Online Appendix. A Simulation Details. A.1 Simulation Design. A.2 Practical Issues

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Online Appendix A Simulation Details A.1 Simulation Design The simulation design follows the approach in Barndorff-Nielsen et al. (211). Specifically, we simulate over the interval t [,1], which corresponds to 6.5 hours of second-by-second trading activity and a number N = 234 of intervals. The simulations are performed using 1 replications. The efficient price process is given by the following bivariate stochastic volatility model: dp j,t = µdt+ρσ j,t dw j,t + 1 ρ 2 σ j,t db t, p j, = σ j,t = exp(β +β 1 v t ), dv j,t = αv j,t dt+dw j,t, for j = 1,2, where dw 1, dw 2 and db are standard independent Brownian motions. In this setup, the second term of the price process is an idiosyncratic factor, while the third term is a common factor, whose strength is determined by the squared root of the correlation between p 1 and p 2, i.e. by 1 ρ 2. There is a perfect correlation (leverage) between the innovations of the idiosyncraticfactor and σ j, i.e. corr(ρσ j dw j,σ j ) = 1, while the leveragebetween the efficient price process and v j is ρ. The parametrization is also as in Barndorff-Nielsen et al. (211). We set [ µ =.3,β 1 =.125,α =.25,ρ =.3 and β = β1/2α, 2 which is a normalization ensuring that ] 1 E σ2 j,u du = 1. To initiate the process v j each day we use its stationary distribution, v j, N(,( 2a) 1 ). To generate the bivariate noise process, we start with an i.i.d. specification, N Noise 1: υ j N(,ωj) 2 with ωj 2 = ξ 2 N 1 σj,i 4. This specification means that the variance of the noise moves together with the spot volatility of the efficient price process. We assign two values to the noise-to-signal ratio.1 (low noise regime), and.1 (high noise regime). To pose an additional challenge we also consider two specifications, which allow for serial dependence (AR(1) and MA(1)) in the noise. Noise 2: υ j,t = φ j υ j,t 1 +υ j,t for φ 1 =.5 and φ 2 =.2. Noise 3: υ j,t = υ j,t +θ j υ j,t 1 for θ 1 =.7 and θ 2 =.4. To obtain different scenarios in terms of trading activity we generate random Poisson sampling times with constant intensities η 1 and η 2 for asset 1 and 2, respectively. This allows us to study the impact of non-synchronous trading and assess the two synchronization schemes, refresh time versus tick time. We consider 36 scenarios for eachnoisemodelbyvarying1/η 1 and 1/η 2 from1to6. Forexample, thepair(1/η 1,1/η 2 )=(1/,1/ )=(1,6) means that on average p 1 and p 2 is observed every 1 and 6 seconds, respectively. i=1 A.2 Practical Issues In our approach there are two parameters that need to be chosen: Q - the number of lags for the (cross) autocovariance function of the noise processes, and S - the number of subsamples. To choose S in the univariate 43

case we rely on results derived in Nolte & Voev (212), who provide the theoretical foundations 18 of how to choose S in the i.i.d. noise case. We denote this S as S and we use it as an indication of how to choose S for all noise models in both the univariate and multivariate estimation. The choice of Q should be data-driven as it depends on the serial dependence of the noise process. In practise we start with a base scenario, which sets S = S and Q = 5. Then, we perform a sensitivity analysis 19 to test whether our results can be further improved by selecting different values of S and Q. The values that minimize the RMSE in each case consist our optimal scenario. Specifically, the optimal scenario for the univariate estimation is S = S and Q = for the i.i.d. noise model and Q = 2 for the 2 dependant noise cases. The optimal scenario for the multivariate estimation is S = S and Q = across all noise models. Although the aforementioned sensitivity analysis is difficult to be implemented in a non-simulation based exercise, it provides insightful findings on how to choose S and Q in practise. On the one hand, a Q larger than might be beneficial when noise exhibits high dependence, especially for assets with very active trading activity. However, one might be conservative, as variance also increases with Q. On the other hand, a higher S might further improve the estimation precision when the trading frequency of the price processes is low. In our sensitivity analysis this occurs in the region of, > 5 mainly for the i.i.d. noise case. Values higher than S = 1.5S do not improve the estimation precision. A few remarks on the implementation of the competing estimators are required. The multivariate Parzen kernel is implemented in the spirit of Barndorff-Nielsen et al. (211). Specifically, we use a refresh time synchronization scheme, with Parzen weights, and with bandwidth H = 3.51n 3/5 mean j=1,...,d (φ 2 j /RV j,1/9) 2/5.The nominator inside the parenthesis approximates the spot variance and is obtained by averaging over subsampled realized variances computed at 6-second grid and dividing by twice the number of returns. The denominator is the realized variance estimator based on 2 min subsampling returns, an approximation for the squared root of the integrated quarticity. To calculate the flat-top realized kernel we follow the recommendations of Varneskov (216). We use the refresh time sampling scheme, with a Tukey-Hanning type kernel function and tuning parameters c = H 1/2 and b = 2. The parameter c controls the flat-top region of the weighting function. Finally, we adopt all Varneskov (216) suggestions for the calculation of the bandwidth. ( 1 ln(ln(n)) ln(n) ), and α = 18 Briefly, optimal S is given by S = α N β 1, where N is the number of intraday prices, β = 2 3 3 33.75ω 4 (π 2 4(γ 2+2γ 1)). Intuitively, α is a noise-to-signal ratio and resembles to a similar quantity which determines IQ the length of the bandwidth in the realized kernel approach. 19 We do not report these result to save space. However, they are available upon request. 44

B Performance Evaluation Metrics In this section, we describe performance evaluation measures we used in out-of-sample asset allocation in Section 5.2 to Section 5.4. We consider five performance measures, i.e. ex post portfolio volatility (VOL), Sharpe ratio (SR), turnover ratio (TO), portolio concentration (CO), and short positions (SP) commonly used in the literature (DeMiguel et al. 213, Hautsch et al. 215, Bollerslev et al. 216). First, we construct the portfolio volatility measure. VOL 2 t+1 = w t RCOV t+1w t (15) where w t is the optimal GMV portfolio weight we obtained at time t, RCOV t,t+1 is five minutes sub-sampled realized covariance matrix at time t + 1, the annualized mean of the square root of VOL 2 t+1 is the ex post portfolio volatility measure (VOL). The lower the portfolio volatility, the better the performance. Second, we compute Sharpe ratio. SR = µ p σ p (16) where µ p and σ p are annualized unconditional mean and volatility of the obtained GMV portfolio. 2 The higher the Sharpe ratio, the better the portfolio performance. Next, we report portfolio turnover ratio. TO = N wt i wi t 1 i=1 1+rt 1 i 1+r p t 1 (17) where w t and w t 1 are optimal GMV portfolio weights at time t and t 1, rt 1 i and rp t 1 are indiviudal stock and portfolio returns at time t 1. Portfolio turnover is closely linked to transaction costs, and hence an optimal portfolio should avoid extreme high turnover in practice. Another portfolio performance measure is portfolio concentration. N CO = ( (wt i )2 ) 1/2 (18) i=1 This measure quantifies the concentrations of weights among different stocks. In practice, portfolios should avoid taking extreme positions in particular assets. The special case is the equal weight portfolio, which provides a lower bound for this measure. Finally, we also consider short selling positions. SP = N wt1 i w i t < (19) i=1 Also, taking too much short selling positions are costly and risky, and hence practical implementation should control for short selling positions. For equal weighted portfolio, the short selling position is zero by construction. 2 Here we closely follow DeMiguel et al. (213) and use raw returns to compute Sharpe ratios, our main results remain valid when excess returns are used. 45

