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:

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

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:

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:

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:

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.

Author

Dr Merwan Roudane
📧 merwanroudane920@gmail.com
🔗 https://github.com/merwanroudane/specauto

License

MIT License - see LICENSE for details.