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

More documents

Recommendations

Info

104 ACTA WASAENSIATable 8. Results of unit root tests as reported in Lux & Marchesi (2000: table 1) upon 40subsamples of 500 observations for each of the four parameter sets. ˆρ < 1andˆρ > 1 stand shorthand for the number of rejections of ρ =1infavourofρ < 1in one-sided tests at 95% level, and the number of rejections of ρ =1infavourofρ > 1 in two-sided tests at 95% level, respectively.Parameters range of ˆρ ˆρ < 1 ˆρ > 1Parameter Set I 0.999819 — 1.000022 0 0Parameter Set II 0.999977 — 1.000021 0 0Parameter Set III 0.999959 — 1.000030 0 3Parameter Set IV 0.999972 — 1.000014 0 2the subsamples, a majority of d-estimates point at long range dependence in absolutereturns for all parameter sets except I, but in squared returns only for parameter set IIIand simulation I of parameter set IV. Overall it appears that while volatility clusteringand heavy tails of the unconditional return distribution are a robust result, the findingof long memory in volatility depends somewhat stronger on the choice of the modelparameters. This contrasts with the findings presented by Lux & Marchesi (2000),who report a clear majority of significantly positive d-estimates for both squared andabsolute returns in all parameter sets, except for squared returns in parameter set I.The difference might be due to the choice of the highest Fourier frequency λ m consideredin the logperiodogram regressions (2.26) of section 2.6, which is somewhat arbitraryin a similar way as the choice of the tail region in the Hill estimator of the tail index.Beran (1994: chapter 4.6) shows that different choices of m may have considerableeffects upon the values and confidence intervals of ˆd. I have chosen m as the largestinteger smaller than the square root of available observations in accordance with Lux(1996a). If Lux & Marchesi (2000) have chosen a different value in their study, theresults regarding the significance of ˆd may well differ. In any case, it is evident fromthe simulations above that the model is capable of generating long memory in volatilityforatleastsomeparameters.As documented in table 8, Lux & Marchesi claimed originally that their simulatedprice series contain a unit root. All slope parameters ρ in 160 regressions of prices p tupon their lagged values p t−1 are confined to a narrow range around 1, with the only
ACTA WASAENSIA 10513Parameter Set I (Simulation I)11.5Parameter Set I (Simulation II)1211price11109price10.51089.570 0.5 1 1.5 2x 10 4Parameter Set II (Simulation I)1190 0.5 1 1.5 2x 10 4Parameter Set II (Simulation II)1110.510.5price10price109.59.590 0.5 1 1.5 2x 10 4Parameter Set III (Simulation I)1190 0.5 1 1.5 2x 10 4Parameter Set III (Simulation II)11price10.5109.598.50 0.5 1 1.5 2x 10 4Parameter Set IV (Simulation I)1110.5price10.5109.590 0.5 1 1.5 2x 10 4Parameter Set IV (Simulation II)1110.5price10price109.59.5990 0.5 1 1.5 2x 10 48.50 0.5 1 1.5 2x 10 4Figure 7. Price series over the full sample of 20,000 observations.
Page 5 and 6:
ACTA WASAENSIA 52.10.1 Cross-Sectio
Page 7 and 8:
ACTA WASAENSIA 7A5 Matlabcodeforerr
Page 10 and 11:
10 ACTA WASAENSIAIn chapter 5 I sha
Page 12 and 13:
12 ACTA WASAENSIA2 Statistical Prop
Page 14:
14 ACTA WASAENSIA2.2 Absence of Ser
Page 17 and 18:
ACTA WASAENSIA 17The survival or ta
Page 19 and 20:
ACTA WASAENSIA 19& Scheinkman (1987
Page 21 and 22:
ACTA WASAENSIA 212.6 Long Range Dep
Page 23 and 24:
ACTA WASAENSIA 23A particular class
Page 26 and 27:
26 ACTA WASAENSIAMultiscaling may t
Page 28 and 29:
28 ACTA WASAENSIAHansen (1982) to c
Page 30 and 31:
30 ACTA WASAENSIAThe leverage hypot
Page 32 and 33:
32 ACTA WASAENSIAIn order to aviod
Page 34 and 35:
34 ACTA WASAENSIAon a risk-adjusted
Page 36 and 37:
36 ACTA WASAENSIAplanations for the
Page 38 and 39:
38 ACTA WASAENSIAspeculative prices
Page 40 and 41:
40 ACTA WASAENSIAindex α is howeve
Page 42 and 43:
42 ACTA WASAENSIAThis approach has
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
Page 52 and 53:
52 ACTA WASAENSIAvolatility into th
