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90 CHAPTER 3. THE MONETARY MODELThe main points that can be drawn from the table are1. The volatility of exchange rate returns ∆s t is virtually indistinguishablefrom stock return volatility.2. Returns for both stocks and exchange rates have low Þrst-orderserial correlation.3. From our discussion about the properties of the variance ratiostatistic in chapter 2.4, the negative autocorrelations in exchangerate returns at 16 quarters suggest the possibility of mean reversion.4. The deviation of the price from the fundamentals display substantialpersistence, and much less volatility than returns. Thebehavior of the dividend yield, while similar to the behavior of theexchange rate deviations from the monetary fundamentals, displaysslightly more persistence and appears to be nonstationaryoverthesampleperiod.The data on returns and deviations from the fundamentals are showninFigure3.4whereyouclearlyseehowtheexchangerateisexcessivelyvolatile in comparison to its fundamentals.Excess Volatility and the Monetary ModelThe monetary model can be made consistent with the excess volatilityin the exchange rate if the growth rate of the fundamentals is apersistent stationary process.(63)⇒iid∆f t = ρ∆f t−1 + ² t . (3.15)with ² t ∼ N(0, σ² 2 ). The implied k−step ahead prediction formulaeare E t (∆f t+k )=ρ k ∆f t . Converting to levels, you get E t (f t+k )=f t +P ki=1ρ i ∆f t = f t +[(1−ρ k )/(1−ρ)]ρ∆f t . Using these prediction formulaein (3.12) givess t = γ∞Xj=0ψ j f t + γ∞Xj=0ψ j1 − ρ ρ∆f t − γ∞Xj=0(ρψ) j1 − ρ ρ∆f t= f t + ρψ1 − ρψ ∆f t, (3.16)