Nonstationarities in Stock Returns
放弃全局平稳假设，对S&P500日收益率绝对值进行局部平稳建模，利用积分周期图拟合优度检验确定平稳区间，发现收益动态几乎全部集中于方差变化，并提出了分段常数方差模型。
Modeling financial returns on longer time intervals under the assumption of stationarity is, at least intuitively, given the pace of change in world's economy, a choice hard to defend. Relinquishing the global stationarity hypothesis, this paper conducts a data analysis focused on the size of the returns, i.e. the absolute values of returns, under the assumptions that, at least locally, the S&P500 daily return series can be modeled by stationary processes. The challenging task when working under the assumption of local stationarity is to define the intervals on which stationary processes provide a good approximation. This task is accomplished by using a goodness of fit test based on the integrated periodogram (Picard ([21]), Kluppelberg and Mikosch ([15])). The conclusion of the paper is that almost all the dynamics of return time series seem to be concentrated in the shifts of the variance. More concretely, the S&P500 absolute returns, jr j can be modeled as jr j = h(t)exp(ffl t ); t = 0; 1; : : : where (ffl t ) is white noise, E ffl = 0, E ffl and h(t) a function of t which can be well approximated by a step function, yielding a model with piecewise constant variance.