C Simulation Tables and Graphs Table B1: Noise Model 1 (i.i.d.) - Covariance (V12) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5 -.7 -.12 -.18 -.9 -.2 -.25 -.21 -.29 -.24 -.32 -.23 -.18 15 -.17 -.12 -.11 -.9 -.15 -.14 -.19 -.15 -.2 -.17 -.17 -.18 3 -.17 -.18 -.8 -.19 -.17 -.7 -.8 -.14 -.18 -.16 -.16 -.18 45 -.28 -.13 -.23 -.16 -.22 -.13 -.17 -.14 -.16 -.16 -.14 -.14 6 -.2 -.28 -.14 -.15 -.8 -.24 -.16 -.19 -.17 -.8 -.7 -.9 Panel B. OLS V12 (optimal Q and S) 5 -.7 -.12 -.18 -.9 -.21 -.25 -.21 -.29 -.23 -.32 -.23 -.18 15 -.17 -.13 -.11 -.9 -.15 -.15 -.19 -.15 -.2 -.17 -.17 -.17 3 -.18 -.18 -.9 -.19 -.18 -.7 -.1 -.14 -.18 -.16 -.17 -.18 45 -.28 -.12 -.22 -.16 -.21 -.14 -.17 -.12 -.15 -.17 -.14 -.15 6 -.19 -.28 -.14 -.14 -.1 -.23 -.16 -.17 -.17 -.7 -.7 -.1 Panel C. HY V12 5 -.8.25 -.5.49 -.7 -.8 -.35..3 -.19.9 -.1 15 -.12.7.24 -.22.1 -.21.1. -.9 -.3.13 -.2 3 -.19.11.11.9.3.3 -.1.15 -.1 -.2 -.1.1 45.8.28.27.14 -.12 -.8 -.14.3 -.12 -.12 -.6.2 6 -.11 -.23.6.15.11 -.6 -.4 -.7 -.9 -.12.15.1 Panel D. HYS V12 5 -.5 -.9 -.14 -.6 -.17 -.2 -.21 -.23 -.18 -.28 -.18 -.16 15 -.12 -.11 -.3 -.9 -.1 -.13 -.14 -.12 -.16 -.15 -.13 -.13 3 -.17 -.14 -.5 -.15 -.13 -.6 -.1 -.9 -.15 -.13 -.14 -.14 45 -.21 -.7 -.13 -.1 -.17 -.9 -.15 -.9 -.11 -.15 -.11 -.1 6 -.19 -.24 -.11 -.9 -.7 -.17 -.15 -.13 -.12 -.8 -.2 -.6 Panel E. MK V12 5 -.5 -.3 -.7.5 -.5 -.6..1.7 -.6.1.1 15 -.2 -.5 -.7 -.8 -.8 -.5 -.2 -.5 -.2 -.1..1 3.2 -.4 -.5 -.15 -.12 -.16 -.16 -.17 -.13 -.11 -.11 -.12 45.7.3 -.5 -.1 -.15 -.14 -.23 -.14 -.17 -.27 -.22 -.19 6.1.3.4 -.1 -.5 -.12 -.19 -.2 -.22 -.31 -.26 -.39 Panel F. FTRK V12 5 -.2 -.1 -.7.5 -.5 -.7 -.4 -.1.6 -.5.1.12 15. -.2. -.4 -.4.. -.5 -.1.3.3.3 3 -.1 -.3 -.3 -.7 -.2 -.6 -.2 -.7 -.2 -.4 -.5 -.4 45.6.3 -.5 -.8 -.1 -.4 -.11 -.5. -.11 -.4 -.6 6.1.4.6.8.3 -.5 -.12 -.13 -.5 -.11.3 -.11 46

Table B2: Noise Model 1 (i.i.d.) - Covariance (V12) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5.114.133.156.195.24.213.229.252.272.299.296.329 15.156.151.156.158.161.179.189.29.2.222.234.237 3.219.177.177.177.176.178.176.18.186.212.2.213 45.259.22.2.22.179.23.186.184.183.186.194.24 6.32.252.231.223.212.223.197.217.195.21.212.27 Panel B. OLS V12 (optimal Q and S) 5.18.127.151.188.22.212.227.25.27.298.293.333 15.151.143.15.154.159.172.182.26.196.22.229.233 3.216.174.173.172.17.17.167.176.181.28.197.26 45.255.218.191.213.178.197.183.183.181.188.19.2 6.317.251.222.215.26.224.194.22.184.22.28.199 Panel C. HY V12 5 1.17.9.795.651.627.585.533.516.54.459.485.451 15.763.653.599.564.561.59.474.495.451.432.426.416 3.571.537.5.485.457.452.435.424.47.397.387.385 45.52.471.471.447.44.439.39.41.41.386.369.377 6.462.435.423.416.387.385.39.392.36.368.389.375 Panel D. HYS V12 5.19.114.13.147.157.161.17.188.2.216.216.237 15.127.124.127.141.141.144.15.165.158.179.185.186 3.161.144.151.155.145.156.153.155.155.168.166.169 45.185.172.159.179.158.19.157.161.165.158.168.182 6.233.196.18.175.168.189.18.18.167.182.188.188 Panel E. MK V12 5.116.138.161.27.213.217.235.257.277.296.298.33 15.163.16.15.163.17.182.23.212.23.225.236.24 3.228.188.181.183.173.172.171.183.19.28.26.216 45.264.227.23.223.181.23.177.188.187.185.192.195 6.323.258.231.237.214.227.196.199.2.195.196.196 Panel F. FTRK V12 5.116.134.158.217.223.226.244.276.296.314.324.367 15.159.17.166.18.19.199.229.233.23.263.27.279 3.239.23.2.27.199.21.21.211.229.25.251.263 45.284.247.224.246.27.236.27.228.232.222.237.237 6.353.3.265.285.265.271.241.242.248.233.28.234 47

