Autocorrelation and Covariance Stationarity in SPY Prices and Returns

Which statement is true regarding the time series of SPY prices and returns?

A. The time series of SPY prices has an autocorrelation close to 0.

B. The time series of SPY prices is (approximately) covariance stationary.

C. The time series of SPY returns is (approximately) covariance stationary.

D. The time series of SPY returns has an autocorrelation close to 1.

Answer:

Without additional information or analysis, we cannot definitively determine which statement is true regarding the time series of SPY prices and returns.

In this question, we are given the time series of SPY prices and asked to determine which statement is true.

Option A states that the autocorrelation of SPY prices is close to 0. Autocorrelation measures the relationship between a time series and a lagged version of itself. A value close to 0 indicates little to no correlation between past and future values. However, without specific data or analysis, we cannot determine the exact autocorrelation of SPY prices.

Option B states that the time series of SPY prices is (approximately) covariance stationary. Covariance stationarity refers to a time series whose statistical properties, such as mean and variance, do not change over time. This statement suggests that the SPY prices exhibit stability in their statistical properties. However, without further analysis, we cannot confirm if this statement is true.

Option C states that the time series of SPY returns is (approximately) covariance stationary. This statement suggests that the returns of SPY, which are calculated as the percentage change in prices, exhibit stability in their statistical properties. Covariance stationarity is often desirable in financial time series analysis. However, without further analysis, we cannot confirm if this statement is true.

Option D states that the autocorrelation of SPY returns is close to 1. Autocorrelation measures the relationship between a time series and a lagged version of itself. A value close to 1 indicates a strong positive correlation between past and future values. However, without specific data or analysis, we cannot determine the exact autocorrelation of SPY returns.

Without additional information or analysis, we cannot definitively determine which statement is true. Further analysis, such as calculating autocorrelation coefficients or conducting statistical tests, would be necessary to make a conclusive determination.