STAT 443 casestudy2

# STAT 443 casestudy2 - STAT 443 Forecasting Simulations...

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STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data STAT 443: Case Studies: Box Jenkins

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STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models In order to understand models simulation is a useful tool Can simulate data from a known model and then see how well model identiﬁcation works Can simulate data: split into two and see how well can forecast rest
STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models Simulate simple model with season effect Fit a SARIMA model Look at acf and pacf plots X t = S t + W t , W t WN ( 0 , σ 2 ) Look at the differenced series Y t := 12 X t This satisﬁes Y t = 12 W t = ( 1 - B 12 ) W t so Y t SARIMA ( 0 , 0 , 0 )( 0 , 1 , 1 ) model

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STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models Simulated Data Time Data 5 10 15 20 -4 -2 0 2 4
STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models Look at 12-differences Differenced Data Time Data 5 10 15 20 -4 -2 0 2 4

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STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models Look at acf and pacf of 12-differences 0 1 2 3 4 -0.5 0.0 0.5 1.0 Lag ACF Series diff(data.sim, lag = 12) 0 1 2 3 4 -0.4 -0.2 0.1 Lag Partial ACF Series diff(data.sim, lag = 12)
STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data Simulation models From acf and pacf looks like MA ( 1 ) on the differences is appropriate So get Y t = Θ( B 12 ) W t where Θ is of degree one So try ARIMA ( 0 , 0 , 0 )( 0 , 1 , 1 ) model

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STAT 443: Forecasting Simulations Forecasting exercise World Temperature Data Unemployment Data R output mod3 <- arima(data.sim, order = c(0, 0, 0), seasonal = list(order = c(0, 1, 1), period = 12)) par(mfcol=c(1,2)) acf(mod3\$residuals) acf(mod3\$residuals, type="partial")
STAT 443: Forecasting Simulations Forecasting exercise World Temperature

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STAT 443 casestudy2 - STAT 443 Forecasting Simulations...

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