Table B3: Noise Model 1 (i.i.d.) - Variance of Process 1 (V1) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5 -.7 -.7 -.7 -.4 -.1 -.4 -.8 -.5 -.5 -.7 -.6 -.5 15 -.2 -.9 -.1 -.2.6.5 -.3 -.3 -.5.1 -.4 -.4 3 -.3 -.3 -.8 -.15.2 -.9 -.11. -.11 -.6 -.4 -.5 45 -.5 -.2 -.3. -.9 -.14 -.1 -.2 -.4 -.9 -.12 -.11 6 -.7 -.8.3 -.8 -.6 -.9 -.15. -.11 -.3 -.4 -.3 Panel B. OLS V1 (optimal Q and S) 5 -.4 -.5 -.8 -.3 -.2 -.5 -.8 -.4 -.4 -.6 -.6 -.6 15 -.1 -.9 -.2 -.5.1.3 -.6 -.6 -.8.1 -.6 -.3 3 -.6 -.4 -.6 -.15 -.1 -.12 -.13. -.9 -.6 -.7 -.5 45 -.5 -.4 -.6 -.1 -.1 -.13 -.2 -.5 -.4 -.8 -.11 -.11 6 -.7 -.7.5 -.8 -.5 -.7 -.15 -.1 -.1 -.4 -.4. Panel C. UK V1 5.99.95.96.13.14.14.97.1.14.95.1.11 15.111.111.115.19.117.12.113.114.113.111.112.11 3.129.125.126.12.13.123.124.122.122.12.123.122 45.145.141.134.14.13.13.135.139.142.135.135.126 6.152.147.145.156.147.15.142.145.15.142.15.151 Panel D. MK V1 5.15.13.76.71.5.48.53.33.51.29.44.49 15.58.79.28.19.148.14.121.1.15.85.83.85 3.49.62.76.88.15.264.265.221.197.163.163.145 45.5.59.67.75.86.1.115.121.272.248.262.239 6.42.46.68.78.89.9.94.11.123.173.142.316 Panel E. FTRK V1 5.17.2.18.24.13.12.22.3.26.6.24.34 15.19.19.27.33.24.27.19.4.15.9.16.23 3.2.15.15.17.23.59.39.34.23.13.1.5 45.29.18.14.9.14.12.17.15.35.25.37.26 6.27.17.2.29.25.17.4.11.18.15.21.36 48

Table B4: Noise Model 1 (i.i.d.) - Variance of Process 1 (V1) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5.192.196.186.2.192.18.182.189.196.193.173.195 15.232.233.249 1.117.25.47.243.279 1.983.264.224.224 3.261.247.262.26.25.478.247.363.266.259.257 1.476 45.287.39.284.34.272.299.273.294.268.291.272.32 6.338.318.327.292.339.351.321.313.344.343.361.316 Panel B. OLS V1 (optimal Q and S) 5.171.173.162.173.167.162.159.162.171.167.152.172 15.28.19.223.225.213.231.25.212.217.211.199.192 3.232.231.242.244.231.235.22.252.237.249.245.238 45.247.29.263.279.249.269.25.276.246.252.249.278 6.29.294.313.292.294.38.295.282.314.313.315.286 Panel C. UK V1 5.238.235.23.238.236.241.229.234.244.244.233.247 15.294.288.295.293.289.39.283.287.291.284.291.285 3.356.335.353.346.335.35.338.343.333.325.33.346 45.39.395.361.395.354.389.363.385.366.381.354.38 6.46.389.46.415.43.44.382.41.42.428.431.394 Panel D. MK V1 5.258.263.296.347.357.385.43.432.493.465.493.559 15.332.268.349.35.345.355.372.37.374.399.413.437 3.455.357.343.328.311.419.418.418.48.43.437.412 45.531.436.41.417.354.373.342.361.46.452.468.45 6.611.58.472.442.426.481.367.395.379.398.392.488 Panel E. FTRK V1 5.26.229.265.326.357.378.422.454.531.498.539.617 15.316.251.288.295.319.331.377.374.396.458.479.512 3.47.373.357.346.319.353.347.384.43.44.474.467 45.56.469.444.475.391.412.372.43.424.429.443.439 6.653.575.528.52.513.587.428.456.434.432.455.426 49

Table B5: Noise Model 1 (i.i.d.) - Variance of Process 2 (V2) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5 -.14 -.13 -.2 -.12 -.14 -.25 -.8 -.17 -.13 -.44 -.14 -.21 15 -.9 -.7 -.11 -.15 -.6 -.11 -.8 -.14 -.12 -.12 -.16 -.7 3 -.18 -.9 -.15 -.8 -.11 -.13 -.2 -.12 -.24 -.16 -.12 -.1 45 -.11 -.14 -.1 -.6 -.2 -.9 -.22 -.28 -.16 -.28 -.11 -.13 6 -.15 -.1 -.1 -.1 -.11 -.7 -.18 -.1 -.16 -.19. -.22 Panel B. OLS V2 (optimal Q and S 5 -.13 -.14 -.18 -.15 -.17 -.27 -.1 -.17 -.12 -.37 -.13 -.17 15 -.1 -.11 -.14 -.14 -.7 -.14 -.11 -.16 -.15 -.15 -.17 -.1 3 -.16 -.11 -.18 -.14 -.12 -.12 -.4 -.11 -.22 -.19 -.17 -.1 45 -.11 -.13 -.11 -.8 -.18 -.12 -.22 -.28 -.14 -.28 -.12 -.14 6 -.13 -.12 -.11 -.9 -.15 -.1 -.21 -.11 -.16 -.2 -.2 -.22 Panel C. UK V2 5.8.88.91.12.99.97.11.12.113.97.119.121 15.85.89.97.99.14.11.19.118.12.123.12.126 3.78.89.96.99.15.19.121.119.119.119.13.128 45.84.88.95.1.99.99.111.11.127.18.123.137 6.79.91.94.99.17.122.11.113.124.122.139.119 Panel D. MK V2 5.97.54.39.4.26.26.25.24.22.1.21.23 15.67.116.1.76.67.62.62.58.54.48.43.43 3.35.73.113.144.174.113.12.87.78.73.76.69 45.32.65.81.96.126.171.26.18.11.9.115.93 6.25.41.7.81.15.126.14.149.198.213.26.132 Panel E. FTRK V2 5.11.13.4.13.1.3..6.3 -.15.5.11 15.14.9.17.11.11.7.12.11.9.7.6.4 3.2.11.9.6.15.4.17.9.3.5.7 -.1 45.9.15. -.1 -.1.7.29.15.15 -.3.14.3 6.6.6.12.11.3. -.2 -.5.1.9.43 -.4 5

