BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

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22 ACTA WASAENSIAThe parameters a and b are related to a long memory parameter called Hurst ExponentH by the identities a =2− 2H and b =2H − 1. The Hurst exponent of a long memoryprocessisthusintherange1/2 0isaconstant.
ACTA WASAENSIA 23A particular class of processes capable of producing long range dependence are thefractionally integrated autoregressive moving average (ARFIMA) models independentlyintroduced by Granger & Joyeux (1980) and Hosking (1981) with spectral densityf(λ) = σ2 1 − e −iλ −2d = σ24sin 2 λ −d. (2.22)2π2π 2The fractional differencing parameter d ∈ (−0.5, 0.5) has the same sign as the autocorrelationsof the observations generated by (2.22) and is related to the Hurst exponentH by the identityd = H − 1/2. (2.23)Fractionally integrated autoregressive moving average processes with 0 < d < 1/2generate therefore positively autocorrelated observations with long range dependence.The spectral representation of the ARFIMA model (2.22) motivated Geweke & Porter-Hudak (1983) to determine d from a log-log regression of the sample analogon I(λ j )tothe spectral density f(λ) in (2.18)I(λ j )= 1n(X2πn t − ¯X)e itλ jt=12, ¯X =1nevaluated at Fourier frequencies λ j in finite samples of size n,nX t , (2.24)λ j = 2πj , j =1, 2,...,(n − 1)/2, (2.25)nagainst the spectral density of an ARFIMA process (2.22),ln I(λ j )=β 0 + β 1 ln 4sin 2 λ j+ j , (2.26)2t=1such thatˆd = − ˆβ 1 , Ĥ = ˆd +1/2. (2.27)In long memory processes other than ARFIMA the spectral representation (2.22) mayhold only approximately for small enough frequencies λ, such that the regression (2.26)of I upon λ j is to be performed upon the lowest m = g(n) Fourier frequencies only,with g usually chosen as m = n u ,whereu ≈ 0.5.Identifying the presence of Long Range Dependence in squares of returns is important,since the slower than n −1 declineinvariance(see(2.19))mayinvalidatestandard
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Page 10 and 11: 10 ACTA WASAENSIAIn chapter 5 I sha
Page 12 and 13: 12 ACTA WASAENSIA2 Statistical Prop
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Page 17 and 18: ACTA WASAENSIA 17The survival or ta
Page 19 and 20: ACTA WASAENSIA 19& Scheinkman (1987
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Page 44 and 45: 44 ACTA WASAENSIAimplying exponenti
Page 46 and 47: 46 ACTA WASAENSIA3.2.4 Descriptive
Page 48 and 49: 48 ACTA WASAENSIAdivisible version
Page 50 and 51: 50 ACTA WASAENSIAto check their ade
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Page 56 and 57: 56 ACTA WASAENSIAarriving at the fo
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72 ACTA WASAENSIASethi (1996) exten
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74 ACTA WASAENSIASummation over all
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76 ACTA WASAENSIAthe microscopic un
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78 ACTA WASAENSIA& Winker (2003) an
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80 ACTA WASAENSIAWe wish to obtain
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82 ACTA WASAENSIAindividual markets
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84 ACTA WASAENSIAreturn series. I l
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86 ACTA WASAENSIASwitches between c
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88 ACTA WASAENSIAfollowing necessar
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90 ACTA WASAENSIATable 1. Parameter
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92 ACTA WASAENSIAin stepwise search
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94 ACTA WASAENSIA0.2Logreturns Para
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96 ACTA WASAENSIA0.8Chartist Index
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98 ACTA WASAENSIATable 3. Kurtosis
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100 ACTA WASAENSIAthe most extreme
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102 ACTA WASAENSIATable 4. Estimate
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104 ACTA WASAENSIATable 8. Results
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106 ACTA WASAENSIATable 9. Results
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108 ACTA WASAENSIATable 11. Paramet
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110 ACTA WASAENSIA1 x 105 Aggr. Inv
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112 ACTA WASAENSIA200Aggr. Inventor
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114 ACTA WASAENSIA5 x 105 Aggr. Wea
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116 ACTA WASAENSIAOverall, we can a
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118 ACTA WASAENSIAby Lux (1998). Th
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120 ACTA WASAENSIAwhere s is a disc
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122 ACTA WASAENSIAprocessing valuat
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124 ACTA WASAENSIAProof. See append
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126 ACTA WASAENSIA2.5Logarithmice T
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128 ACTA WASAENSIA0.4Logreturns Ass
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130 ACTA WASAENSIA0.4Logreturns Ass
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132 ACTA WASAENSIATable 17. Probabi
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134 ACTA WASAENSIATable 18. Median
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136 ACTA WASAENSIAIn order to test
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138 ACTA WASAENSIAReferencesAbhyank
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140 ACTA WASAENSIABaillie, R. T. (1
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142 ACTA WASAENSIABlack, F. & M. Sc
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144 ACTA WASAENSIAButler, R. J., J.
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146 ACTA WASAENSIACont, R. (2001).
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148 ACTA WASAENSIAEmbrechts, P., C.
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150 ACTA WASAENSIAFielitz, B. D. (1
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152 ACTA WASAENSIAGhysels, E., A. C
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154 ACTA WASAENSIAHeston, S. L. (19
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156 ACTA WASAENSIAKaldor, N. (1939)
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158 ACTA WASAENSIALiesenfeld, R. (1
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160 ACTA WASAENSIALye, J. N. & V. L
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162 ACTA WASAENSIAMikosch, T. (2003
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164 ACTA WASAENSIAPindyck, R. S. (1
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166 ACTA WASAENSIASethi, R. (1996).
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168 ACTA WASAENSIATesfatsion, L. &
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170 ACTA WASAENSIAAAppendixA1Matlab
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172 ACTA WASAENSIA87 % a3 = 1; %imp
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174 ACTA WASAENSIA181 nmout = max([
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176 ACTA WASAENSIA275276 figure;277
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178 ACTA WASAENSIA45 end464748 % In
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180 ACTA WASAENSIA454647 % Check wh
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182 ACTA WASAENSIAA4Matlab code for
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184 ACTA WASAENSIA888990 % create P
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186 ACTA WASAENSIA4344 nobs = 500;
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188 ACTA WASAENSIAA6Matlab code for
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190 ACTA WASAENSIA9192 for t = 1:T
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192 ACTA WASAENSIA185 fcash = fcash
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194 ACTA WASAENSIA279280281 %Output
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196 ACTA WASAENSIA(4.20), and o(τ
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198 ACTA WASAENSIAas t = n k P ˙
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200 ACTA WASAENSIA nBn˙f2 = v B n
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202 ACTA WASAENSIA f˙1−c1 = v B
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204 ACTA WASAENSIAlocal stability o
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