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

108 ACTA WASAENSIATable 11. Parameter estimates in Dickey Fuller tests of the form ∆p t =(ρ − 1)p t−1 +const. + t upon the full samples of 20,000 observations with t-statistics inparantheses. The 1% critical values are -3.43 for ρ —1 (one-sided), and 2.58for the constant (two-sided), implying significantly positive constants andrejectionofaunitrootinalltests.Simulation I:Simulation II:(ˆρ − 1) const. (ˆρ − 1) const.Parameter Set I -0.7281 7.2803 -0.6125 6.1261(-107.00) (106.99) (-93.97) (93.96)Parameter Set II -0.3421 3.4203 -0.3140 3.1405(-64.25) (64.25) (-61.04) (61.03)Parameter Set III -0.1435 1.4355 -0.1208 1.2075(-39.36) (39.36) (-35.89) (35.88)Parameter Set IV -0.2489 2.4888 -0.3543 3.5430(-53.34) (53.34) (-65.65) (65.65)Dickey Fuller tests of the form ∆p t =(ρ − 1)p t−1 +const.+ t upon the full samples of20,000 observations, demonstrates that the constant may indeed not be omitted, as itis significantly non-zero at 99% level in all tests. Furthermore, all tests produce teststatisticsfor ρ−1 far below the 1% critical value for rejection of a unit root, confirmingour conjecture from figure 7 that the price series are in fact level stationary. We cantherefore not confirm the claim brought forward by Lux & Marchesi, that the modelwith quasi-meanvalue dynamics (4.51) would generate integrated price series under theassumption of a constant fundamental price p f , but attribute it to a flawed applicationof the Dickey-Fuller test in their study.As has been mentioned earlier in the introduction of section 4.3, this should not beregarded as a criticism of the model, since the failure of the simulations to produceintegrated prices as in real financial data is only due to the unrealistic assumption of aconstant fundamental value. Lux & Marchesi (1999) show that assuming p f to followgeometric Brownian motion does indeed lead to integrated price series with otherwisesimilar statistical properties as presented here.We shall now turn to traders holdings and cash, an issue which has not been investigatedby Lux & Marchesi. I have several times mentioned the criticism by Farmer