Building Statistical Forecast Models.ppt
《Building Statistical Forecast Models.ppt》由会员分享,可在线阅读,更多相关《Building Statistical Forecast Models.ppt(22页珍藏版)》请在麦多课文档分享上搜索。
1、Building Statistical Forecast Models,Wes Wilson MIT Lincoln Laboratory April, 2001,Experiential Forecasting,Idea: Base Forecast on observed outcomes in previous similar situations (training data) Possible ways to evaluate and condense the training data Categorization Seek comparable cases, usually e
2、xpert-based Statistical Correlation and significance analysis Fuzzy Logic Combines Expert and Statistical analysis Belief: Incremental changes in predictors relate to incremental changes in the predictand Issues Requirements on the Training Data Development Methodology Automation,Outline,Regression-
3、based Models Predictor Selection Data Quality and Clustering Measuring Success An Example,Statistical Forecast Models,Multi-Linear Regression F = w0 + S wi Piwi = Predictor Weightingw0 = Conditional Climatology Mean Predictor ValuesGAM: Generalized Additive Models F = w0 + S wi fi(Pi) fi = Structure
4、 Function, determined during regressionPGAM: Pre-scaled Generalized Additive Models F = w0 + S wi fi(Pi) fi = Structure Function, determined prior to regression The constant term w0 is conditional climatology less the weighted mean bias of the scaled predictors,Models Based on Regression,Training Da
5、ta for one predictor P vector of predictor values E vector of observed events Residual R2 = | FP E |2 Regression solutions are obtained by adjusting the parametric description of the forecast model (parameters w) until the objective function J(w) = R2 is minimized Multi-Linear Regression (MLR) J(w)
6、= | Aw E |2 MLR is solved by matrix algebra; the most stable solution is provided by the SVD decomposition of A,Regression and Correlation,Training Data for one predictor P vector of predictor values E vector of observed events Error Residual: R2 = | FP E |2 Correlation Coefficient r(P, E) = DP DE /
7、 sDPsDE Fundamental Relationship. Let F0 be a forecast equation with error residuals E0 (|E0|=R0). Let W0 + W1 P be a BLUE correction for E0, and let F = F0 + E0 . The error residual RF of F satisfiesRF2 = R02 1 - r(P, E0)2 ,Model Training Considerations,Assumption: The training data are representat
8、ive of what is expected during the implementation period Simple models are less likely to capture undesirable (non-stationary) short-term fluctuations in the training data The climatology of the training period should match that expected in the intended implementation period (decade scale) It is irr
9、ational to expect that short training periods can lead to models with long-term skill Plan for repeated model tuning Design self-tuning into the system It is desirable to have many more training cases than model parameters,The only way to prepare for the future is to prepare to be surprised; that do
10、esnt mean we have to be flabbergasted. Kenneth Boulding,GAM,An established statistical technique, which uses the training data to define nonlinear scaling of the predictors Standard implementation represents the structure functions as B-splines with many knots, which requires the use of a large set
11、of training data The forecast equations are determined by linear regression including the nonlinear scaling of the predictors F = w0 + Si wi fi(Pi) The objective is to minimize the error residual The structure functions are influence by all of the predictors, and may change if the predictor mix is a
12、ltered If a GAM model has p predictors and k knots per structure function, then the regression model has np+1 (linear) regression parameters,PGAM: Pre-scaled GAM,A new statistical technique, which permits the use of training sets that are decidedly smaller than those for GAM Once the structure funct
13、ions are selected, the forecast equations are determined by linear regression of the pre-scaled predictors F = w0 + S wi fi(Pi) Determination of the structure functions is based on enhancing the correlation of the (scaled) predictor with the error residual of conditional climatologyMaximize r( fi(Pi
14、), DE ) The structure function is determined for each predictor separately Composite predictors should be scaled as composites The structure functions often have interpretations in terms of scientific principles and forecasting techniques,Predictors,Every Method Involves a Choice of Predictors The G
- 1.请仔细阅读文档,确保文档完整性,对于不预览、不比对内容而直接下载带来的问题本站不予受理。
- 2.下载的文档,不会出现我们的网址水印。
- 3、该文档所得收入(下载+内容+预览)归上传者、原创作者;如果您是本文档原作者,请点此认领!既往收益都归您。
下载文档到电脑,查找使用更方便
2000 积分 0人已下载
下载 | 加入VIP,交流精品资源 |
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- BUILDINGSTATISTICALFORECASTMODELSPPT
