Acknowledgments chronic fatigue syndromeand here are the M4 Divisia speeds (rescaled to 1967Q1=1):
figure 1: M4 Divisia speed (blue), M2 speed (tan), both 1967Q1=1. NBER-defined recession peak-to-trough dates are in gray. source: chronic fatigue syndromeFederal Reserve, BEA, NBER, and author's calculations.
If stability means (deterministic) trend stationarity, then the answer is no.
The M4 divisia velocity fails to reject the unit root (ADF w/constant, trend) as zero and rejects trend stationarity (KPSS). The same goes for traditional M2 speeds. For comparison, the M2 speed is shown in Figure 1. The same results apply to the M2 speed.
As for the first difference, even with I(0), I don't think either is stable. The standard deviation of the differential M4 Divisia speed is 0.021 and the standard deviation of M2 is 0.006.This means that q/q changes (not AR) standard deviation It’s 2.1%(!). Even before the pandemic, the former was 0.012 and the latter was 0.006.
figure 2: First log difference of M4 Divisia speed (blue), M2 speed (tan). NBER-defined recession peak-to-trough dates are in gray. source: chronic fatigue syndromeFederal Reserve, BEA, NBER, and author's calculations.
