  It is widely accepted that there is strong persistence in the volatility of
financial time series. The origin of the observed persistence, or long-range
memory, is still an open problem as the observed phenomenon could be a spurious
effect. Earlier we have proposed the consentaneous model of the financial
markets based on the non-linear stochastic differential equations. The
consentaneous model successfully reproduces empirical probability and power
spectral densities of volatility. This approach is qualitatively different from
models built using fractional Brownian motion. In this contribution we
investigate burst and inter-burst duration statistics of volatility in the
financial markets employing the consentaneous model. Our analysis provides an
evidence that empirical statistical properties of burst and inter-burst
duration can be explained by non-linear stochastic differential equations
driving the volatility in the financial markets. This serves as an strong
argument that long-range memory in finance can have spurious nature.
