a five-step iterative procedure Stationarity Checking and Differencing 2)Model Identification 3)Parameter Estimation 4)Diagnostic Checking 5) Forecasting
6 A five-step iterative procedure 1) Stationarity Checking and Differencing 2) Model Identification 3) Parameter Estimation 4) Diagnostic Checking 5) Forecasting
Step One: Stationarity checking
7 Step One: Stationarity checking
Stationarity Stationarity is a fundamental property underlying almost all time series statistical models a time series yt is said to be stationary if it satisfies the following conditions ( 1)E(=u, for all t (2)Var(y)=elo-u=o+ for all t ()Cov(y,, yi-k)=rk for all t
8 Stationarity “Stationarity” is a fundamental property underlying almost all time series statistical models. A time series yt is said to be stationary if it satisfies the following conditions: 2 2 (1) ( ) . (2) ( ) [( ) ] . (3) ( , ) . t y t t y y t t k k E y u for all t Var y E y u for all t Cov y y for all t − = = − = =
Stationarity The white noise series &, satisfies the stationarity condition because (1)E(6)=0 (2)Var()=02 (3)Cov(1s)= for all s≠0
9 Stationarity The white noise series satisfies the stationarity condition because (1) E( ) = 0 (2) Var( ) = (3) Cov( ) = for all s 0 t 2 t t t t s −
Example of a white noise series Time Series plot 100 20 Time 10
10 Example of a white noise series 4 8 12 16 20 24 28 32 36 100 80 60 40 20 0 Time Time Series Plot