![点击分享此内容可以赚币 分享](/master/images/share_but.png)
Models-for-Time-Series-and-Forecasting.pptx
《Models-for-Time-Series-and-Forecasting.pptx》由会员分享,可在线阅读,更多相关《Models-for-Time-Series-and-Forecasting.pptx(38页珍藏版)》请在咨信网上搜索。
1、CHAPTER 18Models for Time Series and Forecastingto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 18-Learning ObjectivesDescribe the trend,cyclical,seasonal,and irregular component
2、s of the time series model.Fit a linear or quadratic trend equation to a time series.Smooth a time series with the centered moving average and exponential smoothing techniques.Determine seasonal indexes and use them to compensate for the seasonal effects in a time series.Use the trend extrapolation
3、and exponential smoothing forecast methods to estimate a future value.Use MAD and MSE criteria to compare how well equations fit data.Use index numbers to compare business or economic measures over time.2002 The Wadsworth GroupChapter 18-Key TermsTime seriesClassical time series modelTrend valueCycl
4、ical componentSeasonal componentIrregular componentTrend equationMoving averageExponential smoothingSeasonal indexRatio to moving average methodDeseasonalizingMAD criterionMSE criterionConstructing an index using the CPIShifting the base of an index 2002 The Wadsworth GroupClassical Time Series Mode
5、ly=T C S Iwhere y=observed value of the time series variable T=trend component,which reflects the general tendency of the time series without fluctuations C=cyclical component,which reflects systematic fluctuations that are not calendar-related,such as business cycles S=seasonal component,which refl
6、ects systematic fluctuations that are calendar-related,such as the day of the week or the month of the year I=irregular component,which reflects fluctuations that are not systematic 2002 The Wadsworth GroupTrend EquationsLinear:=b0+b1xQuadratic:=b0+b1x+b2x2=the trend line estimate of y x=time period
7、b0,b1,and b2 are coefficients that are selected to minimize the deviations between the trend estimates and the actual data values y for the past time periods.Regression methods are used to determine the best values for the coefficients.2002 The Wadsworth GroupSmoothing TechniquesSmoothing techniques
8、-dampen the impacts of fluctuation in a time series,thereby providing a better view of the trend and(possibly)the cyclical components.Moving average-a technique that replaces a data value with the average of that data value and neighboring data values.Exponential smoothing-a technique that replaces
9、a data value with a weighted average of the actual data value and the value resulting from exponential smoothing for the previous time period.2002 The Wadsworth GroupMoving AverageA moving average for a time period is the average of N consecutive data values,including the data value for that time pe
10、riod.A centered moving average is a moving average such that the time period is at the center of the N time periods used to determine which values to average.If N is an even number,the techniques need to be adjusted to place the time period at the center of the averaged values.The number of time per
11、iods N is usually based on the number of periods in a seasonal cycle.The larger N is,the more fluctuation will be smoothed out.2002 The Wadsworth GroupMoving Average-An ExampleTime Period Data Value1997,Quarter I8181997,Quarter II8611997,Quarter III8441997,Quarter IV9061998,Quarter I8671998,Quarter