Table B6: Noise Model 1 (i.i.d.) - Variance of Process 2 (V2) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5.2.228.239.299.297.314.33.332.334.391.342.354 15.195.217.447.313.296.421.331.346.323.352.358.377 3.196.238.257.289.286.312.311.343.315.366.354.342 45.25.242.263.279.294.273.296.291.343.387.341.375 6.22.232.271.272.344.295.341.327.327.358.376.356 Panel B. OLS V2 (optimal Q and S) 5.173.195.216.251.265.282.297.31.38.347.325.331 15.172.186.247.262.25.289.263.39.298.326.333.341 3.172.26.234.251.262.282.285.36.285.346.32.32 45.178.28.235.235.273.254.278.265.332.343.31.35 6.175.28.229.236.287.267.319.31.3.333.342.356 Panel C. UK V2 5.267.298.315.365.371.378.391.383.414.421.427.434 15.256.299.348.361.374.38.393.49.418.419.425.413 3.249.313.333.355.37.4.395.41.413.413.422.42 45.273.39.321.346.381.365.386.383.428.423.416.438 6.255.35.322.36.378.39.415.413.411.425.438.459 Panel D. MK V2 5.263.39.343.48.448.464.496.539.586.592.62.643 15.344.357.339.358.374.388.415.419.435.485.481.53 3.423.399.4.393.48.385.382.384.396.428.426.436 45.477.439.419.444.49.436.436.436.39.48.396.49 6.573.489.445.463.442.465.452.433.485.471.525.429 Panel E. FTRK V2 5.229.289.333.415.46.476.514.57.62.621.662.698 15.319.343.329.359.394.48.447.45.474.545.532.572 3.436.411.396.384.392.4.47.41.441.476.497.516 45.59.459.442.461.42.448.421.447.427.432.452.462 6.625.561.55.521.54.542.57.478.53.472.538.496 51

Table B7: Noise Model 2 (AR(1)) - Covariance (V12) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5 -.9 -.12 -.14 -.13 -.16 -.19 -.2 -.24 -.3 -.22 -.22 -.27 15 -.15 -.14 -.9 -.16 -.2 -.13 -.19 -.15 -.18 -.11 -.2 -.18 3 -.27 -.13 -.2 -.15 -.8 -.15 -.1 -.17 -.2 -.13 -.13 -.32 45 -.24 -.24 -.17 -.8 -.22 -.18 -.1 -.11 -.12 -.2 -.28 -.9 6 -.22 -.33 -.17 -.19 -.25 -.19 -.18 -.6 -.24 -.2 -.19 -.12 Panel B. OLS V12 (optimal Q and S) 5 -.8 -.12 -.14 -.13 -.16 -.2 -.21 -.25 -.3 -.22 -.22 -.27 15 -.15 -.14 -.9 -.16 -.2 -.13 -.19 -.16 -.18 -.11 -.2 -.19 3 -.27 -.13 -.19 -.16 -.8 -.13 -.1 -.17 -.2 -.11 -.13 -.32 45 -.24 -.24 -.17 -.9 -.22 -.18 -.11 -.1 -.12 -.19 -.29 -.9 6 -.22 -.33 -.17 -.19 -.25 -.18 -.18 -.6 -.25 -.21 -.22 -.12 Panel C. HY V12 5 -.53.15 -.25 -.56 -.1 -.3.14 -.3 -.5 -.1.41 -.14 15 -.41 -.57 -.21 -.37.6.43.16 -.3 -.22 -.22.23 -.19 3.12 -.14 -.12 -.19 -.32 -.17.16 -.23 -.7.19.2 -.3 45 -.2 -.11 -.6.3 -.16 -.7 -.17.3.29.15 -.2 -.1 6 -.19 -.16.1 -.23 -.18.4 -.14.11 -.5 -.1.1.3 Panel D. HYS V12 5 -.1 -.7 -.9 -.14 -.13 -.16 -.15 -.2 -.25 -.2 -.18 -.23 15 -.13 -.14 -.8 -.17 -.13 -.5 -.12 -.15 -.16 -.11 -.14 -.16 3 -.22 -.1 -.13 -.13 -.1 -.1 -.7 -.17 -.17 -.7 -.7 -.25 45 -.21 -.2 -.13 -.9 -.2 -.15 -.11 -.3 -.4 -.13 -.26 -.7 6 -.23 -.29 -.13 -.18 -.24 -.14 -.17 -.3 -.2 -.18 -.16 -.7 Panel E. MK V12 5 -.5 -.6 -.4 -.1.1 -.1 -.1.2 -.2.7.3.7 15 -.5 -.6 -.7 -.8 -.1 -.5 -.2 -.5 -.4 -.3 -.2.1 3 -.3 -.3 -.1 -.14 -.8 -.15 -.13 -.21 -.18 -.11 -.6 -.23 45.7 -.6 -.1 -.6 -.11 -.12 -.14 -.19 -.2 -.21 -.34 -.17 6.11 -.8.2 -.1 -.5 -.13 -.15 -.2 -.24 -.28 -.4 -.3 Panel F. FTRK V12 5 -.3 -.7 -.3 -.1. -.2 -.4 -.2 -.4.5.4.6 15 -.4 -.5 -.1 -.5 -.6 -.4 -.1 -.4 -.3 -.1.2.3 3 -.7 -.5 -.8 -.11.1 -.7 -.2 -.8 -.9 -.8. -.17 45.4 -.6.1 -.3 -.5 -.5 -.3 -.6 -.7 -.5 -.17 -.5 6.13 -.6.3.3.1 -.3 -.6 -.8 -.4 -.11 -.14 -.5 52

Table B8: Noise Model 2 (AR(1)) - Covariance (V12) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5.115.136.164.191.217.237.248.253.277.311.31.32 15.161.148.149.152.167.184.2.215.228.235.238.248 3.26.188.188.165.19.175.179.182.188.211.216.27 45.262.22.22.28.189.189.192.184.19.198.221.28 6.327.26.259.215.243.22.196.256.2.188.218.194 Panel B. OLS V12 (optimal Q and S) 5.11.131.158.187.212.234.246.252.281.315.295.319 15.156.139.144.148.164.182.198.211.224.234.237.245 3.25.185.182.16.183.172.177.177.189.21.21.26 45.259.217.197.27.185.185.187.181.183.192.29.23 6.328.258.253.211.229.197.191.243.188.185.23.191 Panel C. HY V12 5 1.296 1.43.876.793.725.661.641.615.59.535.551.497 15.936.824.736.66.628.598.568.522.536.52.479.459 3.684.619.57.565.545.516.497.47.467.475.459.442 45.577.533.55.496.487.494.465.424.459.441.432.427 6.492.497.477.476.447.476.453.44.413.426.413.46 Panel D. HYS V12 5.118.116.13.148.165.176.187.189.28.227.216.237 15.129.127.139.138.141.154.159.167.175.185.182.195 3.161.151.149.147.164.152.162.162.168.166.19.184 45.195.165.168.165.156.176.167.158.171.181.186.182 6.238.22.22.177.192.174.171.212.18.174.183.186 Panel E. MK V12 5.116.143.174.192.222.236.251.247.273.37.3.321 15.167.153.151.151.178.194.29.219.235.24.239.251 3.218.199.195.169.181.168.176.184.19.21.27.28 45.271.225.214.221.196.193.193.17.182.197.192.196 6.336.273.271.227.235.28.21.222.2.192.199.197 Panel F. FTRK V12 5.118.136.174.191.226.241.257.249.283.319.32.345 15.163.161.162.163.193.217.234.247.273.273.279.29 3.219.214.215.186.25.186.21.215.221.237.248.243 45.281.244.244.245.226.227.229.27.221.235.238.245 6.37.311.37.267.269.249.246.254.25.253.239.251 53

