Time Series Analysis

Section: Time Series Analysis Estimated study time: 60 minutes Content: Time series analysis at CFA Level 2 focuses on modeling and forecasting financial variables that evolve over time, such as GDP growth, earnings per share, interest rates, and asset prices. The most fundamental models are autoregressive (AR) models, where the current value of a variable depends on its own past values. An AR(1) model takes the form: X_t = b0 + b1*X_{t-1} + epsilon_t, where b0 is the intercept, b1 is the autoregressive coefficient, and epsilon_t is a white noise error term. An AR(p) model includes p lagged values. Candidates must determine the appropriate lag length (typically using the Akaike Information Criterion, AIC, or the Bayesian Information Criterion, BIC), test whether the model is well-specified (using autocorrelation of residuals), and interpret the mean-reverting level of the series. The mean-reverting level of an AR(1) model is the long-run equilibrium value toward which the series gravitates: mean-reversion level = b0 / (1 - b1). This formula assumes |b1| < 1, which is the stationarity condition for an AR(1) model. If b1 = 1 exactly, the series is a random walk (a unit root process): X_t = X_{t-1} + epsilon_t. Random walk processes are non-stationary — their variance grows without bound over time and standard regression inference is invalid. The Dickey-Fuller test is used to test for the presence of a unit root. In the Dickey-Fuller regression, X_t - X_{t-1} = b0 + (b1-1)*X_{t-1} + epsilon_t, the null hypothesis is that a unit root exists (b1 = 1, coefficient on X_{t-1} equals zero). Rejection of the null means the series is stationary. Failure to reject means it is a unit root process.…