inordertogetafeelingforacf/pacfandarmamodels,wesimulatefive ... · aic/bic model comparison table...
TRANSCRIPT
![Page 1: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/1.jpg)
ARMA processes
In order to get a feeling for ACF/PACF and ARMA models, we simulate fiveAR/MA processes:1. yt = 1− 0.8yt−1 + εt
2. yt = 1+ 0.8yt−1 + εt
3. yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
4. yt = 1+ εt − 0.8εt−1
5. yt = yt−1 + εt
![Page 2: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/2.jpg)
Time Series Plot
yt = 1− 0.8yt−1 + εt
![Page 3: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/3.jpg)
ACF and PACF Plots
yt = 1− 0.8yt−1 + εt
ACF PACF
![Page 4: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/4.jpg)
Estimated Spectrum
yt = 1− 0.8yt−1 + εt
![Page 5: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/5.jpg)
Time Series Plot
yt = 1+ 0.8yt−1 + εt
![Page 6: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/6.jpg)
ACF and PACF Plots
yt = 1+ 0.8yt−1 + εt
ACF PACF
![Page 7: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/7.jpg)
Estimated Spectrum
yt = 1+ 0.8yt−1 + εt
![Page 8: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/8.jpg)
Time Series Plot
yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
![Page 9: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/9.jpg)
ACF and PACF Plots
yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
ACF PACF
![Page 10: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/10.jpg)
STATA Regression Output
yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
![Page 11: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/11.jpg)
AIC/BIC Model Comparison Table
yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
AIC BIC
• Both AIC and BIC suggest AR(2) specification (not surprisingly!)
![Page 12: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/12.jpg)
Estimated Spectrum
yt = 1+ 1.2yt−1 − 0.5yt−2 + εt
![Page 13: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/13.jpg)
Time Series Plot
yt = 1+ εt − 0.8εt−1
![Page 14: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/14.jpg)
ACF and PACF Plots
yt = 1+ εt − 0.8εt−1
ACF PACF
![Page 15: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/15.jpg)
Estimated Spectrum
yt = 1+ εt − 0.8εt−1
![Page 16: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/16.jpg)
Time Series Plot
yt = yt−1 + εt
![Page 17: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/17.jpg)
ACF and PACF Plots
yt = yt−1 + εt
ACF PACF
![Page 18: InordertogetafeelingforACF/PACFandARMAmodels,wesimulatefive ... · AIC/BIC Model Comparison Table y t = 1+1:2y t 1 0:5y t 2 +" t AIC BIC BothAICandBICsuggestAR(2)specification(notsurprisingly!)](https://reader031.vdocuments.us/reader031/viewer/2022041201/5d48bb9888c9933e258b7118/html5/thumbnails/18.jpg)
Estimated Spectrum
yt = yt−1 + εt