MC simulation - 1 Monte Carlo Simulation of CER Model R(t)...

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 -0.300 -0.200 -0.100 0.000 0.100 0.200 0.300 0.400 1 Monte Carlo Simulation of CER Model R(t) = 0.05 + e(t), e(t) ~ iid N(0, (0.10)^2) time Return
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 -0.300 -0.200 -0.100 0.000 0.100 0.200 0.300 0.400 5 Monte Carlo Samples From CER Model Column L Column M Column N Column O Column P month R(t)
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Monte Carlo Simulation of the CER Model Model Parameters Sample size Simulated values μ σ T ε 0.05 0.1 100 -0.030 0.020 -0.128 -0.078 Sample values of simulated errors 0.024 0.074 mean standard deviation 0.128 0.178 -0.004 0.109 0.120 0.170 skewness excess kurtosis 0.173 0.223 0.091 -0.476 -0.218 -0.168 -0.023 0.027 0.110 0.160 -0.109 -0.059 -0.069 -0.019 -0.169 -0.119 -0.185 -0.135 -0.098 -0.048 -0.077 -0.027 -0.212 -0.162 -0.057 -0.007 -0.040 0.010 0.013 0.063 -0.037 0.013 -0.033 0.017 -0.037 0.013 0.134 0.184 -0.009 0.041 -0.019 0.031 -0.051 -0.001 0.197 0.247 0.087 0.137 0.238 0.288 -0.065 -0.015 0.166 0.216 -0.161 -0.111 0.054 0.104 0.090 0.140 0.192 0.242 -0.008 0.042 -0.052 -0.002 0.068 0.118 -0.038 0.012 0.076 0.126 -0.144 -0.094 -0.085 -0.035 -0.152 -0.102 -0.036 0.014 -0.003 0.047 0.003 0.053 -0.032 0.018 0.219 0.269 R = μ + ε To generate observations from a normal distributions use 1. Tools/DataAnalysis/Random Number Generation 2. StatPlus/Create Data/Random Numbers 100 Monte Carlo s T=50 observations model R(t) = 0.05 + N(0.(0.10)^2) may as follows: 1. Tools/Data Anal Number Generatio 2. Number of varia (samples). Numbe numbers: 50 (sam 3. Distribution: Nor 0.05; SD: 0.10 4. Random Seed: 5. Output Range: s
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-0.174 -0.124 -0.074 -0.024 -0.258 -0.208 0.145 0.195 -0.128 -0.078 -0.065 -0.015 0.076 0.126 0.047 0.097 0.087 0.137 0.060 0.110 -0.137 -0.087 -0.112 -0.062 0.069 0.119 0.032 0.082 -0.094 -0.044 -0.024 0.026 0.013 0.063 0.056 0.106 0.014 0.064 -0.091 -0.041 0.188 0.238 0.049 0.099 0.007 0.057 0.083 0.133 0.086 0.136 -0.064 -0.014 -0.092 -0.042 0.111 0.161 -0.120 -0.070 -0.156 -0.106 0.071 0.121 0.064 0.114 0.221 0.271 0.144 0.194 0.130 0.180 0.011 0.061 0.000 0.050 0.045 0.095 -0.003 0.047 -0.105 -0.055 -0.177 -0.127 0.083 0.133 0.044 0.094 0.062 0.112 0.021 0.071 -0.103 -0.053 0.124 0.174 -0.031 0.019 -0.084 -0.034 -0.082 -0.032 -0.043 0.007 -0.045 0.005 1 1 ˆ N i N μ = N cr th va L5
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Monte Carlo Simulated Samples from CER Model: R(t) = 0.05 + e(t), e(t) ~ iid N(0.05, ( sample 1 sample 2 sample 3 sample 4 sample 5 sample 6 sample 7 sample 8 0.020 -0.078 0.074 0.178 0.170 0.223 -0.168 0.027 -0.002 0.135 0.101 -0.011 0.180 -0.126 0.105 0.038 0.073 0.071 0.049 -0.072 0.074 0.065 0.125 -0.024 -0.013 0.138 -0.034 0.039 0.027 0.202 -0.082 -0.044 0.024 0.114 -0.077 0.102 0.148 -0.036 0.087 0.103 0.121 -0.026 0.081 -0.076 0.278 0.133 -0.062 0.199 -0.028 -0.050 -0.065 -0.202 -0.070 0.117 0.130 0.171 0.130 0.195 0.085 -0.019 0.029 0.121 -0.135 -0.035 0.119 0.099 -0.050 0.161 -0.080 0.117 -0.098 0.162 0.119 0.113 0.110 0.075 -0.163 0.038 -0.043 -0.090 -0.020 0.105 0.143 -0.048 