First, our endowment (consumption) growth follows a slow mean-reverting process
. After the realization of a bad endowment shock, the expected consumption growth rate edges up only slightly because of the trend-reverting property, which makes the autocorrelation of the consumption growth process slightly negative but very close to zero.
In the OU model the stochastic random variable St follows a geometric mean-reverting process
given by the differential equation as:
He modelled temperature as a mean-reverting process
by adapting directly the Hull-White model.
The short-term variance of asset price follows a mean-reverting process
. A mean-reverting process
is introduced to allow for the common long-term volatility risk in the underlying asset price and counterparty's asset value, which differs from assumption that long-term volatility is constant in Wang et al.
A major difference between the two is that the LS model sets the default boundary as a constant K, while the CG model allows the default boundary to be a mean-reverting process
. Default occurs when the firm value hits the threshold K, or [l.sub.t] = ln(K/[V.sub.t]) = 0.
The authors consider that the amount of undervaluation X, is given by a mean-reverting process
In what follows, we provide the solution when [([theta]).sub.t] is a mean-reverting process
Each country's exposure to disaster risk varies over time according to a mean-reverting process
. Risky countries command high risk premia: they feature a depreciated exchange rate and a high interest rate.
Thus, one way of testing the PPP is to test for the mean-reverting property of the nominal exchange rate that incorporates changes in relative prices into its mean-reverting process
, that is, testing for stationarity of the real exchange rate.
These results support the two-regime TAR specification for all five countries--a stationary mean-reverting process
for interest rate differentials outside the bands and a unit root process inside the bands.
Moreover, a comparison of a 30 year and 117 year time series analyses demonstrates that while in the shorter sample the hypothesis of a random walk cannot be rejected, in the longer it is, in favor of a mean-reverting process
. Therefore there are certain markets for which we should acknowledge that the random walk is not an adequate description of the processes involved.
The first model is a one-factor model in which the log of the spot price of the commodity is assumed to follow a mean-reverting process
. The second model assumes that the convenience yield is also stochastic and follows a mean-reverting process