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
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
|
Fstats <- function(formula, from = 0.15, to = NULL, data = list(), vcov. = NULL)
{
if(!inherits(formula, "formula")) {
X <- if(is.matrix(formula$x))
formula$x
else model.matrix(terms(formula), model.frame(formula))
y <- if(is.vector(formula$y))
formula$y
else model.response(model.frame(formula))
} else {
mf <- model.frame(formula, data = data)
y <- model.response(mf)
X <- model.matrix(formula, data = data)
}
k <- ncol(X)
n <- length(y)
e <- lm.fit(X,y)$residuals
## check if tsp are available and may be used
## (potentially not if NAs were removed)
ytsp <- NULL
orig.y <- NULL
tsp_ok <- FALSE
if(is.ts(data)){
if(NROW(data) == n) {
ytime <- time(data)
ytsp <- tsp(data)
tsp_ok <- TRUE
}
} else {
env <- environment(formula)
if(missing(data)) data <- env
orig.y <- eval(attr(terms(formula, data = data), "variables")[[2]], data, env)
if(is.ts(orig.y) & (NROW(orig.y) == n)){
ytime <- time(orig.y)
ytsp <- tsp(orig.y)
tsp_ok <- TRUE
}
}
ts.eps <- getOption("ts.eps")
if(length(from) > 1) {
if(!is.null(ytsp) && from[2] <= ytsp[3]) {
from <- which(abs(ytime-(from[1]+(from[2]-1)/ytsp[3])) < ts.eps)
if(!is.null(to)) to <- which(abs(ytime-(to[1]+(to[2]-1)/ytsp[3])) < ts.eps)
} else {
stop(paste(sQuote("from"), "does not specify a valid time point"))
}
}
else if(from < 1)
{
from <- floor(from*n)
if(!is.null(to)) to <- floor(to*n)
}
if(is.null(to)) to <- n - from
if(from < (k+1))
{
from <- k+1
warning("'from' changed (was too small)")
}
if(to > (n-k-1))
{
to <- n-k-1
warning("'to' changed (was too large)")
}
if(from <= to)
point <- (from:to)
else
stop("inadmissable change points: 'from' is larger than 'to'")
sume2 <- sum(e^2)
lambda <- ((n-from)*to)/(from*(n-to))
np <- length(point)
stats <- rep(0,np)
for(i in 1:np)
{
X1 <- as.matrix(X[(1:point[i]),])
X2 <- as.matrix(X[((point[i]+1):n),])
if(is.null(vcov.)) {
fm1 <- lm.fit(X1,y[1:point[i]])
fm2 <- lm.fit(X2,y[((point[i]+1):n)])
u <- c(fm1$residuals, fm2$residuals)
sigma2 <- (sum(u^2))/(n-2*k)
stats[i] <- (sume2-sum(u^2))/sigma2
}
else {
allX <- cbind(X1, matrix(rep(0, point[i]*k), ncol=k))
allX <- rbind(allX, cbind(X2, X2))
fm2 <- lm(y ~ 0 + allX)
beta2 <- coef(fm2)[-(1:k)]
V <- vcov.(fm2)
stats[i] <- as.vector(t(beta2) %*% chol2inv(chol(V[-(1:k),-(1:k)])) %*% beta2)
}
}
sup.point <- which.max(stats) + from - 1
if(is.null(vcov.))
min.RSS <- sume2/(1 + max(stats)/(n - 2*k))
else
min.RSS <- NA
if(is.ts(data) & tsp_ok){
stats <- ts(stats, start = time(data)[from], frequency = frequency(data))
datatsp <- tsp(data)
}
else if(!is.null(orig.y) & tsp_ok) {
stats <- ts(stats, start = time(orig.y)[from], frequency = frequency(orig.y))
datatsp <- tsp(orig.y)
}
else{
stats <- ts(stats, start = from/n, frequency = n)
datatsp <- c(0, 1, n)
}
retval <- list(Fstats = stats,
nreg = k,
nobs = n,
par = lambda,
call = match.call(),
formula = formula,
breakpoint = sup.point,
RSS = min.RSS,
datatsp = datatsp)
class(retval) <- "Fstats"
return(retval)
}
print.Fstats <- function(x, ...)
{
cat("\nF statistics \n\n")
cat("Call: ")
print(x$call)
cat("\n")
}
sctest.Fstats <- function(x, type = c("supF", "aveF", "expF"), asymptotic = FALSE, ...)
{
dname <- paste(deparse(substitute(x)))
type <- match.arg(type)
switch(type,
supF = {
STATISTIC <- max(x$Fstats)
names(STATISTIC) <- "sup.F"
METHOD <- "supF test"
},
aveF = {
STATISTIC <- mean(x$Fstats)
names(STATISTIC) <- "ave.F"
METHOD <- "aveF test"
},
expF = {
STATISTIC <- log(mean(exp(0.5*x$Fstats)))
names(STATISTIC) <- "exp.F"
METHOD <- "expF test"
})
if((x$par == 1) & !(type == "expF") & !asymptotic)
{
METHOD <- "Chow test"
PVAL <- 1 - pf(STATISTIC, x$nreg, (x$nobs-2*x$nreg))
}
else
PVAL <- pvalue.Fstats(STATISTIC, type = type,
k=x$nreg, lambda=x$par)
RVAL <- list(statistic = STATISTIC, p.value = PVAL,
method = METHOD, data.name = dname)
class(RVAL) <- "htest"
return(RVAL)
}
plot.Fstats <- function(x, pval = FALSE, asymptotic = FALSE,
alpha = 0.05, boundary = TRUE, aveF = FALSE,
xlab = "Time", ylab = NULL,
ylim = NULL, ...)
{
k <- x$nreg
n <- x$nobs
bound <- boundary(x, alpha = alpha, pval = pval, aveF = aveF, asymptotic =
asymptotic)
x <- x$Fstats
if(pval)
{
if(asymptotic)
x <- 1 - pchisq(x, k)
else
x <- 1 - pf(x, k, (n-2*k))
if(is.null(ylab)) ylab <- "p values"
}
else
if(is.null(ylab)) ylab <- "F statistics"
if(is.null(ylim)) ylim <- c(0, max(c(x,bound)))
plot(x, xlab = xlab, ylab = ylab, ylim = ylim, ...)
abline(0,0)
if(boundary)
{
lines(bound, col=2)
if(aveF) lines(ts(rep(mean(x),length(x)),start=start(x),
frequency = frequency(x)),lty=2)
}
}
boundary.Fstats <- function(x, alpha = 0.05, pval = FALSE, aveF =
FALSE, asymptotic = FALSE, ...)
{
if(aveF)
{
myfun <- function(y) {pvalue.Fstats(y, type="ave", x$nreg, x$par) - alpha}
upper <- 40
}
else
{
myfun <- function(y) {pvalue.Fstats(y, type="sup", x$nreg, x$par) - alpha}
upper <- 80
}
bound <- uniroot(myfun, c(0,upper))$root
if(pval)
{
if(asymptotic)
bound <- 1 - pchisq(bound, x$nreg)
else
bound <- 1 - pf(bound, x$nreg, (x$nobs-2*x$nreg))
}
bound <- ts(bound,
start = start(x$Fstats),
end = end(x$Fstats),
frequency = frequency(x$Fstats))
return(bound)
}
lines.Fstats <- function(x, ...)
{
lines(x$Fstats, ...)
}
|
