The time series in the middle and bottom panels of Figure 9.14 are both nonstationary, but they clearly behave in different manners. The time series in the bottom panel exhibits "momentum" in the sense that once it starts moving upward or downward, it often moves consistently in that direction for a large number of steps. In contrast, the series in the middle panel does not have this type of momentum and a step in one direction is quite likely to be followed by a step in the opposite direction. Do you think the time series model with momentum would be a good model for the price of a stock? Why or why not?

Fig 9.14. The top plot is of an AR(1) process with μ = 0 and ϕ = 0.4. The middle and bottom plots are, respectively, the integral and second integral of this AR(1) process. Thus, from top to bottom, the series are I(0), I(1), and I(2), respectively.

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