Table B9: Noise Model 2 (AR(1)) - Variance of Process 1 (V1) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5 -.1 -.6 -.4 -.1 -.5 -.2 -.1 -.8 -.1.1 -.5 -.3 15 -.57 -.6.88 -.8.2.52.18.65 -.6 -.5 -.7 -.47 3 -.5 -.3 -.1 -.11 -.5 -.4 -.4 -.8 -.12 -.5.5.23 45 -.3 -.4 -.9.1 -.24 -.4 -.8 -.17 -.12 -.13 -.12 -.7 6 -.23 -.25 -.12 -.11 -.9 -.7 -.17 -.14.6 -.14 -.13 -.16 Panel B. OLS V1 (optimal Q and S) 5 -.89 -.14 -.96 -.91 -.92 -.95 -.91 -.1 -.11 -.94 -.95 -.97 15 -.32 -.3 -.17 -.34 -.22 -.23 -.29 -.31 -.24 -.26 -.23 -.23 3 -.17 -.11 -.19 -.22 -.8 -.14 -.13 -.25 -.22 -.15 -.7 -.6 45 -.7 -.9 -.12 -.5 -.15 -.14 -.15 -.4 -.19 -.21 -.17 -.15 6 -.23 -.33 -.12 -.13 -.9 -.12 -.2 -.17.1 -.8 -.14 -.17 Panel C. UK V1 5.129.124.125.129.123.126.129.121.126.127.124.126 15.138.135.149.133.144.141.134.135.144.136.137.134 3.15.158.154.158.155.153.152.156.15.154.161.168 45.162.176.169.182.164.174.17.173.16.168.167.159 6.186.172.189.188.197.186.181.175.193.178.186.182 Panel D. MK V1 5.127.129.1.8.72.68.6.65.45.54.58.57 15.71.11.176.222.214.17.138.128.12.11.96.1 3.58.79.98.116.146.142.35.295.243.214.237.156 45.63.77.92.16.117.135.181.31.272.328.332.296 6.59.54.8.91.16.125.132.14.159.161.22.193 Panel E. FTRK V1 5.29.24.32.21.22.27.22.28.16.29.31.33 15.23.23.35.18.24.26.26.22.23.19.26.17 3.2.21.23.19.28.2.47.41.24.22.25 -.6 45.34.28.27.26.2.26.27.51.19.29.41.47 6.45.2.27.25.26.22.17.13.16.13.34.23 54

Table B1: Noise Model 2 (AR(1)) - Variance of Process 1 (V1) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5.195.189.216.25.185.198.22.183.214.217.189.187 15.272.235.451.246.221.533.276.286.294.266.223.29 3.272.262.273.245.273.258.251.281.272.286.281.27 45.278.38.293.36.31.311.287.287.292.281.39.317 6.326.328.355.328.297.333.339.323.366.35.322.32 Panel B. OLS V1 (optimal Q and S) 5.196.198.212.25.189.194.197.197.24.212.195.19 15.195.222.21.217.213.29.211.217.231.218.26.212 3.255.24.253.236.253.24.242.263.256.265.263.25 45.265.268.27.281.275.29.271.258.263.266.27.291 6.288.3.319.318.297.31.297.296.334.273.297.292 Panel C. UK V1 5.264.263.26.272.253.264.271.252.265.264.256.253 15.35.317.39.36.317.319.32.32.316.34.36.313 3.356.351.372.347.373.365.353.361.361.382.382.394 45.383.412.396.415.394.411.41.374.378.39.41.375 6.444.421.447.432.44.444.418.419.47.43.419.437 Panel D. MK V1 5.243.283.31.346.377.414.427.425.45.58.52.528 15.39.287.314.373.382.38.45.414.43.445.471.422 3.453.376.353.314.355.338.464.482.449.43.457.419 45.543.453.422.423.376.386.382.456.437.53.55.485 6.688.546.494.432.438.425.375.387.416.371.418.42 Panel E. FTRK V1 5.211.235.271.311.362.418.43.425.477.538.554.569 15.28.267.261.37.315.353.46.431.477.481.547.471 3.455.385.36.3.344.334.376.417.42.415.437.457 45.552.489.465.463.41.48.371.369.383.432.446.468 6.742.611.564.486.56.494.415.425.446.41.43.439 55

Table B11: Noise Model 2 (AR(1)) - Variance of Process 2 (V2) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5 -.15 -.14 -.56 -.12 -.7 -.17 -.15.28 -.2 -.14 -.25 -.12 15 -.14 -.11.35 -.15 -.5 -.94 -.21 -.37 -.16 -.29 -.11 -.18 3 -.12 -.18 -.5 -.25 -.11 -.16 -.15.4 -.19 -.3 -.2 -.34 45 -.13 -.14.3 -.97 -.17 -.8 -.7 -.13 -.7 -.15 -.26 -.14 6 -.17 -.2 -.87 -.14 -.11 -.17 -.8 -.18.2 -.14 -.8 -.13 Panel B. OLS V2 (optimal Q and S) 5 -.49 -.28 -.19 -.18 -.15 -.21 -.2 -.15 -.29 -.24 -.29 -.18 15 -.5 -.27 -.19 -.25 -.18 -.19 -.24 -.2 -.19 -.29 -.16 -.2 3 -.47 -.31 -.18 -.2 -.16 -.22 -.2 -.19 -.2 -.8 -.5 -.32 45 -.5 -.3 -.24 -.17 -.22 -.2 -.17 -.17 -.11 -.18 -.26 -.18 6 -.53 -.34 -.22 -.16 -.19 -.22 -.11 -.18 -.26 -.15 -.12 -.16 Panel C. UK V2 5.83.92.98.11.19.18.17.118.115.122.117.127 15.85.93.13.98.17.14.14.117.124.12.128.131 3.86.88.15.99.12.13.114.113.123.127.138.116 45.83.89.98.15.13.1.118.114.126.132.118.135 6.79.89.95.14.115.11.113.112.112.124.13.132 Panel D. MK V2 5.135.5.45.4.38.21.19.21.14.19.14.22 15.57.134.166.69.66.57.44.46.44.42.44.41 3.31.63.13.158.177.215.89.86.82.78.87.56 45.25.49.86.98.14.157.199.138.136.16.89.97 6.27.2.6.9.92.138.154.195.215.223.243.235 Panel E. FTRK V2 5.12.9.15.1.13 -.2 -.1 -.1 -.4.1..7 15.5.16.23.9.9.7 -.1.2.3.4.12.3 3 -.5 -.4.2.13.2.2.11.1.9.3.13 -.4 45.1..8.7.9 -.3.24.7.13.14 -.8.9 6.1 -.18.1.11.2.7.4.22.15.1.33.1 56

