specauto 1.0.2

Godfrey's (1987) test strategy for discriminating between autocorrelation and misspecification in regression analysis

specauto

Godfrey's (1987) Alternative Test Strategy for Discriminating Between Autocorrelation and Misspecification in Regression Analysis

Overview

specauto is a Python library implementing the sequential hypothesis testing strategy from:

Godfrey, L. G. (1987). "Discriminating Between Autocorrelation and Misspecification in Regression Analysis: An Alternative Test Strategy." The Review of Economics and Statistics, Vol. 69, No. 1, pp. 128-134.

The library provides publication-ready diagnostic tools for regression analysis, helping researchers distinguish between:

• Misspecification of the regression function
• Higher-order autocorrelation (non-AR(1) errors)
• AR(1) autocorrelation
• Independent errors (no problem)

Installation

pip install specauto

Or install from source:

git clone https://github.com/merwanroudane/specauto.git
cd specauto
pip install -e .

Quick Start

import numpy as np
from specauto import AutoSpec

# Generate sample data
np.random.seed(42)
T = 100
X = np.random.randn(T, 2)
y = 1 + 2*X[:, 0] + 3*X[:, 1] + np.random.randn(T)

# Run the complete test strategy
model = AutoSpec(y, X)
results = model.run_full_strategy()

# Print publication-ready results
print(model.summary())

The Four Hypotheses

Godfrey's strategy tests an ordered sequence of hypotheses:

Hypothesis	Description	Test Used
(a)	Regression function is misspecified; disturbances ARMA	HAC-robust χ² test
(b)	Correct specification; disturbances general ARMA	—
(c)	Correct specification; disturbances AR(1)	F-test: AR(1) vs AR(1+q)
(d)	Correct specification; disturbances independent	t-test / Durbin-Watson

The strategy tests along this sequence until rejection. The last non-rejected hypothesis is adopted.

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Complete API Reference

Main Classes

specauto

The main class implementing Godfrey's (1987) complete test strategy.

from specauto import specauto

specauto = specauto(y, X, significance_level=0.05, add_constant=True)

Parameters:

• y (np.ndarray): Dependent variable (T x 1)
• X (np.ndarray): Regressor matrix (T x k), excluding constant
• significance_level (float): Significance level for tests (default: 0.05)
• add_constant (bool): Whether to add a constant term (default: True)

Methods:

Method	Description
run_full_strategy(reset_powers, truncation_j, ar_p, ar_q)	Execute complete test sequence
test_misspecification(Z, reset_powers, truncation_j)	HAC-robust misspecification test (Eq. 10)
test_ar_structure(p, q)	AR structure F-test (Eq. 18)
test_serial_independence()	Serial independence test (t-test & DW)
summary()	Generate formatted results table
to_dict()	Convert results to dictionary
residuals	Property: Get OLS residuals
ols_result	Property: Get OLS estimation results
results	Property: Get most recent test results

Example:

# Full strategy with custom parameters
results = specauto.run_full_strategy(
    reset_powers=[2, 3],    # Powers for RESET test
    truncation_j=4,         # HAC truncation parameter
    ar_p=1,                 # AR order for null
    ar_q=4                  # Additional AR terms
)

# Individual tests
misspec = specauto.test_misspecification(reset_powers=[2, 3])
ar_test = specauto.test_ar_structure(p=1, q=4)
serial = specauto.test_serial_independence()

---

specautoResults

Complete results from Godfrey's (1987) test strategy.

from specauto import specautoResults

Attributes:

Attribute	Type	Description
ols_result	OLSResult	Results from initial OLS estimation
misspec_result	MisspecTestResult	Misspecification test results
ar_structure_result	ARStructureTestResult	AR structure test results
serial_indep_result	SerialIndepTestResult	Serial independence test results
adopted_hypothesis	str	Adopted hypothesis: "(a)", "(b)", "(c)", or "(d)"
conclusion	str	Human-readable conclusion
recommendation	str	Recommendation for the analyst

---

Test Classes

MisspecificationTest & MisspecTestResult

HAC-robust test for misspecification using Equation (10).

