. 2020 Sep 28;37:101775. doi: 10.1016/j.frl.2020.101775

Table 2.

The Markov switching model: the influence of VIX on the S&P500 index returns. In Model 1 all parameters switch, in Model 2 only the intercept and variance in residuals switch. The independent variable Δlog(VIX) denotes changes in the logarithm of daily VIX. Sigma is the residual standard deviation, p_ii (i = 1, 2) is the transition probability of staying in regime i.

Model 1. SPX vs VIX
	Regime 1			Regime 2
Parameter	Estimate	Std. Error	p-value	Estimate	Std. Error	p-value
Constant	0.0010	0.0003	0.000	0.0010	0.0031	0.761
Δlog(VIX)	−0.0897	0.0036	0.000	−0.2405	0.0245	0.000
Sigma	0.0038	0.0002		0.0247	0.0024
p₁₁	0.9717	0.0172
p₂₂	0.9438	0.0410

Model 2. SPX vs VIX
	Regime 1			Regime 2
Parameter	Estimate	Std. Error	p-value	Estimate	Std. Error	p-value

Constant	0.0011	0.0003	0.000	−0.0009	0.0043	0.827
Δlog(VIX)	−0.0927	0.0036	0.000	−0.0927	0.0036	0.000
Sigma	0.0040	0.0002		0.0327	0.0033
p₁₁	0.9810	0.0107
p₂₂	0.9310	0.0455