In time series analysis, stationarity means the mean and variance are changing over time

Question

BlackTom AI · Accepted Answer

In time series analysis, the term stationarity refers to properties of the process that do not depend on the time at which you observe the series. 
Option 1: True — If we say stationarity means the mean and variance are changing over time, this misstates the concept. A stationary process has a constant mean over time and a constant variance over time. If the mean or variance changes with time, the process is non-stationary in the strict sense. 
Option 2: False — This statement aligns with the standard definition of stationarity. A weakly stationary process has constant mean and variance (and constant autocovariance structure that depends only on lags, not on time). If either the mean or the variance changes with time, or if the autocovariance depends on time, that indicates non-stationarity. 
Additional nuance: In some contexts, people refer to “trend-stationary” or “difference-stationary” processes, where after removing a trend or applying differencing, the series can become stationary. However, the essential criterion remains that strict or weak stationarity requires time-invariant mean and variance (and a time-invariant covariances). If the statement claims that stationarity means changing mean and variance, it contradicts the fundamental definition, and is therefore incorrect.

In time series analysis, stationarity means the mean and variance are changing over time

View Explanation

Log in for full answers

Similar Questions

A time-series which has no significant upward or downward trend is referred to as:[Fill in the blank]

In the context of ARIMA models, what is the main purpose of differencing a time series?

The graph below shows the first difference of the Japanese labor participation rate shown in the previous question. Which of the following is most accurate?

Weak stationarity is less practical than strict (strong) stationarity concept. That's why the latter is used more often than the former

Random walk without drift is a stationary process

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler