ADF(x, dtype = c("ADF", "CADF", "RPADF", "DeltaADF", "ACF"), lag.max = floor(10 * log10(length(x))), alpha = 0.05, num.clas, B = 99, bandwidth, delta = "Delta_1", fres = ".Perm", fdenest = ".denest", fdiv, argacf, R = 1:lag.max, p.adjust.method = p.adjust.methods, plot = TRUE, ...)
"print"(x, digits=3, ...)"ADF" object or a univariate numeric time series object or a numeric vector.
"ADF" (default; see Bagnato, Punzo, Nicolis, 2012)
"CADF" (see Bagnato, Punzo, Nicolis, 2012)
"RPADF" (see Bagnato, De Capitani, Punzo, 2014)
"DeltaADF" (see Bagnato, De Capitani, Punzo, 2013)
"ACF"
10*log10(n) where n is the length of the series .
dtype="ADF" or "CADF" or "RPADF", it sets the number of equifrequency classes for each of the two marginal distributions of the contingency table. If not specified, it is determined internally
using a rule of thumb described in Bagnato, Punzo, Nicolis (2012).
dtype="DeltaADF", it sets the number of permutations used. Default value is 99 (see Bagnato, De Capitani, Punzo, 2013a,b).
dtype="DeltaADF", it sets the bandwidth used for the Gaussian kernel density estimator. Default value is computed with likelihood cross-validation (see Bagnato, De Capitani, Punzo, 2013a,b).
dtype="DeltaADF", it specifies the type of divergence measure used (see Bagnato, De Capitani, Punzo, 2013b);
for each element in delta a different plot is produced. Possible values are:
"Delta_1" (default)
"Delta_0.5"
"Delta_2"
"Delta_3"
"Delta_4"
"Delta_SD"
"Delta_L1"
"Delta_ST"
"Delta_fdiv"; in this case, the external function named fdiv is used to compute divergence.
dtype="DeltaADF", the name of the external function(x,B) specifying the resampling method from the raw series, where x is a time series and B the number of resamples; the function should return a matrix with B rows and length(x) columns. If not specified, permutations are randomly generated.
dtype="DeltaADF", the name of the external function(x,m,ngrid,bandwidth) to use for univariate and bivariate density estimation, where x is the time series, m is the lag considered, ngrid is the number of
points in the grid, and bandwidth is the bandwidth; the function should return:
fi, a matrix of dimension ngrid x ngrid containing conjoint density estimates for lag m
gi, a matrix of dimension ngrid x ngrid containing conjoint density estimates in case of independence, for lag m
ngi, is equal to ngrid.
fdenest is not specified, the Gaussian kernel density estimation is used (see Bagnato, De Capitani, Punzo, 2013a,b).
dtype="DeltaADF" and delta="Delta_fdiv" , the name of the external function(fi,gi,ngi) to use to compute divergence; its arguments are defined as in fdenest; the function should return a scalar.
TRUE (default), the specified ADF is displayed.
dtype="ACF", it is a list with optional arguments for function acf().
1:lag.max
p.adjust.methods.
plot.SDD method, such as graphical parameters.
SDD object which is a list with the following components:
dtype, it may contain:
lag, a numeric vector containing the lags at which the bars of the diagrams are computed
vbar, height of the bars of the diagram
pvalue, p-values associated to the bars of the diagram
pstar, transformed p-values associated to the bars of the diagram. If dtype="DeltaADF" transformed p-values are vbar
n, vector of length lag.max, containing the effective number of pairs considered for each lag
crit.val, vector, of length lag.max, with the critical values
xmin vector of length lag.max, containing the non-centrality parameters for each bar of the RP-ADF
type="DeltaADF", the type divergence measure used.dtype is one of: "ADF", "RPADF", or "CADF".x.
p.adjust.methods.
Bagnato L, De Capitani L, Punzo A (2013a). Improving the autodependogram using the Kulback-Leibler divergence. arXiv:1306.5006 [stat.ME], URL: http://arxiv.org/pdf/1306.5006v1.pdf
Bagnato L, De Capitani L, Punzo A (2013b). Testing Serial Independence via Density-Based Measures of Divergence. Methodology and Computing in Applied Probability, 16(3), 627-641.
Bagnato L, De Capitani L, Punzo A (2014). Detecting Serial Dependencies with the Reproducibility Probability Autodependogram. Advances in Statistical Analysis, 98(1), 35-61.
Bagnato L, Punzo A (2010). On the Use of $\chi^2$ Test to Check Serial Independence. Statistica & Applicazioni, VIII(1), 57-74.
Bagnato L, Punzo A (2012). Checking Serial Independence of Residuals from a Nonlinear Model. In W Gaul, A Geyer-Shulz, L Schmidt-Thieme, J Kunze (eds.), Challenges at the Interface of Data Analysis, Computer Science, and Optimization, volume XIV of Studies in Classification, Data Analysis and Knowledge Organization, pp. 203-211. Springer-Verlag, Berlin Heidelberg.
Bagnato L, Punzo A, Nicolis O (2012). The autodependogram: a graphical device to investigate serial dependencies. Journal of Time Series Analysis, 33(2), 233-254.
Bagnato L, Punzo A (2013). Using the Autodependogram in Model Diagnostic Checking. In N Torelli, F Pesarin, A Bar-Hen (eds.), Advances in Theoretical and Applied Statistics, volume XIX of Studies in Theoretical and Applied Statistics, pp. 129-139. Springer-Verlag, Berlin Heidelberg.
SDD-package, plot.SDD, SMI, acf
# Dependence Diagrams on raw data
data("SMI")
ADF(SMI^2, dtype="ACF", main="")
ADF(SMI, main="")
ADF(SMI, dtype="RPADF", main="")
# Dependence Diagrams on residuals from a fitted model
library("tseries")
residuals <- garch(SMI, order=c(1,1))$residuals[-1]
ADF(residuals^2, dtype="ACF", main="")
ADF(residuals, dtype="RPADF", main="")
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