Stationarity is established by running the Augmented Dickey-Fuller Test on the returns time series.

The null hypothesis of the Augmented Dickey-Fuller is that the time series is non-stationary or the presence of unit-root in the time series. Since the p-value from the test is less than 0.05 the null hypothesis can be rejected, establishing that the time series is stationary. Stationary time series indicated that the different properties like mean, variance, and covariance do not depend on the time of observation.

Interpret the ACF and PACF plots from the following figures

> adf.test(returns_SIEMENS, alternative = "stationary") Augmented Dickey-Fuller Test data: returns_SIEMENS Dickey-Fuller = -3.8233, Lag order = 3, p-value = 0.024 alternative hypothesis: stationary Series returns_SIEMENS 1.0 0.8 0.6 ACF 0.4 0.2 0.0 -0.2 Oe+00 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Lag Series returns_SIEMENS 0.2 0.1 Partial ACF 0.0 -0.1 -0.2 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Lag > adf.test(returns_SIEMENS, alternative = "stationary") Augmented Dickey-Fuller Test data: returns_SIEMENS Dickey-Fuller = -3.8233, Lag order = 3, p-value = 0.024 alternative hypothesis: stationary Series returns_SIEMENS 1.0 0.8 0.6 ACF 0.4 0.2 0.0 -0.2 Oe+00 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Lag Series returns_SIEMENS 0.2 0.1 Partial ACF 0.0 -0.1 -0.2 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Lag