13.3.3 Diagnostics
Diagnostic tools are often employed for an observed series X1, …, Xn in order to investigate if there is trend, if the assumption of equal variance is reasonable, if the sequence is iid, if the assumption of normality is reasonable, etc. Before we discuss the diagnostic methods, let us introduce another descriptive measure called the partial autocorrelation function (PACF) which is commonly used in the analysis of stationary time series data. PACF of order h is the partial correlation between Xt and Xt−h given Xt−1, …, Xt−h+1. More formally, if 
is the best linear predictor of Xt based on Xt−1, …, Xt−h+1 and
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