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318 CHAPTER 10. TARGET-ZONE MODELSand (10.39). The observations are daily DM prices of the Belgian franc,French franc, and Dutch guilder from 2/01/87 to 10/31/90. Log exchangerates are normalized by their central parities and multiplied by100. The parameters to be estimated are (η, α, σ, ¯f). SMM is coveredin Chapter 2.3.Denote the simulated observations with a ‘tilde.’ You need to simulatedsequences of the fundamentals that are guaranteed to stay withinthe bands [f, ¯f]. You can do this by letting ˆf j+1 = ˜f j + η + σu j andsetting˜f j+1 =⎧⎪⎨⎪⎩¯f if ˆfj+1 ≥ ¯fˆf j+1 if f ≤ ˆf j+1 ≤ ¯ff ifˆfj+1 ≤ ffor j =1,...,M. The simulated exchange rates are given by(10.41)˜s j (η, α, σ, ¯f) = ˜f j + αη + Ae λ 1 ˜f j+ Be λ 2 ˜f j, (10.42)the simulated moments by⎡1 P Mj=3⎤∆˜sM j1 PH M [˜s(η, α, σ, ¯f)] Mj=3∆˜s 2 M j=1 P Mj=3 ∆˜s 3 M j⎢ 1 P .Mj=3 ⎥⎣ ∆˜sM j ∆˜s j−1 ⎦1 P Mj=3∆˜sMj ∆˜s j−2ThesamplemomentsarebasedontheÞrst three moments and the Þrsttwo autocovariances⎡1 P Tt=3⎤∆sT t1 P Tt=3∆s 2 T tH t (s) =1 P Tt=3 ∆s 3 T t⎢ 1 P Tt=3 ⎥⎣ ∆sT t ∆s t−1 ⎦1 P Tt=3∆sTt ∆s t−2with M =20T ,whereT =978. 5The results are given in Table 10.1. As you can see, the estimatesare reasonable in magnitude and have the predicted signs, but they arenot very precise. The χ 2 test of the (one) overidentifying restriction isrejected at very small signiÞcance levels indicating that the data areinconsistent with the model.5 No adjustments were made for weekends or holidays.