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
|
\name{predict-methods}
\alias{predict-methods}
\docType{methods}
\alias{predict}
\alias{predict,fGARCH-method}
\concept{VaR}
\concept{value-at-risk}
\concept{ES}
\concept{expected shortfall}
\title{GARCH prediction function}
\description{
Predicts a time series from a fitted GARCH object.
}
\usage{
\S4method{predict}{fGARCH}(object, n.ahead = 10, trace = FALSE, mse = c("cond","uncond"),
plot=FALSE, nx=NULL, crit_val=NULL, conf=NULL, \dots, p_loss = NULL)
}
\arguments{
\item{n.ahead}{ an integer value, denoting the number of steps to be
forecasted, by default 10.}
\item{object}{ an object of class \code{"fGARCH"} as returned by the
function \code{garchFit}.}
\item{trace}{ a logical flag. Should the prediction process be traced?
By default \code{trace=FALSE}.}
\item{mse}{ If set to \code{"cond"}, \code{meanError} is defined as
the conditional mean errors
\eqn{\sqrt{E_t[x_{t+h}-E_t(x_{t+h})]^2}}. If set to \code{"uncond"},
it is defined as \eqn{\sqrt{E[x_{t+h}-E_t(x_{t+h})]^2}}.}
\item{plot}{If set to \code{TRUE}, the confidence intervals are
computed and plotted}
\item{nx}{The number of observations to be plotted along with the
predictions. The default is \code{round(n*0.25)}, where n is the
sample size.}
\item{crit_val}{The critical values for the confidence intervals when
\code{plot} is set to \code{TRUE}. The intervals are defined as
\eqn{\hat{x}_{t+h}} + \code{crit_val[2] * meanError} and
\eqn{\hat{x}_{t+h}} + \code{crit_val[1] * meanError} if two critical
values are provided and \eqn{\hat{x}_{t+h} \pm} \code{crit_val *
meanError} if only one is given. If you do not provide critical
values, they will be computed automatically. }
\item{conf}{The confidence level for the confidence intervals if
\code{crit_val} is not provided. By default it is set to 0.95. The
critical values are then computed using the conditional distribution
that was chosen to create the \code{object} with \code{garchFit}
using the same \code{shape} and \code{skew} parameters. If the
conditionnal distribution was set to \code{"QMLE"}, the critical
values are computed using the empirical distribution of the
standardized residuals. }
\item{\dots}{ additional arguments to be passed. }
\item{p_loss}{
if not null, compute predictions for VaR and ES for loss level
\code{p_loss} (typically, 0.05 or 0.01).
}
}
\details{
The predictions are returned as a data frame with columns
\code{"meanForecast"}, \code{"meanError"}, and
\code{"standardDeviation"}. Row \code{h} contains the predictions for
horizon \code{h} (so, \code{n.ahead} rows in total).
If \code{plot = TRUE}, the data frame contain also the prediction
limits for each horizon in columns \code{lowerInterval} and
\code{upperInterval}.
If \code{p_loss} is not NULL, predictions of Value-at-Risk (VaR) and
Expected Shortfall (ES) are returned in columns \code{VaR} and
\code{ES}. The data frame has attribute \code{"p_loss"} containing
\code{p_loss}. Typical values for \code{p_loss} are 0.01 and 0.05.
These are somewhat experimental and the arguments and the returned
values may change.
}
\value{
a data frame containing \code{n.ahead} rows and 3 to 7 columns,
see section \sQuote{Details}
}
\author{
Diethelm Wuertz for the Rmetrics \R-port
}
\seealso{
\code{\link[stats]{predict}} in base R
\code{\link{fitted}},
\code{\link{residuals}},
\code{\link{plot}},
\code{\link{garchFit}},
class \code{\linkS4class{fGARCH}},
}
\examples{
## Parameter Estimation of Default GARCH(1,1) Model
set.seed(123)
fit = garchFit(~ garch(1, 1), data = garchSim(), trace = FALSE)
fit
## predict
predict(fit, n.ahead = 10)
predict(fit, n.ahead = 10, mse="uncond")
## predict with plotting: critical values = +/- 2
predict(fit, n.ahead = 10, plot=TRUE, crit_val = 2)
## include also VaR and ES at 5\%
predict(fit, n.ahead = 10, plot=TRUE, crit_val = 2, p_loss = 0.05)
## predict with plotting: automatic critical values
## for different conditional distributions
set.seed(321)
fit2 = garchFit(~ garch(1, 1), data = garchSim(), trace=FALSE, cond.dist="sged")
## 95\% confidence level
predict(fit2, n.ahead=20, plot=TRUE)
set.seed(444)
fit3 = garchFit(~ garch(1, 1), data = garchSim(), trace=FALSE, cond.dist="QMLE")
## 90\% confidence level and nx=100
predict(fit3, n.ahead=20, plot=TRUE, conf=.9, nx=100)
}
\keyword{models}
\keyword{ts}
|