Table B12: Noise Model 2 (AR(1)) - Variance of Process 2 (V2) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5.2.228.265.26.35.38.299.34.364.353.369.379 15.186.243.416.28.3.424.34.333.345.319.343.376 3.25.235.249.281.249.298.299.356.343.35.379.365 45.192.231.335.425.35.293.32.324.317.367.374.368 6.187.241.313.265.269.292.319.345.341.356.364.355 Panel B. OLS V2 (optimal Q and S) 5.185.22.21.248.262.276.279.32.336.322.33.33 15.181.28.235.252.254.284.28.293.314.298.39.344 3.188.28.226.25.233.279.271.32.314.325.342.34 45.177.26.221.253.286.274.275.295.3.323.338.324 6.178.215.228.236.249.265.293.315.31.318.322.33 Panel C. UK V2 5.264.295.327.342.372.388.381.387.42.435.47.423 15.276.31.334.345.375.394.389.4.44.419.424.43 3.265.295.355.343.353.385.382.411.47.431.423.423 45.259.29.32.369.37.365.396.399.398.414.439.448 6.257.298.337.345.39.379.394.388.44.45.418.49 Panel D. MK V2 5.293.38.355.392.468.56.521.532.585.632.613.638 15.35.353.359.33.374.397.43.452.482.474.55.57 3.414.42.48.413.42.413.364.43.398.431.428.438 45.498.417.429.428.443.428.427.393.39.392.423.43 6.598.521.58.455.449.449.446.521.467.478.461.47 Panel E. FTRK V2 5.239.278.349.387.466.52.531.542.597.649.651.673 15.326.321.312.329.387.415.465.496.529.526.568.57 3.49.48.44.46.379.369.392.433.433.481.494.491 45.518.441.45.44.458.436.414.418.413.436.477.517 6.664.64.572.53.511.471.474.54.485.486.471.481 57

Table B13: Noise Model 3 (MA(1)) - Covariance (V12) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5 -.9 -.11 -.16 -.18 -.18 -.21 -.18 -.2 -.8 -.32 -.43 -.33 15 -.17 -.11 -.9 -.11 -.16 -.14 -.16 -.21 -.18 -.13 -.19 -.18 3 -.2 -.11 -.13 -.12 -.18 -.18 -.11 -.11 -.4 -.15 -.2 -.14 45 -.33 -.14 -.22 -.17 -.17 -.14 -.5 -.15 -.8 -.2 -.25 -.1 6 -.22 -.18 -.1 -.2 -.17 -.17 -.1 -.9 -.3 -.9 -.2 -.1 Panel B. OLS V12 (optimal Q and S) 5 -.9 -.11 -.16 -.18 -.18 -.22 -.17 -.2 -.8 -.32 -.42 -.33 15 -.16 -.11 -.9 -.12 -.16 -.13 -.16 -.21 -.17 -.13 -.18 -.19 3 -.21 -.12 -.13 -.11 -.18 -.17 -.11 -.11 -.5 -.14 -.21 -.15 45 -.33 -.14 -.2 -.17 -.17 -.14 -.6 -.16 -.9 -.19 -.21 -.11 6 -.22 -.18 -.11 -.2 -.17 -.16 -.9 -.1 -.3 -.8 -.21 -.9 Panel C. HY V12 5 -.2.4 -.6.4.21.5 -.34 -.8 -.39 -.28 -.29.2 15 -.7 -.17 -.3 -.24 -.44..26 -.1.11 -.8 -.6.11 3 -.21.5 -.6.29.17.1 -.3 -.21.15.19 -.8.4 45 -.31 -.1 -.1.8.24.16 -.3.3 -.16.12.6.7 6 -.2.2 -.23.3.36.8.14.8 -.5 -.3.1. Panel D. HYS V12 5 -.9 -.6 -.1 -.14 -.13 -.19 -.17 -.16 -.1 -.26 -.36 -.25 15 -.12 -.1 -.4 -.8 -.17 -.1 -.9 -.17 -.13 -.12 -.17 -.14 3 -.17 -.8 -.9 -.6 -.13 -.12 -.9 -.12 -.3 -.8 -.16 -.13 45 -.3 -.11 -.15 -.13 -.13 -.6 -.7 -.12 -.7 -.12 -.12 -.6 6 -.17 -.17 -.13 -.17 -.9 -.13 -.5 -.7 -.22 -.7 -.17 -.6 Panel E. MK V12 5 -.3 -.3 -.5 -.1 -.1..2.2.11.6..6 15 -.4 -.7 -.9 -.7 -.8 -.5 -.3 -.5 -.2 -.3.4.1 3 -.2. -.7 -.9 -.18 -.22 -.8 -.14 -.1 -.18 -.14 -.9 45 -.4.3 -.2 -.5 -.9 -.17 -.14 -.19 -.22 -.28 -.18 -.3 6.9 -.1.1 -.4 -.9 -.1 -.12 -.18 -.29 -.26 -.32 -.27 Panel F. FTRK V12 5. -.4 -.3. -.1 -.2.1 -.1.1.4 -.2.5 15 -.5 -.5 -.2 -.2 -.2 -.2 -.1 -.3 -.1 -.3.6.2 3 -.6.2 -.6 -.5 -.12 -.11.4 -.5 -.2 -.11 -.1 -.3 45 -.6.2 -.1 -.3 -.4 -.1 -.3 -.4 -.6 -.8 -.9 -.13 6.9..4 -.2 -.5 -.6 -.5 -.4 -.16 -.2 -.15 -.7 58

