User:White Silver

=Variance ratio test=

The variance ratio test is a statistical test that examines whether a time series follows a random walk. The variance ratio test has been proposed by Cochrane (1988) and Lo and MacKinlay (1988).

Motivation and mathematical background
Consider a time series of the following form

Yt = μ + Yt-1 + U t

Ut = ∑ψjεt-j = Ψ(L)εt

Where Yt is the natural logarithm of the value of the time series at time t (e.g. the daily close of the S&P 500 index), μ is the drift of the time series, Yt-1 is the value of the time series at time t-1 (e.g. the daily close of the S&P 500 on the previous day), Ut is a disturbance term governed by a moving average process with coefficients ψj (with the subscript j running from 0 to ∞), Ψ(L) is thus an infinite polynomial in the lag operator, and εt is a covariance stationary white noise process with the following three attributes: 1. E(εt)=0, 2. var(εt)=σ2, and 3. cov(εt, εt-j)=γj.