Theoretical autocorrelation Function(TAc)(Ir) Consider an ar(2) process without drift y=y21+2y12+ The tac functions are 1 0k=Pk1+n22fork≥2
16 Theoretical Autocorrelation Function (TAC) (III) Consider an AR(2) process without drift : The TAC functions are . t 1 t 1 2 t 2 t y = y + y +e − − 2. 1 , 1 1 1 2 2 2 2 1 2 2 2 1 1 = + − = + − = − − for k k k k
Theoretical autocorrelation Function(TAc)(v Then the tac dies down according to a mixture of damped exponentials and/or damped sine waves >In general. the tac of a stationary ar process dies down gradually as k increases 17
17 Theoretical Autocorrelation Function (TAC) (IV) Then the TAC dies down according to a mixture of damped exponentials and/or damped sine waves. ➢In general, the TAC of a stationary AR process dies down gradually as k increases