from specauto import MisspecificationTest, MisspecTestResult

# Direct usage
test = MisspecificationTest()
result = test.test(residuals, X, Z, truncation_j=4)

MisspecTestResult Attributes:

• statistic (float): χ² test statistic
• p_value (float): p-value
• df (int): Degrees of freedom
• critical_value (float): Critical value at significance level
• reject_null (bool): Whether to reject null hypothesis
• reset_powers (list): RESET powers used

---

ARStructureTest & ARStructureTestResult

Tests AR(p) vs AR(p+q) using Equation (18).

from specauto import ARStructureTest, ARStructureTestResult

test = ARStructureTest()
result = test.test(residuals, X, p=1, q=4)

ARStructureTestResult Attributes:

• f_statistic (float): F-test statistic
• p_value (float): p-value
• df1 (int): Numerator degrees of freedom
• df2 (int): Denominator degrees of freedom
• critical_value (float): Critical value
• reject_null (bool): Whether to reject null hypothesis

---

SerialIndependenceTest & SerialIndepTestResult

Tests for serial independence vs AR(1).

from specauto import SerialIndependenceTest, SerialIndepTestResult

test = SerialIndependenceTest()
result = test.test(residuals, X)

SerialIndepTestResult Attributes:

• t_statistic (float): t-test statistic
• p_value (float): p-value
• dw_statistic (float): Durbin-Watson statistic
• rho_estimate (float): Estimated AR(1) coefficient
• critical_value (float): Critical value
• reject_null (bool): Whether to reject null hypothesis

---

Estimation Classes

OLSEstimator & OLSResult

Ordinary Least Squares estimation.

from specauto import OLSEstimator

estimator = OLSEstimator(add_constant=True)
result = estimator.fit(y, X)

OLSResult Attributes:

Attribute	Type	Description
beta	np.ndarray	Coefficient estimates
residuals	np.ndarray	OLS residuals
fitted_values	np.ndarray	Fitted values
ssr	float	Sum of squared residuals
tss	float	Total sum of squares
r_squared	float	R-squared
adj_r_squared	float	Adjusted R-squared
sigma_squared	float	Estimated variance of errors
std_errors	np.ndarray	Standard errors of coefficients
t_stats	np.ndarray	t-statistics
n	int	Number of observations
k	int	Number of regressors

OLSEstimator Methods:

• fit(y, X) → OLSResult
• result → Get most recent result
• get_design_matrix() → Get X matrix
• get_XtX_inv() → Get (X'X)^(-1) matrix

---

HACEstimator

White-Domowitz (1984) HAC covariance matrix estimator (Equation 9).

from specauto import HACEstimator

hac = HACEstimator(truncation_j=4, auto_bandwidth=False)
result = hac.estimate(X, residuals, truncation_j=4)

Parameters:

• truncation_j (int): Truncation parameter (default: floor(T^(1/3)))
• auto_bandwidth (bool): Use automatic bandwidth selection

HACResult Attributes:

• covariance_matrix (np.ndarray): HAC covariance matrix
• robust_std_errors (np.ndarray): Robust standard errors
• truncation_j (int): Truncation parameter used
• meat_matrix (np.ndarray): X'Σ̂X matrix
• bread_matrix (np.ndarray): (X'X)^(-1) matrix

---

Output Functions

format_specauto_results

Generate publication-ready formatted output.

from specauto import format_specauto_results

output = format_specauto_results(results, tablefmt="fancy_grid")
print(output)

Parameters:

• results (specautoResults): Complete results from run_full_strategy()
• tablefmt (str): Table format (default: "fancy_grid")

---

format_test_summary

Generate a compact summary table.

from specauto import format_test_summary

summary = format_test_summary(results, tablefmt="fancy_grid")
print(summary)

---

format_critical_values

Format critical values table for publication.

from specauto import format_critical_values

table = format_critical_values(critical_values_df, tablefmt="fancy_grid")
print(table)

---

format_latex_table

Generate LaTeX table for academic publications.

from specauto.output.tables import format_latex_table

latex = format_latex_table(
    results, 
    caption="Godfrey (1987) Diagnostic Test Results",
    label="tab:specauto"
)
print(latex)

Parameters:

