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shihong · 2022年01月28日

24一个循环，为什么不是Y25-Y1

  1. FRM I
  2. Quantitative

NO.PZ2020011101000020

问题如下：

Suppose an hourly time series has a calendar effect where the hour of the day matters. How would the dummy variable approach be implemented to capture this calendar effect? How could differencing be used instead to remove the seasonality?

解释：

Let s = 24 represent the hour of the day in military time (e.g. 13 = 1 p.m.). Then Yt=g(t)+γ1I1t+...+γ23I23t+ϵtY_t = g(t) + \gamma_1I_{1t} + ... + \gamma_{23}I_{23t} + \epsilon_t.

Differencing this series can be achieved by looking at observation 24 periods (hours) apart from each other (the following presumes that the error terms are iid and normal):

Yt+24−Yt=g(t+24)−g(t)+ϵt+24−ϵtY_{t + 24} - Y_t = g(t + 24) - g(t) + \epsilon_{t + 24} - \epsilon_t

Once the deterministic time trend is removed the remaining is a covariance-stationary MA(1) process.

24小时对应23个哑变量，第24个Yt是前23个哑变量为0。那么是不是要从第25小时开始下一个循环，对应第1小时呢？
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1 个答案

DD仔_品职助教 · 2022年01月30日

嗨，努力学习的PZer你好：


同学你好，

是这样的，24一个循环，第25h就重新reset到第一个小时了，这道题不是在问累计的小时数，而是在估计一天的时间，所以25是重新对应1点。

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努力的时光都是限量版，加油！

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