Page 54 and 55: 54 ACTA WASAENSIAfeedback of the co
Page 56 and 57: 56 ACTA WASAENSIAarriving at the fo
Page 58 and 59: 58 ACTA WASAENSIAat iteration k com
Page 60 and 61: 60 ACTA WASAENSIAmultipliers in the
Page 62 and 63: 62 ACTA WASAENSIALux & Ausloos (200
Page 64 and 65: 64 ACTA WASAENSIAmarkets dominated
Page 66 and 67: 66 ACTA WASAENSIAThe “representat
Page 68 and 69: 68 ACTA WASAENSIA(1983) 114 motivat
Page 70 and 71: 70 ACTA WASAENSIAIn the following w
Page 72 and 73: 72 ACTA WASAENSIASethi (1996) exten
Page 74 and 75: 74 ACTA WASAENSIASummation over all
Page 76 and 77: 76 ACTA WASAENSIAthe microscopic un
Page 78 and 79: 78 ACTA WASAENSIA& Winker (2003) an
Page 80 and 81: 80 ACTA WASAENSIAWe wish to obtain
Page 82 and 83: 82 ACTA WASAENSIAindividual markets
Page 84 and 85: 84 ACTA WASAENSIAreturn series. I l
Page 86 and 87: 86 ACTA WASAENSIASwitches between c
Page 88 and 89: 88 ACTA WASAENSIAfollowing necessar
Page 90 and 91: 90 ACTA WASAENSIATable 1. Parameter
Page 92 and 93: 92 ACTA WASAENSIAin stepwise search
Page 94 and 95: 94 ACTA WASAENSIA0.2Logreturns Para
Page 96 and 97: 96 ACTA WASAENSIA0.8Chartist Index
Page 98 and 99: 98 ACTA WASAENSIATable 3. Kurtosis
Page 100 and 101: 100 ACTA WASAENSIAthe most extreme
Page 102 and 103: 102 ACTA WASAENSIATable 4. Estimate
Page 106 and 107: 106 ACTA WASAENSIATable 9. Results
Page 108 and 109: 108 ACTA WASAENSIATable 11. Paramet
Page 110 and 111: 110 ACTA WASAENSIA1 x 105 Aggr. Inv
Page 112 and 113: 112 ACTA WASAENSIA200Aggr. Inventor
Page 114 and 115: 114 ACTA WASAENSIA5 x 105 Aggr. Wea
Page 116 and 117: 116 ACTA WASAENSIAOverall, we can a
Page 118 and 119: 118 ACTA WASAENSIAby Lux (1998). Th
Page 120 and 121: 120 ACTA WASAENSIAwhere s is a disc
Page 122 and 123: 122 ACTA WASAENSIAprocessing valuat
Page 124 and 125: 124 ACTA WASAENSIAProof. See append
Page 126 and 127: 126 ACTA WASAENSIA2.5Logarithmice T
Page 128 and 129: 128 ACTA WASAENSIA0.4Logreturns Ass
Page 130 and 131: 130 ACTA WASAENSIA0.4Logreturns Ass
Page 132 and 133: 132 ACTA WASAENSIATable 17. Probabi
Page 134 and 135: 134 ACTA WASAENSIATable 18. Median
Page 136 and 137: 136 ACTA WASAENSIAIn order to test
Page 138 and 139: 138 ACTA WASAENSIAReferencesAbhyank
Page 140 and 141: 140 ACTA WASAENSIABaillie, R. T. (1
Page 142 and 143: 142 ACTA WASAENSIABlack, F. & M. Sc
Page 144 and 145: 144 ACTA WASAENSIAButler, R. J., J.
Page 146 and 147: 146 ACTA WASAENSIACont, R. (2001).
Page 148 and 149: 148 ACTA WASAENSIAEmbrechts, P., C.
Page 150 and 151: 150 ACTA WASAENSIAFielitz, B. D. (1
Page 152 and 153: 152 ACTA WASAENSIAGhysels, E., A. C
Page 154 and 155:
154 ACTA WASAENSIAHeston, S. L. (19
Page 156 and 157:
156 ACTA WASAENSIAKaldor, N. (1939)
Page 158 and 159:
158 ACTA WASAENSIALiesenfeld, R. (1
Page 160 and 161:
160 ACTA WASAENSIALye, J. N. & V. L
Page 162 and 163:
162 ACTA WASAENSIAMikosch, T. (2003
Page 164 and 165:
164 ACTA WASAENSIAPindyck, R. S. (1
Page 166 and 167:
166 ACTA WASAENSIASethi, R. (1996).
Page 168 and 169:
168 ACTA WASAENSIATesfatsion, L. &
Page 170 and 171:
170 ACTA WASAENSIAAAppendixA1Matlab
Page 172 and 173:
172 ACTA WASAENSIA87 % a3 = 1; %imp
Page 174 and 175:
174 ACTA WASAENSIA181 nmout = max([
Page 176 and 177:
176 ACTA WASAENSIA275276 figure;277
Page 178 and 179:
178 ACTA WASAENSIA45 end464748 % In
Page 180 and 181:
180 ACTA WASAENSIA454647 % Check wh
Page 182 and 183:
182 ACTA WASAENSIAA4Matlab code for
Page 184 and 185:
184 ACTA WASAENSIA888990 % create P
Page 186 and 187:
186 ACTA WASAENSIA4344 nobs = 500;
Page 188 and 189:
188 ACTA WASAENSIAA6Matlab code for
Page 190 and 191:
190 ACTA WASAENSIA9192 for t = 1:T
Page 192 and 193:
192 ACTA WASAENSIA185 fcash = fcash
Page 194 and 195:
194 ACTA WASAENSIA279280281 %Output
Page 196 and 197:
196 ACTA WASAENSIA(4.20), and o(τ
Page 198 and 199:
198 ACTA WASAENSIAas t = n k P ˙
Page 200 and 201:
200 ACTA WASAENSIA nBn˙f2 = v B n
Page 202 and 203:
202 ACTA WASAENSIA f˙1−c1 = v B
Page 204 and 205:
204 ACTA WASAENSIAlocal stability o
show all

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

Create successful ePaper yourself

Delete template?

Save as template?