• results (specautoResults): Complete results
• caption (str): Table caption
• label (str): Table label for referencing

---

Simulation Functions

simulate_critical_values

Master function to simulate critical values via Monte Carlo.

from specauto import simulate_critical_values

cv_tables = simulate_critical_values(
    test_type="all",           # "misspecification", "ar_structure", or "all"
    n_simulations=10000,       # Number of Monte Carlo replications
    sample_sizes=[50, 100, 200, 500],
    significance_levels=[0.01, 0.05, 0.10],
    seed=42
)

Returns: Dictionary of CriticalValueTable objects

---

CriticalValueTable

Dataclass holding critical values from simulation.

from specauto import CriticalValueTable

Attributes:

• test_name (str): Name of the test
• sample_sizes (list): Sample sizes used
• significance_levels (list): Significance levels
• critical_values (pd.DataFrame): Critical values table
• n_simulations (int): Number of simulations

---

print_critical_value_tables

Print all critical value tables formatted nicely.

from specauto.simulation.critical_values import print_critical_value_tables

print_critical_value_tables(cv_tables)

---

Utility Functions

compute_reset_variables

Compute RESET test variables (powers of fitted values).

from specauto import compute_reset_variables

Z = compute_reset_variables(fitted_values, powers=[2, 3])

---

Example Output

================================================================================
     GODFREY (1987) specauto TEST STRATEGY RESULTS
     Discriminating Between Autocorrelation and Misspecification
================================================================================

MODEL SUMMARY
----------------------------------------
Number of Observations       100
Number of Regressors           3
R-squared                 0.8542
Adjusted R-squared        0.8512
Residual Std. Error       1.0234

SEQUENTIAL TEST RESULTS (at 5% significance level)
--------------------------------------------------------------------------------
| Test                          | Statistic | Value    | p-value  | Decision          |
|-------------------------------|-----------|----------|----------|-------------------|
| Misspecification              | χ²(2)     | 1.2345   | 0.5392   | Do not reject     |
| AR Structure (AR(1) vs AR(5)) | F(4,91)   | 0.8765   | 0.4812   | Do not reject     |
| Serial Independence           | t         | 0.4321   | 0.6665   | Do not reject     |

================================================================================
DIAGNOSIS
================================================================================
Adopted Hypothesis: (d)
Conclusion: NO PROBLEM - Correct specification with independent errors

Recommendation:
  OLS estimator is appropriate. No correction needed.

--------------------------------------------------------------------------------
Signif. codes: *** p<0.01, ** p<0.05, * p<0.10

Reference: Godfrey, L.G. (1987). The Review of Economics and Statistics, 69(1), 128-134.
================================================================================

---

Complete Import Reference

# Main classes
from specauto import specauto, specautoResults

# Test classes
from specauto import (
    MisspecificationTest, MisspecTestResult,
    ARStructureTest, ARStructureTestResult,
    SerialIndependenceTest, SerialIndepTestResult
)

# Estimation classes
from specauto import HACEstimator, OLSEstimator

# Output functions
from specauto import format_specauto_results, format_test_summary, format_critical_values
from specauto.output.tables import format_latex_table

# Simulation
from specauto import simulate_critical_values, CriticalValueTable
from specauto.simulation.critical_values import print_critical_value_tables

# Utilities
from specauto import compute_reset_variables

---

References

• Godfrey, L. G. (1987). "Discriminating Between Autocorrelation and Misspecification in Regression Analysis: An Alternative Test Strategy." The Review of Economics and Statistics, 69(1), 128-134.

• White, H., & Domowitz, I. (1984). "Nonlinear Regression with Dependent Observations." Econometrica, 52, 143-161.

• Thursby, J. G. (1981). "A Test Strategy for Discriminating between Autocorrelation and Misspecification in Regression Analysis." The Review of Economics and Statistics, 63, 117-123.

• Ramsey, J. B. (1969). "Tests for Specification Errors in Classical Linear Least Squares Regression Analysis." JRSS-B, 31, 350-371.

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Author

Dr Merwan Roudane
📧 [e-mail]
🔗 https://github.com/merwanroudane/specauto

License

MIT License - see LICENSE for details.