Description Usage Arguments Value Examples
The function MSPE
computes the empirical mean squared prediction
errors for a collection of h-step ahead, linear predictors
(h=1,…,H) of observations X_{t+h}, where
m_1 ≤q t+h ≤q m_2, for two indices m_1 and m_2.
The resulting array provides
\frac{1}{m_{\rm lo} - m_{\rm up} + 1} ∑_{t=m_{\rm lo}}^{m_{\rm up}} R_{(t)}^2,
with R_{(t)} being the prediction errors
R_t := | X_{t+h} - (X_t, …, X_{t-p+1}) \hat v_{N,T}^{(p,h)}(t) |,
ordered by magnitude; i.e., they are such that R_{(t)} ≤q R_{(t+1)}.
The lower and upper limits of the indices are
m_{\rm lo} := m_1-h + \lfloor (m_2-m_1+1) α_1 \rfloor and
m_{\rm up} := m_2-h - \lfloor (m_2-m_1+1) α_2 \rfloor.
The function MAPE
computes the empirical mean absolute prediction
errors
\frac{1}{m_{\rm lo} - m_{\rm up} + 1} ∑_{t=m_{\rm lo}}^{m_{\rm up}} R_{(t)},
with m_{\rm lo}, m_{\rm up} and R_{(t)} defined as before.
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X |
the data X_1, …, X_T |
predcoef |
the prediction coefficients in form of a list of an array
|
m1 |
first index from the set in which the indices t+h shall lie |
m2 |
last index from the set in which the indices t+h shall lie |
P |
maximum order of prediction coefficients to be used;
must not be larger than |
H |
maximum lead time to be used;
must not be larger than |
N |
vector with the segment sizes to be used, 0 corresponds to using 1, ..., t; has to be a subset of predcoef$N. |
trimLo |
percentage α_1 of lower observations to be trimmed away |
trimUp |
percentage α_2 of upper observations to be trimmed away |
MSPE
returns an object of type MSPE
that has mspe
,
an array of size H
\timesP
\timeslength(N)
,
as an attribute, as well as the parameters N
, m1
,
m2
, P
, and H
.
MAPE
analogously returns an object of type MAPE
that
has mape
and the same parameters as attributes.
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