DefinePK

Research Objective

To propose and evaluate an alternative strategy for unit root testing that addresses the size distortion and power problems associated with conventional methods by testing for structural breaks before applying unit root tests.

Methodology

The study employs a Monte Carlo simulation approach to compare the performance of an existing methodology (which assumes structural breaks and then applies unit root tests) with a proposed strategy. The proposed strategy involves first testing for the existence of structural breaks using a rolling Chow test, and then applying either a Perron-type test (if a break is detected) or a standard unit root test (if no break is detected). The comparison is based on size (probability of Type I error) and power (probability of correctly rejecting a false null hypothesis). Data generating processes are simulated for three models (A, B, and C) representing different types of structural breaks.

Methodology Flowchart

                        graph TD
    A[Generate Data DGP] --> B[Test for Structural BreakRolling Chow Test];
    B -- Break Exists --> C[Apply Perron-type Test];
    B -- No Break --> D[Apply Dickey-Fuller Test];
    C --> E[Evaluate Power];
    D --> E;
    A --> F[Evaluate Size Proposed Strategy];
    E --> G[Compare Performance];
    F --> G;                    

Discussion

The study argues that conventional unit root tests often assume the presence of structural breaks without explicitly testing for them, leading to biased results and power issues. The proposed strategy, by prioritizing the detection of structural breaks, aims to provide a more robust and reliable approach to unit root testing. The findings suggest that while the proposed method is superior in power, further investigation into mitigating size distortion might be beneficial.

Key Findings

The proposed strategy demonstrates better power performance compared to existing strategies (Pierre Perron and Zivot Andrew) across all three models. While the proposed strategy shows some size distortion, particularly in Models A and B, it is generally considered to have a more favorable balance of size and power. The existing strategies suffer from significant power problems, leading to potentially spurious results.

Conclusion

The proposed strategy of testing for structural breaks before applying unit root tests offers a significant improvement in power compared to existing methods like Pierre Perron and Zivot Andrew. Although it exhibits some size distortion, its superior power makes it a more reliable approach for analyzing time series data with potential structural breaks.

Fact Check

1. Nelson and Plossor (1982) found unit roots in 1 out of 14 macroeconomic time series of the US economy. The text states this finding and attributes it to Nelson and Plossor (1982).
2. Perron (1989) reversed findings for 11 out of 14 series using Nelson and Plossor's data set. The text mentions this reversal of findings by Perron (1989) when considering a structural break.
3. The study simulates data 10,000 times for analysis. The text explicitly mentions that the data generating processes are simulated 10,000 times for the Monte Carlo simulations.

Mind Map