Residuals types in time series analysis and their applications

Residuals play an important role for diagnostic checking for time series analysis. In this study, in terms of their difference of calculation, resudials which are classified as ?conditional residuals?, ?unconditional residuals?, ?innovations? and ?normalized residuals?are dealt with as four different types of residuals. Through simulation study done on stationary univariate autoregressive moving average (ARMA) model, different residuals values for different number of observations under certain parameter values for ARMA(1,1) model were calculated and cases for diagnostic checking of these residual types by using test statistics belonging to Ljung-Box were analyzed.Key Words:Time series, ARMA(1,1) model, conditional residuals,unconditional residuals, innovations, normalized residuals,diagnostic checking