Srho.test.AR: Entropy Tests For Nonlinearity In Time Series In tseriesEntropy: Entropy Based Analysis and Tests for Time Series

Description

Entropy test of nonlinearity for time series based on `Srho.ts` and surrogate data obtained through the sieve bootstrap.

Usage

 ```1 2 3 4``` ```Srho.test.AR(x, y, lag.max = 10, B = 100, plot = TRUE, quant = c(0.95, 0.99), bw = c("reference", "mlcv", "lscv", "scv", "pi"), 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 Srho; 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 Srho 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.max` `Srho.test.AR` computes a test for nonlinearity for time series based on `Srho.ts`. The distribution under the null hypothesis of linearity 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 Srho 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 Srho 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 Srho 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<[email protected]>

References

Giannerini S., Maasoumi E., Bee Dagum E., (2015), Entropy testing for nonlinear serial dependence in time series, Biometrika, 102(3), 661–675 http://doi.org/10.1093/biomet/asv007 .

See Also `Srho.ts`, `surrogate.ARs`, `surrogate.AR`. See `Srho.test.AR.p` for the parallel version.
 ```1 2 3 4 5 6 7 8 9``` ```## Not run: ## ************************************************************ ## WARNING: computationally intensive, increase B with caution ## ************************************************************ set.seed(13) x <- arima.sim(n=120, model = list(ar=0.8)); result <- Srho.test.AR(x, lag.max = 5, B = 10, bw='reference', method='integral') ## End(Not run) ```