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issues.append("PD 값이 [0,1] 범위를 벗어남")
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# 2) 단조증가 검증
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for j in range(cumulative_pds.shape[1]):
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diffs = np.diff(cumulative_pds[:, j])
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if np.any(diffs < -1e-10):
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grade_name = grade_names[j] if grade_names else f"Grade{j}"
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issues.append(f"누적 PD 단조증가 위반: {grade_name}")
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# 3) 등급간 순서 검증 (마지막 행, 즉 최종 누적 PD에서)
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final_pds = cumulative_pds[-1]
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for j in range(len(final_pds) - 1):
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if final_pds[j] > final_pds[j + 1] + 1e-6:
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g1 = grade_names[j] if grade_names else f"Grade{j}"
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g2 = grade_names[j + 1] if grade_names else f"Grade{j+1}"
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issues.append(f"등급 순서 위반: PD({g1}) > PD({g2})")
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output = {
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"test_name": "PD Properties Validation",
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"range_valid": not any("범위" in i for i in issues),
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"monotone_valid": not any("단조" in i for i in issues),
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"order_valid": not any("순서" in i for i in issues),
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"all_valid": len(issues) == 0,
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"issues": issues,
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"conclusion": "모든 검증 통과" if len(issues) == 0 else f"이슈 {len(issues)}건"
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}
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return output
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def run_full_validation(
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zt_series: np.ndarray,
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regression_result,
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pd_results: Dict,
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grade_names: List[str] = None
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) -> pd.DataFrame:
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"""
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전체 검증 실행 및 결과 요약 테이블 생성
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Parameters
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----------
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zt_series : np.ndarray
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Zt 추정값 시계열
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regression_result : statsmodels.RegressionResults
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회귀 모형 결과 (또는 None)
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pd_results : Dict
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compute_all_scenarios() 결과
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Returns
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-------
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pd.DataFrame
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검증 결과 요약 테이블
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"""
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all_tests = []
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# 1. Zt 시계열 검증
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adf_result = test_stationarity(zt_series, "Zt")
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all_tests.append({
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"검정": adf_result["test_name"],
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"대상": "Zt 시계열",
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"통계량": f"{adf_result['test_statistic']:.4f}",
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"p-value": f"{adf_result['p_value']:.4f}",
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"결과": "Pass O" if adf_result["is_stationary"] else "Fail X",
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"해석": adf_result["conclusion"]
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})
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norm_result = test_normality(zt_series, "Zt")
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all_tests.append({
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"검정": norm_result["test_name"],
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"대상": "Zt 시계열",
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"통계량": f"{norm_result['test_statistic']:.4f}",
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"p-value": f"{norm_result['p_value']:.4f}",
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"결과": "Pass O" if norm_result["is_normal"] else "Fail X",
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"해석": norm_result["conclusion"]
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})
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# 2. 회귀모형 잔차 검증
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if regression_result is not None:
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residuals = regression_result.resid
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exog = regression_result.model.exog
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serial_result = test_serial_correlation(residuals)
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all_tests.append({
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"검정": "Ljung-Box Q-test",
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"대상": "잔차 자기상관",
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"통계량": f"{serial_result['ljung_box_statistic']:.4f}",
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"p-value": f"{serial_result['ljung_box_pvalue']:.4f}",
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"결과": "Pass O" if serial_result["no_autocorrelation"] else "Fail X",
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"해석": serial_result["conclusion"]
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})
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het_result = test_heteroscedasticity(residuals, exog)
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all_tests.append({
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"검정": "Breusch-Pagan / ARCH-LM",
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"대상": "잔차 이분산",
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"통계량": f"BP={het_result['breusch_pagan_stat']:.4f}" if het_result['breusch_pagan_stat'] else "N/A",
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"p-value": f"{het_result['breusch_pagan_pvalue']:.4f}" if het_result['breusch_pagan_pvalue'] else "N/A",
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"결과": "Pass O" if het_result["is_homoscedastic"] else "Fail X",
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"해석": het_result["conclusion"]
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})
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# R², F-test
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all_tests.append({
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"검정": "R² / F-test",
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"대상": "모형 설명력",
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"통계량": f"R²={regression_result.rsquared:.4f}",
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"p-value": f"{regression_result.f_pvalue:.4f}",
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"결과": "Pass O" if regression_result.f_pvalue < 0.05 else "Fail X",
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"해석": f"R²={regression_result.rsquared:.3f}, "
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f"Adj.R²={regression_result.rsquared_adj:.3f}"
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})
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# 3. PD 성질 검증
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for scenario_name in pd_results.get("by_scenario", {}):
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cum_pd = pd_results["by_scenario"][scenario_name]["cumulative_pd"]
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pd_valid = validate_pd_properties(cum_pd, grade_names)
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all_tests.append({
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"검정": "PD Properties",
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"대상": f"Cumulative PD ({scenario_name})",
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"통계량": "-",
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"p-value": "-",
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"결과": "Pass O" if pd_valid["all_valid"] else "Fail X",
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"해석": pd_valid["conclusion"]
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})
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return pd.DataFrame(all_tests)
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