Testing weak stationarity of stock returns (Q2740077)

The paper deals with a discrete representation of the stock price process \(S_{j+1}=S_{j}\exp(\nu\Delta t+\sigma\varepsilon_{j}\sqrt{\Delta t}),\;j=0,1,\ldots\), where \(S_{j}\) is the stock price at time \(t_{j},\;\Delta t=t_{j+1}-t_{j},\;\nu,\sigma>0\), \(\varepsilon_{j}\) are independent normally \(N(0,1)\) distributed random variables. Consequently, the process \(Z(j)=\log(S_{j+1}/S_{j})-\nu\Delta t,\;j=0,1,\ldots\) should be a Gaussian white noise. Using the test of weak-stationarity by \textit{Y. Okabe} and \textit{Y. Nakano} [Hokkaido Math. J. 20, 45-90 (1991; Zbl 0732.60071)] the authors check to what extend the demeaned logarithmic return sequences represent white noise or at least are weakly stationary in the case of six major Swedish companies and show that \(Z(j)\) may be weakly-stationary without being a white noise or even not weakly-stationary.