(10.3.1)--Chapter10statisticalpredictionme.ppt

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1、10.3 Deterministic factor analysis of time series10.3.1 Deterministic factor decompositionI.Traditional factor decomposition II.Present factor decompositionLong-term trend fluctuation(T)Cycle fluctuations(C)Seasonal variation(S)Random fluctuations(I)Long-term trend fluctuation(T)Seasonal variation(S

2、)Random fluctuations(I)Overcome the influence of other factors and measure the influence of a certain deterministic factor on the sequence.Deduce the interaction between various deterministic factors and their comprehensive influence on the sequence.Decomposed model The additive model:The multiplica

3、tion model:The hybrid model:Some time series have very significant trends,and the purpose of our analysis is to find this trend in the sequence and make a reasonable prediction of the development of the sequence by using this trend.1.Trend fitting2.Smoothing method10.3.2 Trend analysis1.Trend fittin

4、gIt is a method which take time as the independent variable and the corresponding sequence observation value as the dependent variable,and establish the regression model of sequence value changing with time.1).Linear fitting2).Nonlinear fitting1）Linear fitting The long-term trend is linear The struc

5、ture of modelExample1 there is the result of fitting the sequence of Australian government consumption expenditure in each quarter from 1981 to 1990 Model Parameter estimation method Least squares estimation Parameter estimate value Fitting effect drawing2）Nonlinear fitting The long-term trend is no

6、n-linear Guideline of parameter estimation All the models that can be converted to linear models are converted to linear models,and the linear least square method is used for parameter estimation.If it cannot be converted to linearity,the iterative method is used for parameter estimation.Common nonl

7、inear modelsTransformed modelIterative methodIterative methodIterative methodLinear least squares estimationLinear least squares estimationParameter estimation method transformation ModelExample2 There is the result of fitting the series of Shanghai stock exchange index at the end of each month.Mode

8、l Transformation Parameter estimation method Least squares estimation The calibre of the fitting model Fitting effect drawing2.Smoothing methodIt is a method which often used for trend analysis and forecasting.The smoothing technique is used to weaken the effect of short-term random fluctuation on t

9、he sequence and make the sequence smooth,so as to show the law of long-term trend change.Common smoothing method 1）Moving average method 2）Exponential smoothing method1）Moving average method Suppose that the difference between sequence values is mainly caused by random fluctuations in a relatively s

10、hort time interval.According to this assumption,we can use the average value of a certain period of time as an estimate.n-period center moving average5-period centermoving average n-period moving average5-period moving average The principle of determining the number of moving average periods Whether

11、 there is periodicity in the development of events or not The period length is used as the interval length of the moving average to eliminate the influence of the period effect Demand for trend smoothing The more periods the moving average has,the smoother the fitting trend is.Trend is to reflect th

12、e recent changes in the trend of sensitivity The smaller the number of moving average periods,the more sensitive the fitting trend Moving average prediction modelExample 3 The observation value of the last 4-period of a certain observation sequence is:：5，5.5，5.8，6.2（1）Please use the 4-period moving

13、average method to predict;（2）what is the coefficient in front of in the second prediction value?Solution:（1）（2）the coefficient in front of in the second prediction value is.2）Exponential smoothing method In real life,what we know is that for most random events,the recent outcomes tend to have more i

14、mpact on the present,and the long-term outcomes tend to have less impact on the present.In order to better reflect this effect,we will take into account the influence of time interval on the development of events,and each option weight will decay exponentially with the increase of time interval,and

15、this is the basic idea of exponential smoothing method.Simple exponential smoothing prediction Basic formula Equivalent formula Primary predicted value Secondary predicted value-period predicted value Experience to determine Initial value determination Determination of smoothing coefficientGenerally

16、,for sequences with slow change,is always a smaller value;For rapidly changing sequences,is always a larger value.Experience shows that when the value of is between 0.05 and 0.3,the smoothing effect is better.Example 4 Carry exponential smoothing method on a sequence of observed values and given,smo

17、othing coefficient.(1)What the predicted value of in the second prediction value is?(2)What is the coefficient in front of in the second prediction value?Solution:（1）（2）So the coefficient in front of in the second prediction when using the simple exponential smoothing method is equal to the smoothin

18、g coefficient.Holt two-parameter exponential smoothing prediction It is suitable for smoothing sequences with linear trend Suppose that the sequence has a relatively fixed linear trend Trim evenly with two parameters Initial value determination The initial value of the smooth sequence The initial va

19、lue of the trend sequence-period predicted valueExample5 Carry Holt two-parameter index smoothing on specify newspaper circulation in Beijing from 1978 to 2000 and specify Smoothing effect drawingExample 6 We will introduce the basic idea and specific operation steps of seasonal effect analysis by t

20、aking the average temperature sequence of Beijing from 1995 to 2000 as an example.10.3.3 Seasonal effect analysis Seasonal index The relative number of seasonal influences in each period was calculated by the simple average method Seasonal model Calculation of seasonal index Calculate the average of

21、 each period in the cycle:Calculate the total average Calculate the seasonal index Understanding of the seasonal index The seasonal index reflects a more stable relationship between the quarter and the total average If ratio is greater than 1,the quarterly value is often higher than the overall aver

22、age If ratio is less than 1,the quarterly value is often lower than the overall average If the seasonal index of the sequence is approximately equal to 1,it means that the sequence has no obvious seasonal effect Example 6 Calculation of seasonal index Example 6 Seasonal index chart Common Comprehens

23、ive analysis models The additive model:The multiplication model:The hybrid model:10.3.4 Comprehensive analysisExample 7 A deterministic time series analysis was carried out on the total retail sales of consumption goods in China from 1993 to 2000.Selection of the fitting model The long-term increasi

24、ng trend and the seasonal fluctuation with a fixed period of year acted on the sequence at the same time,so a hybrid model(b)was tried to fit the development of the sequence Calculate the seasonal indexMonthSeasonal indexMonthSeasonal index1 0.982 7 0.9292 0.943 8 0.9403 0.920 9 1.0014 0.911 10 1.0545 0.925 11 1.1006 0.951 12 1.335 Seasonal index chart Seasonally adjusted sequence diagram Fit the long-term trend Residual test Short-term predication