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
|
// Copyright (c) Facebook, Inc. and its affiliates.
// This source code is licensed under the MIT license found in the
// LICENSE file in the root directory of this source tree.
functions {
matrix get_changepoint_matrix(vector t, vector t_change, int T, int S) {
// Assumes t and t_change are sorted.
matrix[T, S] A;
row_vector[S] a_row;
int cp_idx;
// Start with an empty matrix.
A = rep_matrix(0, T, S);
a_row = rep_row_vector(0, S);
cp_idx = 1;
// Fill in each row of A.
for (i in 1:T) {
while ((cp_idx <= S) && (t[i] >= t_change[cp_idx])) {
a_row[cp_idx] = 1;
cp_idx = cp_idx + 1;
}
A[i] = a_row;
}
return A;
}
// Logistic trend functions
vector logistic_gamma(real k, real m, vector delta, vector t_change, int S) {
vector[S] gamma; // adjusted offsets, for piecewise continuity
vector[S + 1] k_s; // actual rate in each segment
real m_pr;
// Compute the rate in each segment
k_s = append_row(k, k + cumulative_sum(delta));
// Piecewise offsets
m_pr = m; // The offset in the previous segment
for (i in 1:S) {
gamma[i] = (t_change[i] - m_pr) * (1 - k_s[i] / k_s[i + 1]);
m_pr = m_pr + gamma[i]; // update for the next segment
}
return gamma;
}
vector logistic_trend(
real k,
real m,
vector delta,
vector t,
vector cap,
matrix A,
vector t_change,
int S
) {
vector[S] gamma;
gamma = logistic_gamma(k, m, delta, t_change, S);
return cap .* inv_logit((k + A * delta) .* (t - (m + A * gamma)));
}
// Linear trend function
vector linear_trend(
real k,
real m,
vector delta,
vector t,
matrix A,
vector t_change
) {
return (k + A * delta) .* t + (m + A * (-t_change .* delta));
}
// Flat trend function
vector flat_trend(
real m,
int T
) {
return rep_vector(m, T);
}
}
data {
int T; // Number of time periods
int<lower=1> K; // Number of regressors
vector[T] t; // Time
vector[T] cap; // Capacities for logistic trend
vector[T] y; // Time series
int S; // Number of changepoints
vector[S] t_change; // Times of trend changepoints
matrix[T,K] X; // Regressors
vector[K] sigmas; // Scale on seasonality prior
real<lower=0> tau; // Scale on changepoints prior
int trend_indicator; // 0 for linear, 1 for logistic, 2 for flat
vector[K] s_a; // Indicator of additive features
vector[K] s_m; // Indicator of multiplicative features
}
transformed data {
matrix[T, S] A;
A = get_changepoint_matrix(t, t_change, T, S);
}
parameters {
real k; // Base trend growth rate
real m; // Trend offset
vector[S] delta; // Trend rate adjustments
real<lower=0> sigma_obs; // Observation noise
vector[K] beta; // Regressor coefficients
}
transformed parameters {
vector[T] trend;
if (trend_indicator == 0) {
trend = linear_trend(k, m, delta, t, A, t_change);
} else if (trend_indicator == 1) {
trend = logistic_trend(k, m, delta, t, cap, A, t_change, S);
} else if (trend_indicator == 2) {
trend = flat_trend(m, T);
}
}
model {
//priors
k ~ normal(0, 5);
m ~ normal(0, 5);
delta ~ double_exponential(0, tau);
sigma_obs ~ normal(0, 0.5);
beta ~ normal(0, sigmas);
// Likelihood
y ~ normal(
trend
.* (1 + X * (beta .* s_m))
+ X * (beta .* s_a),
sigma_obs
);
}
|
