"Frontmatter". In: Analysis of Financial Time Series

26 LINEAR TIME SERIES ANALYSIS AND ITS APPLICATIONS(a) Simple returnsacf-0.2 -0.1 0.0 0.1 0.20 20 40 60 80 100lag(b) Log returnsacf-0.2 -0.1 0.0 0.1 0.20 20 40 60 80 100lagFigure 2.1. Sample autocorrelation functions of monthly simple and log returns of IBMstock from January 1926 to December 1997. In each plot, the two horizontal lines denotetwo standard-error limits of the sample ACF.and Q(10) = 32.7 for the log returns. The p values of these four test statistics areall less than 0.0003, suggesting that monthly returns of the value-weighted index areserially correlated. Thus, the monthly market index return seems to have strongerserial dependence than individual stock returns.In the finance literature, a version of the Capital Asset Pricing Model (CAPM)theory is that the return {r t } of an asset is not predictable and should have no autocorrelations.Testing for zero autocorrelations has been used as a tool to check theefficient market assumption. However, the way by which stock prices are determinedand index returns are calculated might introduce autocorrelations in the observedreturn series. This is particularly so in analysis of high-frequency financial data. Wediscuss some of these issues in Chapter 5.2.3 WHITE NOISE AND LINEAR TIME SERIESWhite NoiseA time series r t is called a white noise if {r t } is a sequence of independent andidentically distributed random variables with finite mean and variance. In particular,