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Forecasting Data Using Multiple Regression and Box-Jenkins Model

Learn about the diverse methods in forecasting data, including multiple regression and Box-Jenkins Model. Understand stages of Box-Jenkins forecasting model, from identification to estimation and checking. Utilize R functions like arima() and tsdiag() for accurate predictions.

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Forecasting Data Using Multiple Regression and Box-Jenkins Model

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  1. Stat 153 - 25 Sept 2008 D. R. Brillinger Chapter 5 - Forecasting Data x1 ,..., xN What about xN+h, h>0 No single method universally applicable extrapolation conditional statement scenarios

  2. Conditional expected value, E(Y|X) X can be vector-valued Y = XN+hX=(X1,...,XN)

  3. Multiple regression Fit by least squares lm() Residuals

  4. Linear c's to minimize E(XN+h - c0 XN -...-cN-1 X1 )2 Conditional expected value if {Xt} Gaussian/normal

  5. Prediction/forecast error Linear process The error is Represent series as linear process

  6. Box-Jenkins Model. arima(p,d,q) Stages of Box-Jenkins forecasting model (1) Model identification. Which p,d,q? (2) Estimation. arima() (3) Diagnostic checking. residuals (4) Consideration of alternate models. If necessary Cp. The scientific method

  7. Pertinent R functions arima() tsdiag() predict() - applied to output of arima help("predict.Arima")

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