IN PYTHON

I already did a, b, and c. I need d and e

The data file named robot contains a time series obtained from an industrial robot. The robot was put through a sequence of maneuvers, and the distance from a desired ending point was recorded in inches. This was repeated 324 times to form the time series.

a. Estimate the parameters of an AR(1) model for these data.

b. Estimate the parameters of an IMA(1,1) model for these data.

c. Compare the results from Parts a and b.

d. Use the IMA(1,1) model to forecast five values ahead. Obtain 95% forecast limits also.

e. Display the forecasts, forecast limits, and actual values in a graph and interpret the results.

The robot.txt as follows:

0.0011 0.0011 0.0024 0 -0.0018 0.0055 0.0055 -0.0015 0.0047 -1e-04 0.0031 0.0031 0.0052 0.0034 0.0027 0.0041 0.0041 0.0034 0.0067 0.0028 0.0083 0.0083 0.003 0.0032 0.0035 0.0041 0.0041 0.0053 0.0026 0.0074 0.0011 0.0011 -1e-04 8e-04 4e-04 0 0 -9e-04 0.0038 0.0054 2e-04 2e-04 0.0036 -4e-04 0.0017 0 0 0.0047 0.0021 0.008 0.0029 0.0029 0.0042 0.0052 0.0056 0.0055 0.0055 0.001 0.0043 6e-04 0.0013 0.0013 8e-04 0.0023 0.0043 0.0013 0.0013 0.0045 0.0037 0.0015 0.0013 0.0013 0.0029 0.0039 -0.0018 0.0016 0.0016 -3e-04 0 9e-04 0.0017 0.0017 0.003 -1e-04 0.007 -8e-04 -8e-04 9e-04 0.0025 0.0031 2e-04 2e-04 0.0022 0.002 3e-04 0.0033 0.0033 0.0044 -0.001 0.0048 0.0019 0.0019 0.0031 0.002 0.0017 0.0014 0.0014 0.0039 0.0052 0.002 0.0012 0.0012 0.0031 0.0022 0.004 0.0038 0.0038 7e-04 0.0016 0.0024 3e-04 3e-04 0.0057 6e-04 9e-04 0.004 0.004 0.0035 0.0032 0.0068 0.0028 0.0028 0.0048 0.0035 0.0042 -0.002 -0.002 0.0023 -0.0011 0.0062 -0.0021 -0.0021 0 -0.0019 -5e-04 0.0048 0.0048 0.0027 9e-04 -2e-04 0.0079 0.0079 0.0017 0.0034 0.003 0.0025 0.0025 4e-04 0.0031 0.0057 -3e-04 -3e-04 6e-04 0.0018 0.0022 0.0042 0.0042 0.0055 -5e-04 -0.0053 0.0028 0.0028 5e-04 0.0036 0.0017 -0.0043 -0.0043 0.0066 -0.0016 0.0055 -0.0011 -0.0011 -0.0049 0.0047 0.0056 0.0057 0.0057 -2e-04 0.0056 0.0037 0.0012 0.0012 0.0018 -0.0025 -0.0011 0.0027 0.0027 0.0039 0.0058 3e-04 0.004 0.004 0.0042 0 0.0056 -0.0029 -0.0029 -0.0026 0.0016 0.0019 0.0015 0.0015 7e-04 7e-04 -0.0044 -0.003 -0.003 0.0013 0.0029 -0.001 9e-04 9e-04 -0.0016 0 0 0.0014 0.0014 -3e-04 9e-04 -0.0068 3e-04 3e-04 -0.0012 0.0037 -0.0019 0.0023 0.0023 -0.0033 -2e-04 -0.001 0.0021 0.0021 0.0026 -2e-04 0.0011 0.0028 0.0028 -4e-04 0.0026 -0.0015 2e-04 2e-04 0.0018 -5e-04 4e-04 -8e-04 -8e-04 0.0018 0.0019 0.0029 -0.0022 -0.0022 0.001 -0.0033 0.002 0 0 3e-04 7e-04 -9e-04 -0.0035 -0.0035 0.001 7e-04 0.0028 -8e-04 -8e-04 -0.0034 -0.001 -0.0018 -0.0021 -0.0021 -6e-04 -0.0018 -0.0046 -0.0017 -0.0017 -1e-04 -0.0029 0.002 -0.0049 -0.0049 -0.0021 -0.0027 -0.0018 -0.0015 -0.0015 0.0051 -2e-04 0 -6e-04 -6e-04 -0.0012 0.0012 0 0.0021 0.0021 -1e-04 0.0022 0.0055 -0.001 -0.001 0.0048 6e-04 0.0026 4e-04 4e-04 0 0 8e-04 0.0044 0.0044 2e-04 0.0036