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choi · 2023年06月11日

g(t)是什么东西？讲义里哪里提到过？

  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?

选项：

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.

g(t)是什么东西？讲义里哪里提到过？

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1 个答案

品职答疑小助手雍 · 2023年06月13日

同学你好，你就把它理解成常数项就行了。这道题是老师上课讲过的例题，一模一样的，在讲义的302页，具体是Section8 seasonality这个视频1.5倍速17分钟开始。

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2024-06-03 15:32 1 · 回答

NO.PZ2020011101000020 问题如下 Suppose hourly time series ha calenr effewhere the hour of the y matters. How woulthe mmy variable approaimplementeto capture this calenr effect? How coulfferencing useinsteto remove the seasonality? Let s = 24 represent the hour of the y 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_tYt​=g(t)+γ1​I1t​+...+γ23​I23t​+ϵt​.fferencing this series cachievelooking observation 24 perio (hours) apart from eaother (the following presumes ththe error terms are iiannormal):Yt+24−Yt=g(t+24)−g(t)+ϵt+24−ϵtY_{t + 24} - Y_t = g(t + 24) - g(t) + \epsilon_{t + 24} - \epsilon_tYt+24​−Yt​=g(t+24)−g(t)+ϵt+24​−ϵt​Onthe terministic time trenis removethe remaining is a covariance-stationary MA(1) process.

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