# 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

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.

LOS 5 (c) Explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary.

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