DS 809 Baptist University of The Americas Load Data Analysis

-2.24 -0.51-0.54 -0.96
1.39 0.93
-0.27 -0.93
-0.93 -0.05
3.25 0.34
-4.17 -0.36
6.07 0.6
-1.81 1.09
2.3 -1.62
-7.21 -0.68
6.11 -0.67
-5.73 0.79
10.42 0.89
-8.8 -0.79
9.93 0.88
-3.85 0.89
3.25 -1.13
-2.59 0.68
5.5 0.47
-4.68 -0.06
4.51 -0.35
-8.62 -2.06
4.63 0.03
0.39 0.65
-0.74 -0.97
1.13 0.32
0.71 0.79
4 1.27
-1.08 0.06
1.95 -0.73
-0.45 0.55
3.4 0.91
-0.33 0.17
-0.4 0.13
2.77 -0.4
-6.5 -1.6
3.98 -0.29
-2.61 -0.64
0.05 -0.58
0.51 0.14
0.25 0.73
1.1 -0.61
-2.17 0.01
4.27 0.07
-1.6 0.45
3.26 -0.23
-7.24 -1.7
4.97 1.23
-1.61 -0.42
1.46 -0.05
1.48 0.97
5.57 0.46
-4.78 -0.07
5.65 0.75
-2.23 0.38
3.93 0.19
-2.26 -0.21
0.96 -0.99
0.55 0.5
2.75 1.06
-1.42 -0.83
3.03 0.96
1.06 0.79
-0.16 -1.21
-6.16 -1.66
6.16 1.12
-0.48 1.23
3.72 -0.31
-8.26 -2.24
4.73 -0.51
-6.82 -0.44
9.1 -0.04
-8.11 0.12
5.23 -0.53
-1.39 0.09
5.95 2.42
1.66 1.03
-0.34 -1.15
-4.43 -2.08
1.12 0.3
-0.69 0.14
1.49 0.63
2.27 0.77
2.17 0.42
-1.8 -1.07
2.37 0.98
0.32 0.25
-0.09 -0.44
0.64 -0.46
-1.13 -0.71
-1.95 -0.9
-5.53 -2.81
0.44 -0.01
-1.47 -0.51
6.48 1.93
-0.31 1.34
3.35 -1.14
-2.68 1.35
7.63 -0.22
-10.48 -0.54
12.49 0.67
-10.26 0.16
9.19 -0.87
-5.89 1.85
15.3 2.19
-8.95 -0.11
6.26 -0.68
-6.14 0
8.65 1.63
-2.05 0.34
-0.09 -1.27
-0.82 1.12
5.47 -0.2
-0.67 1.8
4.77 -0.16
-3.64 0.43
6.83 1.01
-4.28 -0.71
6.7 1.49
-8.95 -2.3
4.7 -0.43
-0.68 1.9
8.24 1.91
0.71 1
-2.91 -1.13
4.11 1.33
0.67 -1.23
-1.85 0.36
2.82 0.01
-5.31 -2.45
1.36 0.26
0.97 0.75
0.06 -0.53
0.1 0.11
-0.07 -0.42
-0.34 0.18
4.18 0.65
-3.31 -0.33
5.9 1.52
-2.23 -0.92
1.18 0.36
-1.89 -1.88
-1.98 -0.16
3.95 0.93
-1.85 -0.55
0.8 -0.86
-1.68 -0.19
0.49 -0.25
-2.51 -0.88
2.28 0.32
0.27 -0.45
-2.04 -0.34
1.29 -0.48
0.49 0.78
-0.28 -0.88
-0.83 -0.18
3.46 0.21
-3.08 -0.9
2.77 0.87
-1.72 -0.3
0.61 -1.33
-2.24 -0.7
0.64 -0.31
-0.44 -0.14
0.68 0.23
-1.76 -0.99
0.66 -0.44
-1.66 0.3
1.05 -1.47
-3.23 -0.32
6.6 0.65
-3.51 0.98
8.66 1.15
-3.81 -0.22
2.58 -0.99
-11.08 -2.98
6.97 -0.58
-7.04 0.18
6.51 -0.46
-8.18 -1.05
5.9 0.39
-2.13 -0.23
1.44 0.26
3.07 1.51
-0.58 -0.29
2.74 -0.66
-7.23 -1.19
4.43 -0.66
-5.19 -0.33
3.75 -0.06
-2.83 -1.22
-0.5 -0.23
2.46 0.61
1.06 0.7
-0.01 -0.76
0.8 -0.01
-0.74 -0.12
0.22 -0.97
0.43 0.08
coh94 x1 x2 x3 x4
0 129.05 4.883 9.62 6.3
1 129.05 4.872 9.62 6.3
6 129.05 4.928 9.62 6.2
8 128.89 5.007 9.5 6.1
11 128.89 5.1 9.5 6
13 128.89 5.238 9.5 5.9
48 129.25 5.353 9.48 5.8
56 129.25 5.446 9.48 5.8
49 129.25 5.562 9.48 5.7
65 129.55 5.676 9.47 5.6
77 129.55 5.797 9.47 5.5
85 129.55 5.971 9.47 5.4
81 129.83 6.129 9.55 5.4
85 129.83 6.25 9.55 5.3
110 129.83 6.336 9.55 5.3
100 131.76 6.38 9.63 5.4
98 131.76 6.387 9.63 5.4
125 131.76 6.352 9.63 5.5
131 133.92 6.311 9.62 5.5
141 133.92 6.272 9.62 5.5
98 133.92 6.254 9.62 5.5
203 135.25 6.225 9.56 5.5
149 135.25 6.177 9.56 5.4
253 135.25 6.152 9.56 5.4
283 136.95 6.084 9.46 5.4
153 136.95 5.988 9.46 5.3
179 136.95 5.957 9.46 5.3
123 137.19 5.929 9.44 5.3
107 137.19 5.92 9.44 5.3
98 137.19 5.935 9.44 5.2
173 137.88 5.951 9.43 5.2
