Save 30% on all 2023 Study Packages with Code: BLACKFRIDAY30. Valid until Nov. 28th.

Covariance Stationary Property

Covariance Stationary Property

A time series is said to be covariance stationary if its properties, such as the mean and variance, remain constant over time. A time series that is nonstationary leads to invalid linear regression estimates with no economic meaning.

A time series is covariance stationary if it satisfies the following three conditions:

  • The expected value of the time series is constant and finite over time;
  • The volatility of the time series around its mean is constant and finite in all periods; and
  • The covariance of the time series with leading or lagged values of itself is constant.

Covariance stationarity can be detected by plotting the time series. We may assume covariance stationarity if the time series appears to have the same mean and variance, with no apparent seasonality.

Question

Which of the following is least likely a condition for covariance stationary property?

  1. The expected value of the time series is constant and finite overtime.
  2. The volatility of the time series around its mean varies at a constant rate with time.
  3. The covariance of the time series with leading or lagged values of itself is constant.

Solution

The correct answer is B.

A time series is covariance stationary if its volatility around its mean is constant and finite in all periods

Options A and C are true statements.

Reading 3: Time Series Analysis

LOS 3 (c) Explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop GMAT® Exam Prep


    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.