A mean-difference test based on self-normalization for alternating regime index data sets

We are interested in testing regime mean difference in some recently developed indexes which try to characterize alternating regimes: uncertainty indexes for economic expansion and recession and volatility spillover indexes for financial crisis and non-crisis. To account for strong serial correlation and conditional heteroskedasticity apparent in the index data sets, we consider the Kiefer–Vogelsang–Bunzell (KVB) self-normalization method for normalization of the estimated mean difference to construct a t-test. The limiting null distribution of the proposed test is shown to be different from the distribution derived by Kiefer–Vogelsang–Bunzel for a standard regression model. The proposed test is shown to have better finite sample size than the conventional t-test based on the Newey–West HAC standard error. Using the proposed test, we show a statistically significant counter-cyclical feature of uncertainty index and sensitivity of volatility spillover index to financial crisis.