大二下商統(tǒng)羽隊給商統(tǒng)18forecast

1、StatisticsforStatisticsforBusiness& Ch 18Components of a time Smoothing Trend Seasonal Multiplicative in Qualitative 市定市場 是在對影響市場供求變化的諸因素 研究的基礎(chǔ)上，運用科學的方估計和判斷。 的目的在于最大限度的減少不確定性對 對象的影響，為科學市市原理與要求慣性原類推原因果原概率原客觀全面及時科學持續(xù)經(jīng)濟步確目選方建模分誤種種長中短宏微戰(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 時間時間序

5、列分析移動平均指數(shù)平滑時間趨勢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 移動平均法是取 對象最近一組歷史數(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)平滑法平均值作對象全部歷史數(shù)據(jù)值的一方法指數(shù)平滑法對移動平均法有兩個方面的術(shù)平均而是采用 平均，近期歷史數(shù)據(jù)這和近期實力數(shù)據(jù)對 有較大影響，遠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