0.183 0.039 0.120 0.084 -0.018 -0.247 0.024 0.212 0.053 0.023 0.165 -0.204 0.137 -0.121 -0.140 -0.135 0.065 0.076 0.016 0.068 0.317 0.150 0.051 -0.048 -0.143 -0.123 -0.012 -0.120 0.230 0.048 0.017 0.093 0.052 0.109 0.077 0.077 0.170 0.241 0.104 0.140 -0.034 0.035 0.009 0.153 -0.030 0.307 0.091 0.120 0.004 -0.063 0.041 0.212 -0.050 -0.037 -0.116 0.033 0.030 0.055 -0.095 -0.029 0.132 0.030 0.061 0.071 0.045 0.056 0.029 0.042 0.103 0.043 0.097 0.019 -0.040 0.277 0.105 -0.006 0.061 0.234 0.001 0.093 -0.001 -0.033 0.120 0.105 0.047 0.100 0.096 0.016 0.072 0.168 -0.056 0.013 0.170 -0.032 0.117 -0.072 -0.163 0.190 -0.109 0.055 -0.076 0.230 0.278 0.068 0.209 0.108 0.039 0.001 0.199 0.113 -0.039 0.062 0.175 0.009 0.114 -0.005 0.036 0.083 0.061 0.023 0.055 -0.007 0.058 0.107 0.115 0.043 0.085 0.099 0.073 -0.049 0.133 0.155 0.051 0.153 0.035 0.150 0.024 -0.117 0.159 0.043 0.095 0.065 -0.109 0.055 0.062 0.139 0.080 0.230 0.000 0.138 -0.007 0.057 0.040 -0.040 0.028 -0.046 0.162 0.172 0.116 -0.066 0.065 0.143 0.208 0.037 0.227 0.076 0.086 -0.002 0.053 -0.019 0.091 0.375 0.163 -0.005 0.163 -0.070 0.033 0.127 0.216 0.221 0.143 0.093 0.081 0.050 0.051 0.036 0.107 0.008 0.016 -0.007 -0.075 0.106 0.136 0.197 0.041 0.004 0.136 0.179 0.074 0.147 0.186 0.064 0.083 0.195 -0.119 0.055 0.025 0.032 -0.116 0.026 -0.011 0.073 0.137 0.023 -0.217 0.166 -0.025 0.043 0.118 0.103 0.071 0.129 0.169 0.020 0.010 -0.096 0.077 0.083 -0.015 0.115 0.009 -0.029 0.061 0.007 -0.014 -0.026 0.124 0.098 0.159 -0.021 0.150 0.309 0.103 0.024 0.130 -0.100 -0.026 -0.040 0.006 0.010 0.142 0.117 0.110 0.194 0.287 0.130 0.232 0.061 0.057 0.137 -0.114 0.068 0.072 -0.015 -0.013 -0.051 0.009 0.188 -0.006 -0.031 0.056 -0.064 0.151 -0.073 0.073 -0.018 0.081 0.128 -0.125 -0.123 -0.021 0.193 0.161 -0.095 0.046 0.130 0.108 0.043 0.155 0.039 0.188 0.102 -0.099 0.024 0.000 0.188 0.044 0.219 0.077 -0.031 simulations of s from the CER + e(t), e(t) ~ iid y be computed lysis/Random on. ables: 100 er of random ple size). rmal; Mean: leave blank specify Cell L6
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-0.054 0.078 0.012 0.078 -0.004 0.101 -0.067 0.045 -0.069 0.120 0.140 -0.009 0.118 0.308 -0.097 0.055 Sample Average 0.066 0.078 0.045 0.034 0.053 0.067 0.049 0.061 Sample Variance 0.009 0.010 0.010 0.008 0.010 0.012 0.009 0.011 Sample SD 0.096 0.101 0.099 0.091 0.099 0.109 0.093 0.104 Using Monte Carlo samples to Evaluate E[muhat], E[sigma2hat] and E[sigmahat] Using Mon Average muhat 0.050 muhat sigma2hat 0.010 sigma2hat sigmahat 0.099 sigmahat Analytic fo muhat sigma2hat sigmahat Histograms of Monte Carlo Estimates Bin Frequency 0.02 1 0.03 6 0.03 11 0.04 9 0.05 20 0.05 20 0.06 13 0.07 6 0.08 9 0.08 4 More 1 For each of the N=100 Monte Carlo samples of size T=50, the CER model parameters mu, sigma2 and sigma are estimated using the sample mean, variance and std. Deviation. This gives
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This note was uploaded on 09/13/2011 for the course ECON 503 taught by Professor Pujara during the Spring '11 term at Punjab Engineering College.

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MC simulation - 1 Monte Carlo Simulation of CER Model R(t)...

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