12、II8993-Quarter Centered Moving Average for 1997,Quarter IV:4-Quarter Centered Moving Average for 1997,Quarter IV:2002 The Wadsworth GroupExponential SmoothingEt=ayt+(1 a)Et1whereEt=exponentially smoothed value for time period tEt1=exponentially smoothed value for time period t 1yt=actual time series
13、 value for time period ta=the smoothing constant,0 a 1The larger a is,the closer the smoothed value will track the original data value.The smaller a is,the more fluctuation is smoothed out.2002 The Wadsworth GroupExponential Smoothing-An ExampleData Smoothed ValueSmoothed ValuePeriod Value (a=0.2)(a
14、=0.8)1818818818 2861826.6852.4 3844830.1845.7 4906845.3893.9Calculation for smoothed value for Period 2(a=0.2):E2=a y +(1 a)E1 =0.2(861)+0.8(818)=826.62 2002 The Wadsworth GroupSeasonal IndexesA seasonal index is a factor that adjusts a trend value to compensate for typical seasonal fluctuation in t
15、hat period of a seasonal cycle.A seasonal index is expressed as a percentage with a value of 100%corresponding to an average position in a seasonal cycle.2002 The Wadsworth GroupSeasonal Indexes-An ExampleSeasonIndex(Annual Quarter)ValueI 84.5II102.3III 95.5IV117.7If the trend value for Quarter I in
16、 the given year was 902,the value with seasonal fluctuation would bey=T S=902 84.5%=762.2 2002 The Wadsworth GroupRatio to Moving Average MethodA technique for developing a set of seasonal index values from the original time series.Steps:1.Construct a centered moving average of the time series.Set N
17、=number of periods in the seasonal cycle.2.Express each original time series value as a percentage of the corresponding centered moving average.The result is the ratio to moving average.Example:If the original data value is 906 and the corresponding centered moving average is 872.3,Ratio to moving a
18、verage=(906/872.3)100=103.86 2002 The Wadsworth GroupRatio to Moving Average MethodSteps,cont.:3.For each period in the seasonal cycle,average all the ratio to moving average values(from Step 2)corresponding to that period in the seasonal cycle.The result is the unadjusted seasonal index for that pe
19、riod in the seasonal cycle.Example:If ratios corresponding to Quarter I are 80.4,87.3,82.1,89.5,and 78.7,the unadjusted seasonal index value is 2002 The Wadsworth GroupRatio to Moving Average MethodSteps,cont.:4.The average of the seasonal index values should be 100.0 or their sum should be N100.If
- 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:
- Models for Time Series and Forecasting
![提示](https://www.zixin.com.cn/images/bang_tan.gif)
1、咨信平台为文档C2C交易模式,即用户上传的文档直接被用户下载,收益归上传人(含作者)所有;本站仅是提供信息存储空间和展示预览,仅对用户上传内容的表现方式做保护处理,对上载内容不做任何修改或编辑。所展示的作品文档包括内容和图片全部来源于网络用户和作者上传投稿,我们不确定上传用户享有完全著作权,根据《信息网络传播权保护条例》,如果侵犯了您的版权、权益或隐私,请联系我们,核实后会尽快下架及时删除,并可随时和客服了解处理情况,尊重保护知识产权我们共同努力。
2、文档的总页数、文档格式和文档大小以系统显示为准(内容中显示的页数不一定正确),网站客服只以系统显示的页数、文件格式、文档大小作为仲裁依据,平台无法对文档的真实性、完整性、权威性、准确性、专业性及其观点立场做任何保证或承诺,下载前须认真查看,确认无误后再购买,务必慎重购买;若有违法违纪将进行移交司法处理,若涉侵权平台将进行基本处罚并下架。
3、本站所有内容均由用户上传,付费前请自行鉴别,如您付费,意味着您已接受本站规则且自行承担风险,本站不进行额外附加服务,虚拟产品一经售出概不退款(未进行购买下载可退充值款),文档一经付费(服务费)、不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
4、如你看到网页展示的文档有www.zixin.com.cn水印,是因预览和防盗链等技术需要对页面进行转换压缩成图而已,我们并不对上传的文档进行任何编辑或修改,文档下载后都不会有水印标识(原文档上传前个别存留的除外),下载后原文更清晰;试题试卷类文档,如果标题没有明确说明有答案则都视为没有答案,请知晓;PPT和DOC文档可被视为“模板”,允许上传人保留章节、目录结构的情况下删减部份的内容;PDF文档不管是原文档转换或图片扫描而得,本站不作要求视为允许,下载前自行私信或留言给上传者【可****】。
5、本文档所展示的图片、画像、字体、音乐的版权可能需版权方额外授权,请谨慎使用;网站提供的党政主题相关内容(国旗、国徽、党徽--等)目的在于配合国家政策宣传,仅限个人学习分享使用,禁止用于任何广告和商用目的。
6、文档遇到问题,请及时私信或留言给本站上传会员【可****】,需本站解决可联系【 微信客服】、【 QQ客服】,若有其他问题请点击或扫码反馈【 服务填表】;文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“【 版权申诉】”(推荐),意见反馈和侵权处理邮箱:1219186828@qq.com;也可以拔打客服电话:4008-655-100;投诉/维权电话:4009-655-100。