大二下商統(tǒng)羽隊(duì)給商統(tǒng)18forecast

1、StatisticsforStatisticsforBusiness& Ch 18Components of a time Smoothing Trend Seasonal Multiplicative in Qualitative 市定市場(chǎng) 是在對(duì)影響市場(chǎng)供求變化的諸因素 研究的基礎(chǔ)上，運(yùn)用科學(xué)的方估計(jì)和判斷。 的目的在于最大限度的減少不確定性對(duì) 對(duì)象的影響，為科學(xué)市市原理與要求慣性原類(lèi)推原因果原概率原客觀全面及時(shí)科學(xué)持續(xù)經(jīng)濟(jì)步確目選方建模分誤種種長(zhǎng)中短宏微戰(zhàn) 定定Time-SeriesA time-series plot is a two-dimensional plot of time

2、series datathe vertical . . Infl i n measures the variable ofinterestthe horizontal axis corresponds to the timeperiods Time Trend Long-run increase or decrease over time (overall upward or downward movement)Data taken over a eriod of TrendTrendTrend can be upward or Trend can be linear or non-Downw

3、ard linearUpward nonlinearSeasonal Short-term regular wave-like Observed within 1 Often monthly or Cyclical Cyclical Long-term wave-like Regularly occur but may vary in Often measured peak to peak or trough to 1IrregularUnpredictable, random, “residual” Due to random variations Accidentsorunusual“No

4、ise” in the time Time-Series Time-Series Used primarily for Observed value in time series is the sum or product of Additive Xt Tt St CtMultiplicative model (linear in log where T=TrendvalueatperiodS=Seasonalityvalueforperiodt C= Cyclical value at time tI=Irregular(random)valueforperiodXt Trend 時(shí)間時(shí)間序

5、列分析移動(dòng)平均指數(shù)平滑時(shí)間趨勢(shì)SmoothingMoving Averages WeightedMovingAverages Exponential SmoothingCalculating Moving LetCalculating Moving Letm=Average 3533 46 erage is for a consecutive block of (2m+1) years294 234025275Example:Annual123456789Annual 01 2 3 4 5 1324576841 7989oving Moving Moving 移動(dòng)平均法是取 對(duì)象最近一組歷史數(shù)

6、據(jù)的平均值作為 值的方法。這種方法不為下一期的 值，這一方法使近期歷史數(shù)據(jù)參與 ，是歷史數(shù)據(jù)的隨機(jī)成分有可能ky kny nAnnual Annual vs. Moving The5-year movingaverage smoothes the data and shows the underlying 01 2 3 4 5 6 7 8 9 10 Exponential 指數(shù)平滑法平均值作對(duì)象全部歷史數(shù)據(jù)值的一方法指數(shù)平滑法對(duì)移動(dòng)平均法有兩個(gè)方面的術(shù)平均而是采用 平均，近期歷史數(shù)據(jù)這和近期實(shí)力數(shù)據(jù)對(duì) 有較大影響，遠(yuǎn)FFY(1Yt (1)(Yt1(1)Ft1Y (1)Y (1)2Y (1) n

7、1Y(1)nExponentialFt+1 =Yt +(1 )F:Forecast ofthetime Y:Actualvalueofthetimeseries : Smoothing constantExponential A weighted moving WeightsdeclineMostrecentobservationweightedUsed for smoothing and short term forecasting (often one or two periods into the future)Exponential Exponential The weight (sm

8、oothing coefficient) is Subjectively Rangefrom 0 to Smaller givesmoresmoothing,larger giveslessThe weight Closeto 0 forsmoothingoutunwanted cyclical and irregular componentsClose to 1 forExponential Smoothing Exponential smoothing xt xt1(1)xt (0 1; t x= exponentiallysmoothedvalueforperiod x=exponent

9、iallysmoothedvaluealready computed for period i - 1x= observed value in period = weight (smoothing coefficient), 0 0, xn j is theforecastofXt+jstandingattime n and for j x0n ,jis simply the observed value of X(hYear Units TheOfficeConceptCorp.hasacquiredanumberofofficeunits(inthousandsof squarefeet)

10、overthelasteightyears.Developthesecondorderautoregressive xt-xt-4-34-2343232223422642100 x 100 x (100) 25 Calculating a Seasonal Calculating Seasonal Quarter 29 1. Findthemedianofall of the same-seasonInterpreting Seasonal Supposewe getthese seasonal indexes: = 4 000 - fourseasons, so mustsum to Sum

11、mersalesare310%higher than the annual average salesS rin salesavera e825%ofthe annual average salesAutoregressiveModel Example:AutoregressiveModel Example:xt 3.50.8125xt10.9375xx2007 3.50.8125(x2006)0.9375(x2005 3.50.8125(6) Usethesecond-orderequationtoforecast number of units for 2007:Seasonal 12329 432 534 636 7839 94432 534 636 averageover7seasonsis839 9 MultiplicativeinMultip