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CFA Level 2
Quantitative Methods

Improving ARIMA Model Residual Autocorrelation

Very Hard Time-series Analysis Autoregressive Models

Consider a time series representing the quarterly revenue of a firm over the past five years, which exhibits both seasonality and autocorrelation. An analyst attempts to model this series using an Autoregressive Integrated Moving Average (ARIMA) approach. After fitting the model, it is found that residuals from the ARIMA model display some autocorrelation, indicating potential model inadequacy.

The analyst decides to improve the model by adapting it. In this context, the analyst contemplates the following modifications:

  1. Incorporating seasonal differencing to better capture quarterly seasonality.
  2. Adding an exogenous variable that captures economic indicators alongside revenue.
  3. Increasing the lag order of the autoregressive components to account for longer memory in the series.

Which of the following modifications to the ARIMA model would be the most effective in addressing the residual autocorrelation?

Hint

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