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Course: SS 3861, Fall 2009
School: UWO
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Word Count: 150

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Sciences 1 Statistical 3861B Todays Topics 1. Model identication 2. Modelling philosophies 3. Identication methods 4. Examples Model identication The process of choosing a proper model The rst step of a model construction Also the most dicult and important step Modelling philosophies Randomness (uncertainty) Natural uncertainty Parameter uncertainty 2 Model uncertainty (model misspecication) Model...

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Sciences 1 Statistical 3861B Todays Topics 1. Model identication 2. Modelling philosophies 3. Identication methods 4. Examples Model identication The process of choosing a proper model The rst step of a model construction Also the most dicult and important step Modelling philosophies Randomness (uncertainty) Natural uncertainty Parameter uncertainty 2 Model uncertainty (model misspecication) Model discrimination There is a model overtting issue Modelling principles Model building: Chapters 6,7,8,12 Identication methods Know the data (background information) and Quantity quality of data? Enough sample size? (time series contains less information than iid data) The ratio of sample size to number of parameters 3 Did an intervention(s) occur? Intervention is also refer to structure change Intervention analysis Plot of the data Autocorrelation describes linear dependence Seasonality Chapter 12 Non...

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UWO - SS - 3861
1Statistical Sciences 3861BToday's Topics 1. Review 2. Examples 3. Chapter 6: Parameter estimation 4. Yule-Walker estimator 5. Some estimation theory Review Model identification: The process of choosing a proper model The most difficult and impo
UWO - SS - 3861
1Statistical Sciences 3861BTodays Topics 1. Review 2. Yule-Walker estimator 3. Some estimation theory 4. Eciency of estimatorsReview Chapter 6 will do Find a criteria to choose proper p and q Estimate 1, . . . , p and 1, . . . , q Estimate the
UWO - SS - 3861
1Statistical Sciences 3861BTodays Topics 1. Review 2. Maximum likelihood estimation 3. Model discrimination using AIC 4. Examples of ARMA parameter estimation Review Sample mean estimation of : CLT =&gt;n/4 Xn N (, /n) , = k=n/4|k| 1 nk
UWO - SS - 3861
1Statistical Sciences 3861BToday's Topics 1. Review 2. Model discrimination using AIC 3. Examples of ARMA parameter estimation 4. Purposes of Chapter 7 5. Overfitting Review For time series, L() = f (x1, . . . , xN ) = f1(x1)f2(x2|x1) fN (xN
UWO - SS - 3861
1Statistical Sciences 3861BTodays Topics 1. Review 2. Residuals 3. Tests on ARMA parameters 4. Whiteness tests Review AIC=Akaike Information Criterion ARMA(p,q) models: AIC = 2 ln(max L() + 2k, k = p + q + 1 + . ARIMA models: AIC =N N d (2 ln
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1Statistical Sciences 3861BToday's Topics 1. Review 2. Minimum MSE forecasts Review Constant variance tests Constant variance of innovations =&gt; homoscedasticity Changing (conditional) variance of innovations =&gt; heteroscedasticity One of main pu
UWO - SS - 3861
1Statistical Sciences 3861BTodays Topics 1. Review 2. Nonzero mean parameter in time series 3. Minimum MSE forecasts Review Use linear predictor Xt+l = b0 + b1Xt + + btX1 Use minimum MSE to nd b0, b1, . . . , bt? One-step prediction of an
UWO - SS - 3861
1Statistical Sciences 3861BToday's Topics 1. Review 2. Minimum MSE forecasts Review Time series with nonzero mean parameter : centering and estimation Model discrimination for an AR(p) model Fit a time series X1, . . . , XN with an AR(p) model
UWO - SS - 3861
1Statistical Sciences 3861BTodays Topics 1. Review 2. ARMA forecasts 3. ARIMA forecasts Review2 2 2 E(Xt+l Xt+l )2 = (1 + 1 + + l1)a E(Xt+1 Xt+1)2 = 2 a E(Xt+l Xt+l )2 Rules of prediction2 2 (1 + 1 + 2 + )a = V ar(Xt) 2 Xt+l
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