Use the corresponding coefficients to calculate the predicted output p_test_hat for test input t for polynomial p.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1.We need to  develop an autoregression model to predict the stock price for the PRAN group.  We have been given stock values for one month. Use AR (6) model for your prediction. Let’s design the AR model and measure its quality with regards to unseen test data.

a.       Select first 60% data for training  and  40% data for test

b.      Your AR model should be as follows:

Yt+1   = c0  + c1yt-5 + c2yt-4   + c3yt-3 + c4yt-2 + c5yt-1 + c6yt

Where yt is the stock value at time t. So the future value yt+1 can be predicted using the above equation.

c.       Learn the coefficients (all c’s)  using the train data.

d.      Use the learned coefficients to predict the stock values for the test data.

e.      Plot actual stock value  (red line) and predicted stock value (blue line)  for the test data

f.        Calculate SSE for actual stock and predicted stock values. Then calculate R2

Data:

5-Oct-2020	34
6-Oct-2020	67
7-Oct-2020	66
8-Oct-2020	71
9-Oct-2020	77
10-Oct-2020	79
11-Oct-2020	80
12-Oct-2020	79
13-Oct-2020	86
14-Oct-2020	88
15-Oct-2020	87
16-Oct-2020	88
17-Oct-2020	89
18-Oct-2020	92
19-Oct-2020	94
20-Oct-2020	95
21-Oct-2020	93
22-Oct-2020	96
23-Oct-2020	96
24-Oct-2020	97
25-Oct-2020	97
26-Oct-2020	99
27-Oct-2020	100
28-Oct-2020	101
29-Oct-2020	101
30-Oct-2020	102
31-Oct-2020	105
1-Nov-2020	106
2-Nov-2020	106
3-Nov-2020	110
4-Nov-2020	110

 

2.   In this part, you we will fit the following two cubic polynomials p(t) and q(t) at the same time

Train data:

 p(1) = 2,

 p(2) = 7,

p(5) =2,

p(7) =12,

p(8) = 13,

p(10) =6,

p(17) = 6,

q(5) = 4,

q(10) = 5,

q(12) = 10,

q(10) = 8,

q(12) = 19,

p(7) = q(7),

p’(19) = q’(10),

p’’(1) = q’’(7),

 

Test Data:

p(6) =1,

p(10) =2,

p(18) = 30,

p(20) =36,

p(22) = 16,

q(15) = 14,

q(20) = 15,

q(22) = 29,

q(18) = 18,

 

a)      From train data, create vandermonde matrix A. And output vector b_train

b)      Use A and b_train, calculate the coefficients c_hat =  [c0, c1, c2, d0, d1, d2]T. You cannot use pinv() function anyway.

c)       Now you have coefficients for both polynomials.

d)      Use the corresponding coefficients to calculate the predicted output  p_test_hat for test input t for polynomial p.  Plot actual  p(t) and  p_test_hat(t) for test input t

e)      Use the corresponding coefficients to calculate the predicted output  q_test_hat for test input t for polynomial q.  Plot actual q(t) and  q_test_hat(t) for test input t

Attachments:

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