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CFA Level 2
Quantitative Methods

Implication of High Autoregressive Coefficient

Medium Time-series Analysis Autoregressive Models

A financial analyst is assessing the quarterly sales data for a retail company over the last five years. The analyst notices a pattern in the data, suggesting that previous sales figures are correlated with current and future sales. To model this relationship, the analyst decides to use an Autoregressive (AR) model.

In a typical AR model, sales in the current quarter ($Y_t$) can be expressed in terms of past sales values. The analyst contemplates using the following AR(1) equation: $$Y_t = eta_0 + eta_1 Y_{t-1} + u_t$$, where $Y_t$ is the sales in the current quarter, $Y_{t-1}$ is the sales from the previous quarter, $eta_0$ is a constant, $eta_1$ is the coefficient for the lagged sales term, and $ u_t$ represents a white noise error term.

What is the implication if the estimated value of $eta_1$ is greater than 1?

Hint

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