-
-
Notifications
You must be signed in to change notification settings - Fork 300
/
regression.jl
192 lines (145 loc) · 4.04 KB
/
regression.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
#=
Created November 2, 2013
Author: Spencer Lyon
This Julia script implements routines described in 'Numerically Stable
and Accurate Stochastic Simulation Approaches for Solving Dynamic
Economic Models' by Kenneth L. Judd, Lilia Maliar and Serguei Maliar,
(2011), Quantitative Economics 2/2, 173-210 (henceforth, JMM, 2011).'
As such, it is adapted from the file 'Num_Stab_Approx.m'.
=#
using MathProgBase # load in linprog function
function normalize_data(X, Y, intercept=true)
T, n = size(X)
X1 = (X[:, 2:n] .- ones(T) * mean(X[:, 2:n], 1)) ./ (ones(T) * std(X[:, 2:n], 1))
Y1 = (Y .- ones(T) * mean(Y)) ./ (ones(T) * std(Y))
return X1, Y1
end
function de_normalize(X, Y, beta)
# Allocate memory for new coefs
T, n = size(X)
B = Array(Float64, size(beta, 1) + 1, size(beta, 2))
# Infer de-normalized slope coefficients
B[2:end, :] = (1.0 ./ std(X[:, 2:n], 1)') * std(Y) .* beta
# Infer intercept from others.
B[1, :] .= mean(Y) .- mean(X[:, 2:n], 1) * B[2:end, :]
return B
end
function OLS(X, Y, normalize=true)
# Normal OLS.
# Verified on 11-2-13
T, n = size(X)
if normalize
X1, Y1 = normalize_data(X, Y)
B1 = X1 \ Y1
B = de_normalize(X, Y, B1)
else
B = X \ Y
end
return B
end
function LS_SVD(X, Y, normalize=true)
# OLS using singular value decomposition
# Verified on 11-2-13
if normalize
X1, Y1 = normalize_data(X, Y)
U, S, V = svd(X1, thin=true)
S_inv = diagm(0 => 1.0 ./ S)
B1 = V*S_inv * U' * Y1
B = de_normalize(X, Y, B1)
else
U, S, V = svd(X, thin=true)
S_inv = diagm(1.0 ./ S)
B = V * S_inv * U' * Y
end
return B
end
function LAD_PP(X, Y, normalize=true)
T, n1 = size(X)
N = size(Y, 2)
if normalize
n1 -= 1
X1, Y1 = normalize_data(X, Y)
else
X1 = X
Y1 = Y
end
#lower and upper bound
LB = [zeros(n1)-100; zeros(2*T)]
UB = [zeros(n1)+100; fill(Inf, 2T)]
f = [zeros(n1); ones(2*T)]
Aeq = [X1 Matrix(I, T, T) -Matrix(I, T, T)]
B1 = zeros(size(X1, 2), N)
for j = 1:N
beq = Y1[:, j]
sol = linprog(f, Aeq, '=', beq, LB, UB)
B1[:, j] = sol.sol[1:n1]
end
B = normalize ? de_normalize(X, Y, B1) : B1
return B
end
function LAD_DP(X, Y, normalize=true)
T, n1 = size(X)
N = size(Y, 2)
if normalize
n1 -= 1
X1, Y1 = normalize_data(X, Y)
else
X1 = X
Y1 = Y
end
LB = - ones(T)
UB = ones(T)
Aeq = X1'
beq = zeros(n1)
B1 = zeros(size(X1, 2), N)
for j=1:N
f = - Y1[:, j]
sol = linprog(f, Aeq, '=', beq, LB, UB)
B1[:, j] .= -sol.attrs[:lambda][1:n1]
end
B = normalize ? de_normalize(X, Y, B1) : B1
return B
end
function RLS_T(X, Y, penalty=-7)
T, n = size(X)
n1 = n - 1
X1, Y1 = normalize_data(X, Y)
# B1 = inv(X1' * X1 + T / n1 * eye(n1) * 10.0^ penalty) * X1' * Y1
B1 = inv(X1' * X1 + T / n1 * I * 10.0^ penalty) * X1' * Y1
B = de_normalize(X, Y, B1)
return B
end
function RLS_TSVD(X, Y, penalty=7)
T, n = size(X)
n1 = n - 1
X1, Y1 = normalize_data(X, Y)
U, S, V = svd(X1; thin=true)
r = sum((maximum(S)./ S) .<= 10.0^penalty)
Sr_inv = zeros(Float64, n1, n1)
Sr_inv[1:r, 1:r] = diagm(1./ S[1:r])
B1 = V*Sr_inv*U'*Y1
B = de_normalize(X, Y, B1)
return B
end
function RLAD_PP(X, Y, penalty=7)
# TODO: There is a bug here. linprog returns wrong answer, even when
# MATLAB gets it right (lame)
T, n1 = size(X)
N = size(Y, 2)
n1 -= 1
X1, Y1 = normalize_data(X, Y)
LB = 0.0 # lower bound is 0
UB = Inf # no upper bound
f = [10.0^penalty*ones(n1*2)*T/n1; ones(2*T)]
# Aeq = [X1 -X1 eye(T, T) -eye(T,T)]
Aeq = [X1 -X1 I -I]
B1 = zeros(size(X1, 2), N)
for j=1:N
beq = Y1[:, j]
sol = linprog(f, Aeq, '=', beq, LB, UB)
xlp = sol.sol
B1[:, j] = xlp[1:n1] - xlp[n1+1:2*n1]
end
B = de_normalize(X, Y, B1)
return B
end