Please help,

Consider the market closing daily prices onIBM in fileIBMclose.dat.

Estimate the ARCH(1) and ARCH(2) models using the code in file SAS code.

Are the squared returns on IBM serially correlated?

Is thereforeIBM volatility predictable?

Does your finding contradict the former conclusion that returns on IBM are white noise?

IBMclose.dat

 100.87000 101.08000 97.440000 96.400000 94.030000 94.730000 96.280000 94.110000 99.180000 98.120000 97.930000 97.420000 99.630000 97.530000 102.23000 103.01000 100.71000 101.15000 102.23000 101.80000 103.21000 105.10000 104.00000 101.19000 100.20000 98.990000 99.890000 101.70000 103.04000 104.87000 102.65000 102.68000 101.56000 104.32000 103.43000 104.53000 106.47000 110.63000 112.64000 111.46000 110.13000 110.49000 111.92000 111.61000 108.83000 110.21000 110.28000 112.67000 113.23000 112.11000 111.46000 111.76000 114.53000 113.11000 114.45000 115.16000 114.11000 113.08000 111.74000 110.82000 111.37000 112.67000 111.05000 112.22000 111.97000 112.50000 112.46000 112.94000 114.89000 112.20000 113.44000 113.33000 116.52000 119.05000 120.32000 120.28000 119.62000 119.55000 120.12000 119.05000 117.70000 118.83000 116.75000 119.56000 119.14000 118.03000 118.80000 120.56000 121.32000 120.49000 121.63000 122.93000 123.85000 124.76000 124.14000 122.85000 121.57000 120.06000 121.11000 120.62000 123.65000 125.81000 125.97000 125.70000 123.69000 124.16000 123.88000 124.77000 121.34000 122.23000 122.31000 119.70000 120.28000 122.52000 123.06000 121.50000 120.58000 121.42000 119.20000 119.90000 119.90000 120.99000 117.64000 116.59000 115.12000 115.83000 115.67000 116.10000 118.00000 120.31000 116.93000 119.63000 118.60000 118.04000 119.65000 122.31000 122.88000 126.15000 124.95000 126.26000 125.79000 126.26000 124.83000 122.61000 123.98000 125.15000 124.29000 122.99000 123.89000 125.16000 125.93000 125.82000 125.59000 123.43000 122.09000 122.65000 123.76000 123.20000 121.47000 119.49000 119.44000 119.91000 121.80000 119.79000 119.43000 120.29000 121.46000 118.68000 115.45000 115.38000 112.12000 111.47000 114.36000 112.16000 115.09000 116.22000 115.99000 112.31000 113.15000 108.68000 112.24000 115.88000 113.30000 112.47000 113.55000 117.10000 116.43000 111.60000 114.03000 107.37000 102.12000 100.85000 98.100000 93.260000 88.280000 86.770000 85.550000 89.900000 91.260000 86.080000 89.230000 88.510000 90.200000 86.640000 81.510000 82.240000 80.020000 77.670000 85.100000 85.990000 88.420000 90.640000 90.360000 91.060000 87.690000 83.480000 84.580000 82.230000 81.120000 78.180000 82.560000 78.760000 75.960000 78.510000 74.480000 70.340000 73.410000 78.330000 79.070000 80.070000 80.000000 75.390000 78.280000 79.090000 75.920000 79.010000 83.200000 81.070000 81.240000 79.000000 80.590000 81.150000 84.710000 84.160000 82.360000 81.890000 80.390000 79.020000 78.940000 79.740000 79.660000 81.910000 82.510000 85.660000 85.120000 87.480000 86.070000 85.470000 83.040000 84.030000 83.670000 81.560000 82.470000 83.260000 80.380000 89.630000 88.310000 87.740000 89.810000 89.870000 92.960000 90.700000 89.860000 89.150000 91.650000 91.010000 90.600000 94.770000 95.440000 91.940000 93.810000 93.720000 92.500000 89.380000 90.210000 87.660000 87.530000 83.170000 85.170000 84.680000 87.700000 90.720000 87.780000 86.520000 88.220000 86.230000 84.590000 82.290000 86.010000 87.360000 89.110000 89.070000 89.920000 91.590000 90.640000 91.340000 91.190000 97.300000 96.900000 96.560000 97.370000 92.810000 93.170000 95.510000 96.220000 99.380000 100.76000 100.11000 97.340000 99.750000 100.25000 98.530000 97.860000 97.440000 99.990000 99.830000 99.000000 100.85000 101.09000 99.980000 98.660000 98.530000 100.49000 102.56000 101.74000 103.12000 104.68000 104.34000 103.67000 101.66000 100.57000 101.96000 103.00000 101.33000 100.13000 100.45000 103.63000 104.55000 103.10000 101.89000 100.96000 104.07000 101.99000 103.74000 105.31000 107.38000 105.86000 105.52000 105.36000 106.27000 106.51000 107.16000 107.37000 108.41000 107.23000 106.64000 106.34000 106.03000 105.36000 104.93000 103.57000 103.49000 103.20000 105.10000 104.72000 104.87000 103.47000 103.89000 100.81000 100.73000 99.280000 99.760000 101.15000 99.910000 102.68000 102.31000 106.25000 109.63000 114.37000 115.38000 115.98000 114.52000 116.00000 116.57000 116.56000 116.21000 116.19000 116.79000 116.86000 118.83000 118.51000 117.39000 116.86000 118.80000 118.17000 117.26000 118.76000 119.05000 118.04000 116.34000 117.10000 118.04000 118.42000 119.36000 118.79000 118.30000 118.94000 118.90000 117.69000 117.52000 116.17000 115.57000 115.81000 116.94000 116.64000 116.24000 117.14000 117.52000 118.35000 118.82000 121.28000 121.34000 121.56000 121.03000 121.07000 120.28000 120.40000 120.54000 118.80000 118.28000 119.08000 117.37000 118.49000 119.21000 120.81000 122.23000 121.74000 125.37000 126.47000 126.45000 127.78000 127.41000 121.10000 122.51000 122.27000 120.33000 122.14000 119.82000 119.57000 120.11000 120.96000 122.32000 120.07000 120.02000 120.62000 120.75000 122.55000 123.49000 126.00000 126.91000 127.19000 126.26000 127.03000 128.21000 128.63000 128.15000 127.54000 126.96000 128.20000 127.93000 127.28000 125.70000 126.35000 127.94000 127.21000 127.55000 127.25000 127.04000 126.80000 128.39000 129.34000 129.68000 129.93000 128.49000 128.71000 127.40000 127.91000 128.65000 129.93000 130.00000 130.57000 132.31000 131.85000 132.57000 130.90000 132.45000 130.85000 130.00000 129.55000 130.85000 129.48000 130.51000 130.23000 132.31000 131.78000 134.14000 130.25000 

SAS code

options linesize=78; * read in the data *; data ibm; infile 'IBMclose.dat'; input price; return = dif(log(price)); t=_n_; * squared returns lag 1 and lag 2 *; retsq= return**2; retsql1 = lag (retsq); retsql2 = lag2(retsq); * estimate the ARCH(1) model *; proc reg; model retsq = retsql1; run; * estimate the ARCH(2) model *; proc reg; model retsq = retsql1 retsql2; run;