starma (version 1.3)

stcor.test: Space-time series non correlation test

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)
"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

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

Details

Since (Pfeifer and Deutsch, 1981) gives: $$Var(\hat{\rho}_l(s)) \approx \frac{1}{N(T-s)}$$ We can extend Box-Pierce test statistic to space-time series: $$N \sum (T-s) \hat{\rho}_l(s)^2 \sim \chi^2(slag \times tlag)$$

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.

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)