129 137.88 5.977 9.43 5.1
144 137.88 5.991 9.43 5.2
227 139.1 5.977 9.41 5.2
156 139.1 5.97 9.41 5.2
157 139.1 5.94 9.41 5.1
182 140.66 5.928 9.42 5.2
130 140.66 5.934 9.42 5.2
102 140.66 5.943 9.42 5.1
122 141.62 5.96 9.44 5
121 141.62 5.986 9.44 5
126 141.62 5.984 9.44 5
111 143.75 5.973 9.42 4.9
147 143.75 5.971 9.42 4.8
156 143.75 5.963 9.42 4.8
131 145.71 5.941 9.35 4.6
113 145.71 5.924 9.35 4.6
81 145.71 5.93 9.35 4.5
93 148.1 5.937 9.19 4.5
91 148.1 5.911 9.19 4.5
102 148.1 5.895 9.19 4.5
83 148.69 5.871 9.11 4.4
92 148.69 5.855 9.11 4.4
106 148.69 5.838 9.11 4.5
100 150.76 5.827 9.04 4.5
87 150.76 5.809 9.04 4.4
105 150.76 5.768 9.04 4.4
125 152.61 5.669 9.01 4.4
69 152.61 5.579 9.01 4.3
78 152.61 5.522 9.01 4.2
82 154.07 5.505 9.04 4.2
54 154.07 5.457 9.04 4.2
77 154.07 5.443 9.04 4.2
56 155.79 5.414 9.09 4.2
56 155.79 5.396 9.09 4.1
56 155.79 5.405 9.09 4
40 158.21 5.422 9.15 4.1
52 158.21 5.446 9.15 4.1
50 158.21 5.461 9.15 4.1
62 160.07 5.508 9.14 4.1
77 160.07 5.547 9.14 4.1
64 160.07 5.612 9.14 4
54 162.62 5.6705 9.03 4
44 162.62 5.752 9.03 4
48 162.62 5.8635 9.03 4
38 165.32 5.897 9.13 3.9
45 165.32 5.9605 9.13 3.9
46 165.32 6.0085 9.13 3.9
26 168.38 6.053 9.14 3.9
47 168.38 6.0955 9.14 3.9
52 168.38 6.1245 9.14 3.9
45 171.11 6.166 9.24 3.9
51 171.11 6.185 9.24 3.9
42 171.11 6.1705 9.24 3.9
34 176.09 6.0775 9.26 4
35 176.09 5.9155 9.26 4.1
29 176.09 5.7285 9.26 4.2
23 179.06 5.571 9.37 4.4
37 179.06 5.2905 9.37 4.4
34 179.06 5.117 9.37 4.5
22 182.37 4.9845 9.22 4.7
42 182.37 4.8105 9.22 4.9
35 182.37 4.695 9.22 5
34 185.14 4.4885 9.47 5.2
25 185.14 4.17 9.47 5.4
32 185.14 4.0035 9.47 5.5
24 188 3.8405 9.33 5.5
28 188 3.6865 9.33 5.6
22 188 3.6455 9.33 5.6
11 191.75 3.582 9.41 5.6
13 191.75 3.5255 9.41 5.6
20 191.75 3.51 9.41 5.6
26 196.01 3.437 9.58 5.6
21 196.01 3.373 9.58 5.6
24 196.01 3.278 9.58 5.6
17 198.91 3.214 9.69 5.6
16 198.91 3.125 9.69 5.7
21 198.91 3.013 9.69 5.7
16 201.66 2.919 9.71 5.8
17 201.66 2.829 9.71 5.8
12 201.66 2.77 9.71 5.8
18 204.92 2.717 9.71 5.8
16 204.92 2.663 9.71 5.8
22 204.92 2.566 9.71 5.9
21 208.38 2.512 9.65 5.8
13 208.38 2.465 9.65 5.7
15 208.38 2.43 9.65 5.7
19 216.24 2.408 9.76 5.6
14 216.24 2.401 9.76 5.6
12 216.24 2.371 9.76 5.5
11 221.38 2.373 9.81 5.4
12 221.38 2.339 9.81 5.3
10 221.38 2.3 9.81 5.3
14 228.27 2.293 9.92 5.3
12 228.27 2.295 9.92 5.3
5 228.27 2.339 9.92 5.3
15 239.01 2.425 10.12 5.2
12 239.01 2.466 10.12 5.2
9 239.01 2.558 10.12 5.2
12 247.57 2.633 10.11 5.2
6 247.57 2.684 10.11 5.2
12 247.57 2.78 10.11 5.2
14 257.12 2.869 10.46 5.1
5 257.12 2.96 10.46 5.1
3 257.12 3.096 10.46 5
5 269.37 3.182 10.66 5
8 269.37 3.233 10.66 5
11 269.37 3.315 10.66 4.9
5 282.58 3.401 10.95 4.9
5 282.58 3.498 10.95 4.8
5 282.58 3.589 10.95 5.1
3 294.2 3.689 11.06 5.1
7 294.2 3.785 11.06 5
7 294.2 3.88 11.06 4.7
DS 809 – Assignment 5
For statistical inference purposes you can use an 𝜶 (significance) level of 0.05. For
each case, please clearly state your hypotheses, rejection criteria, and conclusion
when needed.
