Understanding AR(1) Model Implications in Stock Returns

Very Hard Time-series Analysis Autoregressive Models

A financial analyst is studying the monthly returns of a stock and suspects that the returns exhibit autocorrelation. In order to model this behavior, the analyst decides to employ an Autoregressive Integrated Moving Average (ARIMA) model.

The analyst fits the data to an AR(1) model and notes that the estimated coefficient for the lagged return is 0.6. Following that, they analyze the residuals and find that they are white noise. They then decide to explore the impact of lagged dependent variables and execute a Granger causality test, which indicates that the lagged returns do not Granger-cause the current returns.

Based on this information, the analyst concludes the following:

The stock returns are non-stationary due to the presence of a unit root.

The model suggests that past returns have predictive power for future returns.

Using an AR(1) model appropriately captures the time-dependent structure of the returns.

Hint

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