Modeling and Multivariate Methods - SAS

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378 Performing Time Series Analysis Chapter 14 Smoothing Models The Simple Moving Average report shows a time plot of the data and the fitted model. The red triangle menu has the following options: Add Model Select this option to fit another model. When additional models are fit, the model is added to the time plot of the data. Save to Data Table Saves the original data, and forecasts of all moving average models. Show Points Shows or hides the points on the plot. Connecting Lines Shows or hides the lines on the plot. Smoothing Model Dialog The Smoothing Model dialog appears in the report window when you select one of the smoothing model commands. The Confidence Intervals popup list allows you to set the confidence level for the forecast confidence bands. The dialogs for seasonal smoothing models include a Periods Per Season box for setting the number of periods in a season. The Constraints popup list lets you to specify what type of constraint you want to enforce on the smoothing weights during the fit. The constraints are: Zero To One keeps the values of the smoothing weights in the range zero to one. Unconstrained Stable Invertible invertible. allows the parameters to range freely. constrains the parameters such that the equivalent ARIMA model is stable and Custom expands the dialog to allow you to set constraints on individual smoothing weights. Each smoothing weight can be Bounded, Fixed, or Unconstrained as determined by the setting of the popup menu next to the weight’s name. When entering values for fixed or bounded weights, the values can be positive or negative real numbers.
Chapter 14 Performing Time Series Analysis 379 Smoothing Models The example shown here has the Level weight (α) fixed at a value of 0.3 and the Trend weight (γ) bounded by 0.1 and 0.8. In this case, the value of the Trend weight is allowed to move within the range 0.1 to 0.8 while the Level weight is held at 0.3. Note that you can specify all the smoothing weights in advance by using these custom constraints. In that case, none of the weights would be estimated from the data although forecasts and residuals would still be computed. When you click Estimate, the results of the fit appear in place of the dialog. Simple Exponential Smoothing The model for simple exponential smoothing is y t = μ t + α t . The smoothing equation, L t = αy t +(1– α)L t-1 , is defined in terms of a single smoothing weight α. This model is equivalent to an ARIMA(0, 1, 1) model where ( 1 – B)y t = ( 1 – θB)α t with θ = 1 – α . The moving average form of the model is ∞ y t = a t + αa t– j j – 1 Double (Brown) Exponential Smoothing The model for double exponential smoothing is y t = μ t + β 1 t+ a t . The smoothing equations, defined in terms of a single smoothing weight α are L t = αy t + ( 1 – α)L t – 1 and T t = α( L t – L t – 1 ) + ( 1 – α)T t – 1 . This model is equivalent to an ARIMA(0, 1, 1)(0, 1, 1) 1 model ( 1 – B) 2 y t = ( 1 – θB) 2 a t where θ 11 , = θ 21 , with θ = 1 – α .
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Version 10 Modeling and Multivariat
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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6 Emphasis Options for Standard Lea
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8 Models with Crossed, Interaction,
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12 Examining the Residuals . . . .
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14 Response Frequencies . . . . . .
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16 19 Analyzing Principal Component
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18 Interpreting the Profiles . . .
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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24 Learn about JMP Chapter 1 Book C
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26 Learn about JMP Chapter 1 Book C
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28 Learn about JMP Chapter 1 Additi
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Contents Launch the Fit Model Platf
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Contents Overview of Stepwise Regre
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136 Fitting Stepwise Regression Mod
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158 Fitting Multiple Response Model
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Contents Overview of Generalized Li
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180 Fitting Generalized Linear Mode
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Contents Introduction to Logistic M
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200 Performing Logistic Regression
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Contents Overview of the Screening
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232 Analyzing Screening Designs Cha
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Contents Introduction to the Nonlin
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244 Performing Nonlinear Regression
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Contents Overview of Neural Network
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280 Creating Neural Networks Chapte
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Contents Launching the Platform. .
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296 Modeling Relationships With Gau
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Contents Overview of the Loglinear
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306 Fitting Dispersion Effects with
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318 Recursively Partitioning Data C
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Contents Launch the Multivariate Pl
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444 Correlations and Multivariate T
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462 Clustering Data Chapter 18 The
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470 Clustering Data Chapter 18 K-Me
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478 Clustering Data Chapter 18 Self
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Contents Principal Components. . .
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484 Analyzing Principal Components
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Contents Introduction . . . . . . .
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494 Performing Discriminant Analysi
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Contents Surface Plots . . . . . .
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538 Plotting Surfaces Chapter 23 La
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544 Plotting Surfaces Chapter 23 Th
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556 Visualizing, Optimizing, and Si
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640 References Becker, R.A. and Cle
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642 References Draper, N. and Smith
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646 References Matsumoto, M. and Ni
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648 References Rawlings, J.O. (1988
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650 References Umetrics (1995), Mul
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654 Statistical Details Appendix A
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690 Index Birth Death Subset.jmp 46
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692 Index Ellipses Transparency 451
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694 Index test for curvature 46 Kru
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696 Index Customizing 267 Nonlinear
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698 Index reliability analysis 453-
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700 Index Stable 363 Stable Inverti
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702 Index
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Modeling and Multivariate Methods - SAS

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