Forecasting 预测

1. Forecasting 预测

2. Contents 目录 • 18.1 Components Of A Time Series 时间序列的组成 Trend Component 趋势 Cyclical Component 循环 Seasonal Component 季节 Irregular Component 不规则 • 18.2 Smoothing Methods 平滑法 Moving Averages 移动平均 Weighted Moving Averages 加权移动平均 Exponential Smoothing 指数平滑 • 18.3 Trend Projection 趋势预测

3. Contents 目录 • 18.4 Trend And Seasonal Components 趋势 和季节因素 Multiplicative Model 乘法模型 Calculating The Seasonal Indexes 季节指数的计 算 Deseasonalizing The Time Series 无季节影响的时间序列 Using The Deseasonalized Time Series To Identify Trend 使用无季节影响的时间序列识别趋势 Seasonal Adjustments 季节性调整 Models Based On Monthly Data 基于月数据模型 Cyclical Component 循环因素

4. Contents 目录 • 18.5 Regression Analysis 回归分析 • 18.6 Qualitative Approaches 定性方法 Delphi Method 德尔菲法 Expert Judgment 专家判断法 Scenario Writing 远景方案论述法 Intutive Approaches 直观法

5. Overview Of Forecasting Methods预测方法的归纳 Forecasting Methods 预测方法 Quantitative 定量 Qualitative 定性 Causal 因果 Time Series 时间数列 Smoothing 平滑法 Trend Projection 趋势推测法 Trend Projection Adjusted For Seasonal Influence 调整季节影响的趋势推测法

6. 18.1 Components Of A Time Series时间序列的组成 • Trend Component 趋势因素 The long-run shift or movement in the time series observable over several periods of time. • Cyclical Component 循环因素 The component of the time series model that results in periodic above-trend and below-trend behavior of the time series lasting more than one year.

7. Seasonal Component 季节因素 The component of the time series model that shows a periodic pattern over one year or less. Irregular Component 不规则因素 The component reflects the random variation of the time series values beyond what can be explained by the trend, cyclical, and seasonal components.

8. Examples Of Some Possible Time Series Trend Patterns Nonlinear Linear decreasing trend No trend

9. 18.2 Smoothing Methods平滑法 • Moving Averages 移动平均法 A method of forecasting or smoothing a time series by averaging each successive group of data points. Moving Averages=∑(most recent n data values)/n NOTE: Forecast Accuracy 预测精度 Mean squared error (MSE) 均方误差 The average of the sum of the squared differences between the forecast values and the actual time series values.

10. Weighted Moving Averages 加权移动平均法 A method of forecasting or smoothing a time series by computing a weight average of past data values. NOTE: The sum of the weights must equal one.

11. Exponential Smoothing 指数平滑 A forecasting technique that uses a weighted average of past time series values to arrive at smoothed time series values that can be used as forecasts. Exponential Smoothing Model F t+1 =αY t +（1-α）F t Ft+1 = forecast of the time series for period t+1 Yt = actual value of the time series in period t Ft = forecast of the time series for period t α= smoothing constant ( 0 ≤α≤1 )

12. 18.3 Trend Projection趋势预测 • Trend Projection 趋势预测法 ŷ = b0 + b1x Equation For Linear Trend: Tt = b0 + b1t Tt=trend value of the time series in period t b0=intercept of the trend line b1=slope of the trend line t=time

13. Computing The Slope (b1) And Intercept (b0) : b1 = ∑tYt - (∑t∑Yt )/n ∑t*2 - (∑t)*2/n b0 = Y - b1t

14. 18.4 Trend And Seasonal Components趋势和季节因素 • Multiplicative Time Series Model 成法模型 A model whereby the separate components of the time series are multiplied together to identify the actual time series value. When the four components of trend, cyclical, seasonal, and irregular are assumed present, we obtain Yt = Tt×Ct×St×It When the cyclical component is not modeled, we obtain Yt = Tt×St×It

15. Deseasonalized Time Series 无季节影响的时间序列 A time series from which the effect of season has been removed by dividing each original time series observation by the corresponding seasonal index.

16. 18.5 Regression Analysis回归分析 • Causal Forecasting Methods 因果预测法 Forecasting methods that relate a time series to other variables that are believed to explain or cause its behavior. • Autoregressive Model 自动回归模型 A time series model whereby a regression relationship based on past time series values is used to predict the future time series values.

17. 18.6 Qualitative Approaches定性方法 • Delphi Method 德尔菲法 A qualitative forecasting method that obtains forecasts through group consensus. • Expert Judgment 专家判断法 Qualitative forecasts are based on the judgment of a single expert or represent the consensus of a group of experts.

18. Scenario Writing 远景方案论述法 A qualitative forecasting method that consists of developing a conceptual scenario of the future based on a well-defined set of assumptions. Intuitive Approaches 直观法 Qualitative approaches are based on the ability of the human mind to process a variety of information.