Heteroscedasticity

Sample (material)

Mathematics

Statistical hypothesis testing

Homoscedasticity

Statistics

Granger causality

Econometrics

Estimator

Artificial intelligence

Null hypothesis

Predictability

Chemistry

Contrast (vision)

Computer science

Chromatography

Asymptotic distribution

Journal of Time Series Analysis

Causal relationships in econometrics are typically based on the concept of predictability and are established by testing Granger causality. Such relationships are susceptible to change, especially during times of financial turbulence, making the real‐time detection of instability an important practical issue. This article develops a test for detecting changes in causal relationships based on a recursive evolving window, which is analogous to a procedure used in recent work on financial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity and conditional heteroskedasticity of an unknown form. Bootstrap methods are used to control family‐wise size in implementation. Simulation experiments compare the efficacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that the recursive evolving approach offers the best finite sample performance, followed by the rolling window algorithm. The testing strategies are illustrated in an empirical application that explores the causal relationship between the slope of the yield curve and real economic activity in the United States over the period 1980–2015.

Change Detection and the Causal Impact of the Yield Curve