# Example 11.4, Efficient Markets Hypothesis # Data set: nyse # Function for result reporting source("_report.R") # Load the data and estimate the model in the background load("nyse.Rdata") names(data)[names(data)=="return"]="return.t" names(data)[names(data)=="return_1"]="return.t_1" data=ts(data,start=1,frequency=1) model=lm(return.t~return.t_1,data=data) dig=c(3,3,4) # Describe the model cat("The data set contains weekly returns of New York Stock Exchange over about 13 years, with the maximum being ", round(max(data[-1,"return.t"]),2), "% and the minimum ", round(min(data[-1,"return.t"]),2), "%. We want to test the efficient markets hypothesis (EMH), which states that that information observable to the market prior to week t should not help to predict the return during week t. To test this hypothesis, we estimate an AR(1) model:", "\nreturn.t = beta0 + beta1 * return.t_1 + u.t", "\nwhere return is ", paste(desc[desc[,1]=="return",2]), "\nFor this model, the EMH can be stated as H0: beta1 = 0. We assume the homoskedasticity assumption to be true for now. Under the H0, returns are serially uncorrelated, so we can safely assume that they are weakly dependent", sep="") # Report results { cat("The estimated regression line is") reportreg(model,dig,suffix=".hat",adj=T) } # Interpretation cat("The t statistic for beta1hat is ", printt(model,2,dig[2]), ", so we cannot reject H0 at the 10% level. That is, while there appears to be a slight positive correlation in the NYSE return from one week to the next, it is not strong enough to warrant rejection of the EMH", sep="")