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7.4. LONG-RUN ANALYSES OF REAL EXCHANGE RATES 2214020Real-20-400-60-80Nominal-1001871 1883 1895 1907 1919 1931 1943 1955 1967 1979 1991Figure 7.1: Real and nominal dollar-pound rate 1871-1997Variance Ratios of Real Exchange RatesWe can use the variance-ratio statistic (see chapter 2.4) to examinethe relative contribution to the overall variance of the real depreciationfrom a permanent component and a temporary component. Table 7.4shows variance ratios calculated on the Lothian—Taylor data along withasymptotic standard errors. 8The point estimates display a ‘hump’ shape. They initially riseabove 1 at short horizons then fall below 1 at the longer horizons. Thisis a pattern often found with Þnancial data. The variance ratio fallsbelow 1 because of a preponderance of negative autocorrelations at thelonger horizons. This means that a current jump in the real exchangerate tends to be offset by future changes in the opposite direction. Suchmovements are characteristic of mean—reverting processes.Even at the 20 year horizon, however, the point estimates indicatethat 23 percent of the variance of the dollar—pound real exchange rate8 Huizinga [77] calculated variance ratio statistics for the real exchange rate from1974 to 1986 while Grilli and Kaminisky [68] did so for the real dollar—pound ratefrom 1884 to 1986aswellasovervarioussubperiods.