Alternative Tests for Parameter Stability

ABSTRACT

We propose new tests for parameter stability based on estimates computed from a sequence of subsamples moving forward and backward across the sample. We obtain a sequence of moving estimates tests and we derive their asymptotic null distribution based on the functional central limit theorem. The critical values are approximated using Durbin's method. Our simulation results show that these tests have comparable size and slightly higher power in detecting structural change than other competing tests.

Keywords:

• Central Limit Theory
• Monte Carlo methods
• Moving estimators
• Structural change

Mathematics Subject Classification:

• 62J05
• 65C05

Acknowledgment

The author thanks Professors J. Chu and Q. Vuong for their helpful suggestions.

Notes

¹These moving estimates of the mean should be calculated from a sequence of subsamples excluding the first [Tδ] observations which are used to compute the fixed estimate of the mean (β₁). This is the main difference between the formulation of our tests and the ME tests. Thus δ should be between 1/3 and 1/2 according to our specific testing procedure, otherwise the test limiting distribution becomes degenerate.

²See Appendix B.

Note: The critical values are computed using Durbin's method (Durbin, 1985): H ₀: b = b ₀, H ₁: b ≠ b ₀.

³See Chu et al. (1995) for more detail. However, it should be noted that these empirical values depend essentially on the choice of the parameters. This may lead to slightly different values reported elsewhere.

Note: The observations are generated from i.i.d N(5,1). The significance level is 10%, and the number of replications is 2,500. The numbers in parentheses refer to the window sizes of the RTs.

Note: Empirical power is based on asymptotic critical values. The significance level is 10% and the number of replications is 2,500: λ₁ = 0.3, λ₂ = 0.6.

⁴2,500 replications were used in the computations.

Note: The significance level is 10%. DGP(1) and DGP(4) are defined in the text.

Note: In each cell, the first number is the size-corrected power for sample T = 180; the second number is for T = 300. The significance level is 10% and the number of replications is 2,500. The values of λ are defined in the text for each DGP.

Note: Empirical power simulation is based on asymptotic critical values computed using Durbin's method. The number of replications is 2,500, and the significance level is 10%. λ₁ = 0.3, λ₂ = 0.6.