stcor.test: Space-time series non correlation test

In starma: Modelling Space Time AutoRegressive Moving Average (STARMA) Processes

Description

stcor.test computes an extension of the Box-Pierce test statistic to accept or reject the non correlation of the distinct observations of a given space-time series. It is one of the main functions for the diagnostic part of the three-stage iterative model building procedure.

Usage

stcor.test(data, wlist, tlag=NULL, slag=NULL, fitdf=0)

## S3 method for class 'stcor.test'
print(x, ...)

Arguments

data	a matrix or data frame containing the space-time series: row-wise should be the temporal observations, with each column corresponding to a site.
wlist	a list of the weight matrices for each k-th order neighbours, first one being the identity.
tlag	the maximum time lag for the space-time autocorrelation functions. If tlag = NULL, it will use a large enough number of time lags.
slag	the maximum space lag for the space-time autocorrelation functions. If slag = NULL, it will use as many space lags as possible (as many as length(wlist)).
fitdf	number of degrees of freedom to be subtracted if data is a series of residuals.
x	a starma class object.
...	unused

Details

Since (Pfeifer and Deutsch, 1981) gives:

Var(rho[l](s)) ~ 1 / N(T-s)

We can extend Box-Pierce test statistic to space-time series:

N ∑[(T-s)*rho[l](s)^2] ~ chisq(slag*tlag)

stcor.test can be applied to a space-time series to test the null hypothesis of non correlation.

It is useful to check if the residuals of a STARMA models are multivariate white noise. In this case, fitdf should be set equal to the number of parameters in the model.

Please note that this is an empirical extension and it has not yet been the subject of a paper. The specifications of the weight matrices has not been studied either and could lead to inconsistencies.

Value

A data.frame containing the following elements:

X_squared	The value of the chi squared statistic
df	The degrees of freedom of the statistic (taking fitdf into account)
p.value	The p-value of the test

Author(s)

Felix Cheysson

References

- Pfeifer, P., & Deutsch, S. (1980). A Three-Stage Iterative Procedure for Space-Time Modeling. Technometrics, 22(1): 35-47. doi:10.1080/00401706.1980.10486099

- Pfeifer, P., & Deutsch, S. (1981). Variance of the Sample Space-Time Autocorrelation Function. Journal of the Royal Statistical Society. Series B (Methodological), 43(1): 28-33.

Examples

data(nb_mat)

eps <- matrix(rnorm(94*200), 200, 94)
sim <- eps
for (t in 3:200) {
	sim[t,] <- (.4*blist[[1]] + .25*blist[[2]]) %*% sim[t-1,] +
		(.25*blist[[1]]                ) %*% sim[t-2,] +
		(            - .3*blist[[2]]) %*% eps[t-1,] +
		eps[t, ]
}

sim <- sim[101:200,]
sim <- stcenter(sim)	# Center and scale the dataset

# Test for multivariate normality
stcor.test(sim, blist)	# Data is correlated
stcor.test(eps, blist)		# Data should not be correlated (unless you're 5% unlucky)

Example output

	Multivariate Box-Pierce Non Correlation Test
	--------------------------------------------

  X.squared  df p.value
1  10505.41 100       0

Decision: Non Correlation Hypothesis should be rejected.
	Multivariate Box-Pierce Non Correlation Test
	--------------------------------------------

  X.squared  df   p.value
1  132.8467 115 0.1221484

Decision: Can't reject Non Correlation Hypothesis.

starma documentation built on May 2, 2019, 1:26 p.m.