Limited Time Offer: Save 10% on all 2022 Premium Study Packages with promo code: BLOG10

Coefficient Instability

Coefficient Instability

Time series coefficient estimates can change over time. Regression coefficient estimates derived from an earlier sample period can differ from those approximated using a later period. Therefore, sample period selection is crucial in estimating valuable models. As a result, different models are best suited for different periods. Using only one model for the entire period can result in a poorly fitting model.

Similarly, the estimated regression coefficients vary depending on the length of the sample periods. The choice of the model to be used in the analysis depends on the sample period. An AR(1) model may be best suited for a single period, but an AR(2) model may fit a previous or later period better. When the two periods are combined, we are likely to select either the AR(1) or AR(2) model for the combined period. This implies that at least a one-time span of the data will be fitted poorly.

Moreover, a longer period increases the risk of mean and variance being unstable over time. Conversely, using a shorter period could produce insufficient data, resulting in lower confidence in estimated parameters.

There are no definitive guidelines for determining the appropriate sample period. However, some basic guidelines are recommended, including:

  • Use basic sampling theory: Avoid using two distinctly different populations.
  • Consider basic time-series properties: Do not combine stationary and nonstationary series. Additionally, do not mix series with different mean and variance terms.
  • The length of the sample period: A longer sample period implies that the sample probably comes from different populations.

Question

Which of the following statements is most accurate?

  1. Coefficients of models estimated with longer time series are usually more stable than those with shorter time series.
  2. Using a shorter period to estimate coefficients results in higher confidence in estimated parameters.
  3. Coefficients of models estimated with shorter time series are usually more stable than those with longer time series

 Solution

 The correct answer is C.

Models estimated with shorter time series are usually more stable than those with longer time series. A longer sample period increases the risk of the mean and variance being unstable over time.

A is incorrect. Models estimated with longer time series are usually unstable relative to those with shorter time series because a longer sample period increases the likelihood that the underlying economic process has changed.

B is incorrect. Using a shorter period could produce insufficient data, resulting in lower confidence in estimated parameters.

Reading 3: Time Series Analysis

LOS 3(h) Explain the instability of coefficients of time-series models.

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.