Moving Average问题求科普

搬砖 学术
1

Disclaimer：Time Series小白，还请大家多包容。

请教以下问题的业界和学术界的convention，以及rationale：
如果我们想用前七天的moving average做prediction，那么明天y_8我只需求前七天x_1,…, x_7的average。我的问题是，那明天之后的呢？比如后天y_9, 是=y_8， 还是x_2,…，x_7,y_8的average？

个人对把predicted value当作historical data有点uncomfortable。。

2

Not super sure of the notation you are using. To be a bit pedantic I think what you are referring is the AutoRegressive model. MA model has a very specific meaning: the recent value you see is a linear combination of random noises.

More formally, suppose you observe

Y_1, Y_2, ..., Y_8

and build an AR(7):

Y_8 \sim Y_1 + ... + Y_7

up untill now everything is fine. A fully fledged AR model (or indeed more general ARIMA models) will come with distributional assumptions that allows you generate prediciton intervals as well. The width of prediciton intervals inform you how ‘hard’ the forecast is.

Then to predict Y_9 you just plug in \hat{Y}_8, but the key fact here is that the distribution uncertainty propagates, which is roughly the reason you see hurricane paths have larger and larger intervals as forecast date gets further (not saying they actually use an AR model, but you get the idea)

3 个赞
3

非常感谢，很喜欢你整个解释思路。与其问更多的问题，请问可否推荐书或别的资料，比较pedantic的。一本即可

另外根据你的notation我也编辑了一下问题。

4

你学的的time series怎么跟我学的不一样 :yaoming:

5

你学的是什么版本

6

我学的ARIMA里的版本
你这个好像就是单纯的一种data smoothing处理方式 :yaoming:

7

Kinda…

8

如果按你思路
y_8应该是真实值

我感觉你这不是time series课的作业
更像是predictive analysis之类的课 :yaoming:

9

可以clarify下吗?

目前只有x1,…,x7是真实数据，想要之后预测两天的

已经不是学生了:neutral_face:。。。当时没上过time series/predictive analysis的课。。现在工作上需要用才看

10

看到前面lz问推荐的书，虽然我ts基本已经忘光，但是当年学的时候用的是这本： Robert H. Shumway, David S. Stoffer–Time Series Analysis and Its Applications。感觉还挺易懂的。

2 个赞
11

这书确实不错

1 个赞
12

楼主的notation不太对；我估计他想说的是个AR(7)，但是写成了一个过去7天的average；然后和MA model clash了

1 个赞