Entropy test of nonlinearity for time series based
on Srho.ts and surrogate data obtained through the sieve bootstrap (AR modeling).
The statistics Trho is based on the quadratic divergence between the nonparametric estimator of Srho
and the parametric estimator under the null hypothesis of a linear Gaussian process.
univariate numeric time series object or numeric vectors (y is missing in the univariate case).
lag.max
maximum lag at which to calculate Trho; default is trunc(N/4) where N is the number of observations.
B
number of surrogate time series.
plot
logical. If TRUE (the default) produces a plot of Trho together with confidence bands under the null hypothesis of linearity at 95% and 99%.
quant
quantiles to be specified for the computation of the significant lags and the plot of confidence bands. Up to 2 quantiles can be specified.
Defaults are 95% and 99%.
bw
see Srho.ts.
method
see Srho.ts.
maxpts
see Srho.ts.
tol
see Srho.ts.
order.max
see surrogate.ARs.
fit.method
see surrogate.ARs.
smoothed
logical. If TRUE (the default) uses the smoothed sieve bootstrap in surrogate.ARs to generate surrogates. Otherwise uses the classic sieve by calling surrogate.AR.
Details
For each lag from 1 to lag.maxTrho.test.SA computes a test for nonlinearity for time series based
on Srho.ts. The distribution under the null hypothesis of a linear Gaussian process is obtained through the sieve bootstrap.
Value
An object of class "Srho.test", which is a list with the following elements:
.Data
vector of lag.max elements containing Trho computed at each lag.
call:
Object of class "call": contains the call to the routine.
call.h:
Object of class "call": contains the call to the routine used for obtaining the surrogates or the bootstrap replicates under the null hypothesis
quantiles
Object of class "matrix": contains the quantiles of the surrogate distribution under the null hypothesis.
test.type
Object of class "character": contains a description of the type of test performed.
significant.lags
Object of class "list": contains the lags at which Trho exceeds the confidence bands at quant% under the null hypothesis.
p.value
Object of class "numeric": contains the bootstrap p-value for each lag.
lags
integer vector that contains the lags at which Trho is computed.
stationary
Object of class "logical": TRUE if the stationary version is computed. Set to FALSE by default as only the non-stationary version is implemented.
data.type
Object of class "character": contains the data type.
notes
Object of class "character": additional notes.
Author(s)
Simone Giannerini<simone.giannerini@unibo.it>
References
Giannerini S., Maasoumi E., Bee Dagum E., (2015), Entropy testing
for nonlinear serial dependence in time series, Biometrika, forthcoming
http://doi.org/10.1093/biomet/asv007.
See Also
See Also Srho.ts, surrogate.ARs, surrogate.AR, Trho.test.SA. See Trho.test.AR.p for the parallel version.
Examples
## Not run:
set.seed(1345)
x <- arima.sim(n=120, model = list(ar=0.8));
result <- Trho.test.AR(x, lag.max = 5, B = 10, bw='reference', method='integral')
## End(Not run)