1. Consider the mortgage default data provided by the Federal Housing Administration
(FHA) of the U.S. Department of Housing and Urban Development (HUD) in the Atlanta
region given in “coh94w.txt”.
We will focus on the analysis of the variable called “coh94” which represents the
monthly number of households who defaulted their mortgages for the mortgage pool
(cohort) of 1994 in the Atlanta region. There are other economic indicators in the data
which we will ignore for now.
1. Obtain the time series plot, ACF, and PACF of the series. What do you observe?
2. Find a suitable ARIMA process for the default data where you obtain white noise
residuals (it does not need to be perfect, try to get as close as possible).
3. Investigate if the conditional variance from your ARIMA model from part 2 is
white noise (using the squared residuals from your ARIMA model).
4. Consider fitting a GARCH process on the residuals. Re-estimate the model with
your ARIMA structure on the means and your GARCH structure on the variance.
Investigate the significance of the model parameters and make sure to obtain
white residuals and squared residuals.
5. Plot the fitted model with confidence bounds against the actual data.
6. Consider transforming the data via the “sqrt(coh94+.5)” function. Recall that the
original data is not continuous (in fact it is discrete as it is count data). Repeat
septs 1-5 above using the transformed data. What do you observe? Are the results
drastically different?
2. Consider the same data from Q1 given in “coh94w.txt”. There are four additional
covariates (independent variables) in the data.
Since default behavior is influenced by factors relating to both the housing equity
and the mortgage borrower’s ability to pay the loan, we can consider two equity
and two ability-to-pay covariates in the analysis. Housing equity is mainly determined
by the housing price level and interest rate. Therefore, we can include the
regional conventional mortgage home price index (CMHPI, denoted by x1) and the
federal cost of funds index (COFI, denoted by x2) as aggregate equity factors. In
addition, in order to take into account borrowers’ overall repayment ability, we can
consider the homeowner mortgage financial obligations ratio (FOR Mortgage, denoted by
x3) from The Federal Reserve Board which reflects periodical mortgage repayment
burden of borrowers, and regional unemployment rate (denoted by x4) from the U.S.
Census.
First transform the dependent variable “coh94” using the square root transformation via
“sqrt(coh94+.5)”. Since the data is integer based, this is an approach used to transform
count data into a continuous scale.
1. Estimate a regression model with transformed coh94 as the dependent variable
and x1, x2, x3, and x4 as the independent variables. Investigate if the residuals
from the fitted regression model are white noise.
2. Find a suitable ARMA process for the residuals of the model from part 1.
3. Re-estimate the corrected regression model. Investigate if the model parameters
are significant and/or if there are any differences between those obtained from
part 1. Are the residuals from the corrected regression model white noise?
4. Plot the fitted models from part 1 and 3 against the actual data. Compare the AIC
estimates for both models to assess which one provides a better fit to data.
3. Consider the example from page 4 of Lecture Set 5 with the dataset given in
“regarma.txt”.
Define the same 2 models from the example: a linear regression model (M1) and a linear
regression model with ARMA residuals (M2).
Using the first 180 observations as your training sample and the last 20 observations as a
test sample, obtain sequential predictions for both M1 and M2 for all the samples in the
test sample. For instance, in predicting data point no: 181 use all the previous data
(1:180), in predicting point no:182 use all the previous data (1:181), etc. For each case,
re-estimate the respective model using the past data and obtain the prediction for the next
time period.
Compute the MAPE estimates and plot the predictions against the actual data. Which
model provides a better forecasting performance?

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