Forecasting (一)：introduction

本篇文章希望对demand forecasting涉及的技术进行框架性的整理。首先参考的是供应链及库存相关的著作，一般其中都会有关于forecasting的一章。

References

1. Waters, D. (2003). Inventory control and management 2nd. John Wiley & Sons. (偏OM)
2. Axsäter, S. (2015). Inventory control (Vol. 225) 3rd. Springer. (更新，信息更多些)
3. Wheelwright, S., Makridakis, S., & Hyndman, R. J. (1998). Forecasting: methods and applications. John Wiley & Sons.(Add seasonality to ARIMA)
4. Nahmias, S. (1994). Demand estimation in lost sales inventory systems. Naval Research Logistics (NRL), 41(6), 739-757. citation 175
5. https://lovvge.github.io/Forecasting-Tutorial-KDD-2019/  （TODO 还没来得及细看）

方法论

哲学

1. Fcst is unavoidable, no-fcst implies casual fcst
2. fcst->realization->analysis->fcst again...  is a loop
3. Not only demand needs to be fcsted, uncertainty is everywhere: when we assume a futre cost, this is also fcst
4. 系统： input->fcst->anomaly detection后处理-> 叠加expert opinon -> final plan
5. A good fcst is :
   1. Accurate and unbiased
   2. Sensitive to changes but robust
   3. White box, easy to explain

方法分类

• Demand forecasting -> Time series forecasting
  • Qualicative
    • Judgemental fcst (based on expert opinion) 
      • Personal insight：一个人。不可靠
      • panel consensus: 一群人达成共识。太主观
      • delphi：一群人提交意见然后公示，再讨论等。稍微好些
      • market survey
      • historical analogy:适合新品
  • Quantitative
    • Projective : 假定历史pattern将反应到未来
      • Simple average
      • Moving average
      • Exponential Smoothing
    • Causal： 假定demand由一些因素导致，进行拟合
      • Linear regression
      • ML, tree models
    • Combined
      • Trend+Seasonal model. 既有历史pattern也使用causal model进行叠加，例如对季节性的处理

 

Practical Concerns

Time series

1. Always start by data analysis and visualization: dray the graph
2. Point fcst is never correct: there is random noises

Causal

1. LR or ML: use r-square and r to check goodness of fit and correlations

Projective

1. MA: window size determines sensibility to demand change
2. ES: 当品数较大，有必要设置一些自动监控测试，例如通过tracking signal探测异常。一个可能的定义: sum of errors/MAD。
   1. ES with trends: Holt's algo. two parameters. For monthly update: consider alpha 0.2 beta 0.05
   2. Winters Trend-Seasonal method. 在seasonality上，可以通过聚合来减少random deviation带来的影响.这也提醒我们，不同的components可以用不同维度的聚合数据
   3. use lr for trend model is not preferred wrt ES with trend. p21 Axsater.
3. Sporadic demand：稀疏但每次量比较大。把出现间隔作为变量，做es
4. Box-Jenkins technique (ARIMA)
   1. 可以处理非独立的demand
   2. Add seasonality to ARIMA. Makridakis et al. 1998.
5. 灵魂拷问：Projective假设合理吗？历史pattern 序列可以延伸到未来？

Trend and seasonality models

1. LR->baseline+trend->season index->average index->future by LR->multiple index
2. 使用causal approach处理类似seasonality这种叠加因素，与baseline叠加。可以额外加入迭代的机制。

Some facts： fcst needs to be planned

1. Decision makers' opinions are biased: 听众希望偏高/偏低的预测
2. 预测的精度要看听众需要
3. More uncertainty the fcst is, more safty stock needed:体现了传统供应链中预测和库存的关系
4. 系统性的异常检测和后处理流程，基于MAD

Forecast error treatement

1. 使用MAD衡量预测偏差。假定预测值为mean，则MAD = |x_t - x_t^|. 含义与sigma类似并且近似等于sigma/1.25, assuming normal distribution
2. 初期信息不全，也有方法determine the standard deviation as a function of demand
3. 如何考虑censored demand。 Nahmias 1994
4. 基于MAD进行异常值检测