To analyze whether stock-market prices follow a random walk, the algebraic sign of their returns has been compared with a coin toss, which is a prominent example for a Bernoulli trial with equiprobable outcomes. Like coin tosses, signed returns lend themselves for a simple runs test for...

This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is proposed and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially...

We derive the probability limit of the standard Dickey-Fuller-test in the context of an exponential random walk. This result might be useful in interpreting tests for unit roots when the test is inadvertantly applied to the levels of the data when the true random walk is in the logs.