Table B14: Noise Model 3 (MA(1)) - Covariance (V12) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V12 (base scenario) 5.124.147.177.2.215.23.255.269.287.293.34.337 15.163.15.146.157.18.193.199.214.234.243.243.248 3.212.182.173.185.172.171.186.184.214.221.217.222 45.261.219.26.211.22.189.26.2.212.191.21.224 6.298.251.249.213.224.215.199.2.198.225.241.28 Panel B. OLS V12 (optimal Q and S) 5.119.14.173.197.211.228.25.273.287.29.34.341 15.156.143.141.152.18.189.196.212.234.239.236.245 3.211.178.173.183.17.17.184.181.198.217.216.212 45.264.214.2.21.2.184.21.196.2.191.199.211 6.31.247.238.211.218.29.199.192.195.223.217.197 Panel C. HY V12 5 1.446 1.16 1.5.885.856.734.691.681.616.633.599.582 15.99.896.824.754.688.666.645.627.579.557.548.51 3.755.697.663.67.586.575.558.541.542.496.54.476 45.652.627.582.581.564.521.51.499.48.46.494.467 6.586.572.532.516.536.51.481.466.464.471.435.448 Panel D. HYS V12 5.122.13.147.15.162.177.185.22.212.218.223.252 15.137.137.143.142.161.16.166.175.187.192.185.195 3.161.149.152.162.148.168.17.161.175.192.186.172 45.194.17.17.168.178.171.185.177.181.173.187.186 6.218.195.19.175.193.183.178.188.174.218.197.188 Panel E. MK V12 5.121.154.189.28.217.229.252.267.286.283.297.33 15.168.155.144.155.184.199.197.216.236.237.241.251 3.225.194.181.183.183.175.185.184.22.224.213.219 45.271.23.213.212.24.194.198.196.191.186.27.25 6.311.26.25.22.228.218.195.22.23.2.27.191 Panel F. FTRK V12 5.117.147.193.213.219.229.254.271.297.291.36.342 15.159.158.153.168.28.216.214.243.255.259.274.289 3.224.26.199.21.223.197.216.214.246.259.253.266 45.279.248.238.235.234.227.227.235.246.224.245.248 6.333.297.294.257.261.264.237.257.249.255.243.234 59

Table B15: Noise Model 3 (MA(1)) - Variance of Process 1 (V1) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5 -.3 -.9 -.9 -.6 -.4 -.5 -.3.1 -.7 -.3 -.5 -.2 15.13 -.18 -.21.14 -.8.13.1.24 -.78 -.19.7.44 3 -.3.2 -.2.27 -.13 -.3 -.42.9 -.3 -.38.7.8 45 -.18 -.9. -.2.5.11.1. -.1 -.6 -.6.2 6 -.11 -.12 -.21 -.1 -.16 -.1 -.1 -.2 -.18 -.3 -.19 -.3 Panel B. OLS V1 (optimal Q and S) 5 -.76 -.76 -.73 -.77 -.85 -.83 -.77 -.78 -.78 -.77 -.8 -.78 15 -.32 -.37 -.27 -.33 -.37 -.36 -.36 -.35 -.31 -.36 -.3 -.38 3 -.17 -.14 -.21 -.14 -.28 -.22 -.7 -.17 -.13 -.23 -.8 -.23 45 -.31 -.18 -.4 -.26 -.4 -.15 -.2 -.11 -.11 -.13 -.15 -.7 6 -.12 -.18 -.31 -.13 -.23 -.13 -.2 -.5 -.25 -.7 -.25 -.6 Panel C. UK V1 5.133.128.132.134.137.131.133.137.133.133.134.135 15.155.143.15.148.147.156.153.155.155.153.153.149 3.172.171.163.17.153.169.185.173.163.163.171.178 45.173.183.197.174.194.181.197.189.2.196.186.22 6.21.197.29.197.189.26.26.26.195.211.187.25 Panel D. MK V1 5.186.143.17.92.86.71.66.75.67.63.53.56 15.81.111.324.265.193.178.168.152.127.131.122.115 3.62.93.16.117.138.153.35.325.249.254.224.217 45.52.9.11.14.129.149.173.173.199.438.332.354 6.73.75.98.12.119.128.148.165.149.185.174.264 Panel E. FTRK V1 5.37.32.24.32.33.26.25.39.33.32.24.31 15.31.24.56.38.27.27.22.28.31.26.41.27 3.21.32.22.2.26.23.48.51.23.11.14.3 45.21.35.33.21.27.13.31.28.28.67.37.53 6.53.31.43.22.28.28.22.17.8.21.6.33 6

Table B16: Noise Model 3 (MA(1)) - Variance of Process 1 (V1) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V1 (base scenario) 5.216.195.186.192.19.185.19.194.24.196.21.22 15.351.267.328.257.427.26.258.263.241.259.241.32 3.255.275.248.298.263.38.468.299.277.273.298.272 45.321.298.37.279.313.34.288.332.293.3.37.351 6.313.36.342.34.349.36.339.363.346.344.353.333 Panel B. OLS V1 (optimal Q and S) 5.235.23.221.218.216.223.22.224.238.215.226.224 15.26.21.28.223.213.212.232.223.219.233.222.28 3.233.257.23.257.249.271.256.26.256.248.289.244 45.32.269.283.258.287.32.267.314.273.279.285.321 6.291.336.316.36.315.327.38.325.325.38.337.296 Panel C. UK V1 5.28.268.266.272.278.26.259.27.27.263.268.27 15.315.32.325.339.316.323.343.334.322.334.332.316 3.373.388.358.377.371.396.397.377.378.366.378.379 45.418.43.423.45.433.413.48.423.46.423.48.454 6.437.443.456.442.435.467.441.437.452.449.438.451 Panel D. MK V1 5.295.39.331.36.37.414.437.472.476.478.51.551 15.39.278.433.414.39.399.399.418.427.438.452.445 3.463.376.343.346.35.36.58.49.427.455.445.438 45.554.436.43.411.4.387.365.389.372.592.51.536 6.634.547.477.458.436.434.47.398.421.47.41.447 Panel E. FTRK V1 5.222.253.298.335.348.49.441.483.488.494.529.585 15.267.254.35.318.344.375.378.421.442.463.487.494 3.458.373.347.346.352.361.391.43.385.441.423.441 45.557.459.464.449.436.392.37.389.378.433.438.453 6.665.61.536.528.495.48.441.433.466.436.417.427 61

Table B17: Noise Model 3 (MA(1)) - Variance of Process 2 (V2) - BIAS. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5 -.14 -.13 -.18 -.1 -.12 -.22 -.2 -.25 -.1 -.17 -.22 -.14 15 -.14 -.14.18 -.5 -.14 -.1 -.19 -.12 -.15 -.15.2 -.9 3 -.11 -.13 -.24 -.9 -.13 -.16 -.1 -.12 -.21 -.8 -.16 -.19 45 -.11 -.15.36.59 -.18 -.13 -.24 -.11 -.16 -.7 -.25 -.24 6 -.14 -.16 -.24 -.65 -.31 -.12 -.16 -.11. -.15 -.18 -.1 Panel B. OLS V2 (optimal Q and S) 5 -.9 -.44 -.39 -.27 -.27 -.29 -.26 -.24 -.9 -.2 -.25 -.16 15 -.92 -.47 -.34 -.26 -.25 -.22 -.27 -.2 -.17 -.17 -.3 -.12 3 -.86 -.5 -.37 -.27 -.22 -.26 -.19 -.2 -.28 -.17 -.18 -.2 45 -.87 -.46 -.35 -.25 -.26 -.22 -.33 -.18 -.27 -.13 -.33 -.26 6 -.91 -.44 -.33 -.32 -.25 -.28 -.23 -.17 -.7 -.18 -.21 -.21 Panel C. UK V2 5.92.11.12.111.114.113.119.122.147.134.129.142 15.93.97.12.113.113.121.124.126.136.139.141.142 3.93.99.13.112.117.116.125.129.125.143.137.14 45.9.97.1.113.19.122.12.128.125.138.133.13 6.9.97.14.11.119.11.125.126.133.142.145.147 Panel D. MK V2 5.119.51.41.4.37.28.33.19.38.31.23.22 15.69.146.88.83.68.6.64.58.5.51.54.55 3.4.79.119.136.188.251.16.1.11.91.82.79 45.21.69.77.18.14.194.218.243.248.118.11.12 6.31.49.64.89.111.116.152.21.188.263.265.229 Panel E. FTRK V2 5.19.9.7.13.11.5.15.1.2.11.7.5 15.9.14.13.2.1.4.13.9.6.6.1.14 3.6.9.8.11.6.31.2.1.13.1.1.3 45 -.4.1.1.8.8.14.3.23.19.4.8 -.7 6.12.11 -.3..4 -.2.1.2.5.44.13.29 62

