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SHAO · 2024年06月24日

老师,请问为什么Conclusion 2和covariance stationary矛盾呢?有什么关系呀

NO.PZ2023040502000042

问题如下:

Which of the conclusions regarding the exchange rate time series is consistent with both the properties of a covariance-stationary time series and the properties of a random walk?

Conclusion 1The variance of xt increases over time.

Conclusion 2The mean-reverting level is undefined.

Conclusion 3b0 does not appear to be significantly different from 0.

选项:

A.

Conclusion 1

B.

Conclusion 2

C.

Conclusion 3

解释:

A simple random walk can be described by the equation xt = b0 + b1xt–1+ εt, where b0 = 0 and b1 = 1. So b0 = 0 is a characteristic of a simple random walk time series.

A covariance-stationary series must satisfy the following three requirements:

1.The expected value of the time series must be constant and finite in all periods.

2. The variance of the time series must be constant and finite in all periods.

3. The covariance of the time series with itself for a fixed number of periods in the past or future must be constant and finite in all periods.

b0 = 0 does not violate any of these three requirements and is thus consistent with the properties of a covariance-stationary time series.

老师,请问为什么Conclusion 2和covariance stationary矛盾呢?有什么关系呀

1 个答案

品职助教_七七 · 2024年06月26日

嗨,努力学习的PZer你好:


“The mean-reverting level is undefined”相当于在说是random walk,random walk和covariance stationary矛盾。

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