A data scientist is analyzing a stationary time series representing the daily returns of a specific stock. They observe that external shocks, such as unexpected regulatory news, introduce significant but temporary volatility. The impact of these shocks is fully absorbed by the market and vanishes completely after exactly two trading days. Which time series model component is specifically designed to capture this type of short-term, finite-duration shock structure?
The correct answer is the Moving Average (MA) component. An MA(q) model represents the current value of a series as a linear combination of current and past random error terms (shocks). A key characteristic of an MA process is its finite memory; the effect of a random shock persists for exactly 'q' periods and then disappears completely. The scenario describes a shock whose impact vanishes after exactly two days, which is perfectly modeled by an MA(2) process.
An Autoregressive (AR) component is incorrect because in an AR(p) process, a shock's influence diminishes exponentially over time but theoretically never vanishes completely. The effect persists indefinitely into the future, which contradicts the scenario.
An Integrated (I) component is incorrect. This component, which corresponds to differencing, is used to transform a non-stationary series (e.g., one with a trend) into a stationary one. The question stem explicitly states the series is already stationary, so this transformation is not what is needed to model the shock structure.
A Seasonal (S) component is incorrect. This component is used in models like SARIMA to capture predictable, periodic patterns that repeat at regular intervals (e.g., monthly or yearly). The scenario describes random, unexpected shocks, not seasonality.
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What does 'finite memory' mean in the context of a Moving Average (MA) model?
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How does an Autoregressive (AR) model differ from a Moving Average (MA) model in handling shocks?
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Why can't a Seasonal (S) component capture the shocks mentioned in the scenario?