Table B18: Noise Model 3 (MA(1)) - Variance of Process 2 (V2) - RMSE. 5 1 15 2 25 3 35 4 45 5 55 6 Panel A. OLS V2 (base scenario) 5.198.241.529.294.39.297.328.333.336.375.345.38 15.28.239.319.297.297.34.321.342.363.48.385.381 3.2.231.27.313.292.296.33.322.354.39.344.369 45.22.228.393.389.271.33.364.341.541.354.379.357 6.23.256.269.435.29.39.321.354.353.338.356.391 Panel B. OLS V2 (optimal Q and S) 5.23.213.26.255.274.278.296.34.34.329.313.345 15.29.215.232.252.278.281.284.314.333.346.332.354 3.198.28.225.265.264.27.33.293.32.36.34.343 45.21.26.236.256.255.276.32.37.299.314.342.326 6.26.221.226.24.255.281.297.328.314.299.319.352 Panel C. UK V2 5.271.31.361.381.393.383.391.387.426.439.42.449 15.272.311.337.364.383.397.388.424.44.435.457.436 3.278.311.33.39.384.391.396.44.449.453.433.446 45.266.31.33.371.369.42.413.46.45.438.447.436 6.276.39.33.366.386.376.43.427.417.49.446.446 Panel D. MK V2 5.279.315.378.434.455.49.524.562.588.589.586.656 15.352.36.319.351.381.394.412.458.471.479.58.51 3.434.393.396.44.423.466.378.398.433.455.443.436 45.57.437.435.432.44.466.485.471.479.41.422.42 6.544.495.469.443.448.439.442.493.454.513.54.466 Panel E. FTRK V2 5.235.287.37.423.447.492.527.568.61.62.67.683 15.325.315.33.35.398.417.425.49.511.528.563.563 3.423.391.385.44.49.413.393.435.48.489.58.513 45.527.449.464.45.45.467.46.455.478.431.462.489 6.583.55.539.488.487.493.474.49.477.525.56.474 63

.6.5.4.3.2.1 6 5 4 3 2 1 1 2 3 4 5 6 (h) OLS V12 1.2.6 1.5.8.4.3.6.2.4.1.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (i) HY V12 (j) HYS V12.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (k) MK V12 (l) FTRK V12 Graph B1: Noise Model 1 (i.i.d.) - Covariance (V12) - RMSE. 64

.2.15.1.5.5.1.15.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (b) HY V12 (c) HYS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (d) MK V12 (e) FTRK V12 Graph B2: Noise Model 1 (i.i.d.) - Covariance (V12) - BIAS. 65

.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1 1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V1 (d) FTRK V1 Graph B3: Noise Model 1 (i.i.d.) - Variance of Process 1 (V1) - RMSE. 66

.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1.4.2.3.15.2.1.5.1.5.1.1.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V1 (d) FTRK V1 Graph B4: Noise Model 1 (i.i.d.) - Variance of Process 1 (V1) - BIAS. 67

.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2.8.8.7.7.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B5: Noise Model 1 (i.i.d.) - Variance of Process 2 (V2) - RMSE. 68

.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B6: Noise Model 1 (i.i.d.) - Variance of Process 2 (V2) - BIAS. 69

.8.7.6.5.4.3.2.1 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V12 1.2 1.8.8.7.6.5.4.6.3.4.2.1.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (b) HY V12 (c) HYS V12.8.8.7.7.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (d) MK V12 (e) FTRK V12 Graph B7: Noise Model 2 (AR(1)) - Covariance (V12) - RMSE. 7

.2.15.1.5.5.1.15.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (b) HY V12 (c) HYS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (d) MK V12 (e) FTRK V12 Graph B8: Noise Model 2 (AR(1)) - Covariance (V12) - BIAS. 71

1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1 1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) RK V1 (d) FTRK V1 Graph B9: Noise Model 2 (AR(1)) - Variance of Process 1 (V1) - RMSE. 72

.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V1 (d) FTRK V1 Graph B1: Noise Model 2 (AR(1)) - Variance of Process 1 (V1) - BIAS. 73

1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2 1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B11: Noise Model 2 (AR(1)) - Variance of Process 2 (V2) - RMSE. 74

.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B12: Noise Model 2 (AR(1)) - Variance of Process 2 (V2) - BIAS. 75

.8.7.6.5.4.3.2.1 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS 1.2 1.8.8.7.6.5.4.6.3.4.2.1.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (b) HY V12 (c) HYS V12.8.8.7.7.6.6.5.5.4.4.3.3.2.2.1.1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (d) MK V12 (e) FTRK V12 Graph B13: Noise Model 3 (MA(1)) - Covariance (V12) - RMSE. 76

.2.15.1.5.5.1.15.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (b) HY V12 (c) HYS V12.2.2.15.15.1.1.5.5.5.5.1.1.15.15.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (d) MK V12 (e) FTRK V12 Graph B14: Noise Model 3 (MA(1)) - Covariance (V12) - BIAS. 77

1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1 1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V1 (d) FTRK V1 Graph B15: Noise Model 3 (MA(1)) - Variance of Process 1 (V1) - RMSE. 78

.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V1 (b) UK V1.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V1 (d) FTRK V1 Graph B16: Noise Model 3 (MA(1)) - Variance of Process 1 (V1) - BIAS. 79

1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2 1 1.8.8.6.6.4.4.2.2 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B17: Noise Model 3 (MA(1)) - Variance of Process 2 (V12) - RMSE. 8

.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (a) OLS V2 (b) UK V2.4.4.3.3.2.2.1.1.1.1.2 6 5 4 3 2 1 1 2 3 4 5 6.2 6 5 4 3 2 1 1 2 3 4 5 6 (c) MK V2 (d) FTRK V2 Graph B18: Noise Model 3 (MA(1)) - Variance of Process 2 (V12) - BIAS. 81

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