tseriesEntropy (version 0.5-12)

Trho.test.AR: Entropy Tests For Nonlinearity In Time Series

Description

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.

Usage

Trho.test.AR(x, y, lag.max = 10, B = 100, plot = TRUE, quant = c(0.95, 0.99), bw = c("reference", "mlcv", "lscv"), method = c("integral", "summation"), maxpts = 0, tol = 0.001, order.max = 10, fit.method=c("yule-walker", "burg", "ols", "mle", "yw"), smoothed = TRUE)

Arguments

x, y

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.

Value

.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.

Details

For each lag from 1 to lag.max Trho.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.

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)