Hi,I was recently reading an article on covariance and cointegration, when I came across the fact that correlation measures only the short run linear relationship between two variables. Can one explain what is meant by linear relationshipSecondly, in non-quant terms what is stationarity of a time-series.-STJ

Corr(X,Y)=Cov(X,Y)/(Var(X)*Var(Y))^0.5Since Cov(X,Y)=E((X-E(X)(Y-E(Y)) Cov(X,Y) is linear in X, Y.We could instead want to look at a nonlinear realtionship such as V=E((X^2)(Y^2)). Do you see what I am saying?There are two forms of stationarity, weak stationarity and strong stationarity.Strong stationarity means that the distribution of X(t+a) given X(t) is independent of t and only dependent on the lag length a.Weak stationarity means that the first two moments of the distribution are independent of t and only dependent on the lag length a, however there could be dependence at higher moments.What context are your questions in?

This is the context.Why is firstly correlation a short run measure of relationship and secondly, why is their a stress on the word linear.Are there any non-linear relationships b/w variables worth knowing about or helpful in analysis.About stationarity- why do basic econometric time series analysis require stationarity ie can you explain non-mathematically the implications if a time series is non stationary.

Check out Embrecht's paper which describes the limitations of correlation as a measure of dependency.http://www.math.ethz.ch/~strauman/prepr ... tfalls.pdf. It also explains linear dependency.Whether or not correlation is "short term" depends on what you're looking at. In non-maths terms, stationarity is important because with a stationary time series maybe it is more likely that we can say something about future (or general) behaviour of the process using the historical data. This is important in finance compared to other situations because we cannot rerun history to get a range of sample paths.Standard models require stationarity they assume stationarity. If the series are not stationary than the results may not be valid, and the inferences from standard hypothesis testing may not be valid etc.