stacf: Space-Time Autocorrelation Function (STACF) and Partial...

In alstat/stcor: Correlograms of Space-Time ARIMA

Description

The stacf and stpacf estimate the autocorrelation function and partial autocorrelation function of the space-time series, respectively.

Usage

stacf(data, max.timelag = 15, wmatrices = list(NULL, ...),
  conf.level = 0.95)

stpacf(data, max.timelag = 15, wmatrices = list(NULL, ...),
  conf.level = 0.95)

Arguments

data	space-time series data in data.frame or matrix object.
max.timelag	the maximum time lag at which to calculate the STACF, default is set to 15.
wmatrices	the weights matrices of the spatial order.
conf.level	the confidence level for significant lags.

Details

The data which is either in data.frame or matrix object should have at least 2 columns to meet the requirements of STARIMA model. The columns will be the spatial locations of the data, and the rows will be the series of observations from each location or space. Analogous to the univariate time series, the STACF determines the lag order of the space-time moving average (STMA) model both for time and space; and STPACF identifies the time and spatial lag order of the space-time autoregressive (STAR) model.

The STPACF is computed using the space-time analogue of the Yule-Walker equation for univariate time series (Pfeifer and Deutsch, 1980 pg. 39).

γ_{h0}(s)=∑_{j=1}^k∑_{l=0}^{λ}φ_{jl}γ_{hl}(s-j)

for s = 1, 2, ..., k and h = 0, 1, 2, ..., λ. The last coefficient \hat{φ}_{kl} obtained from solving the system of equations as l = 0, 1, 2, ..., λ for k = 1, 2, ... is called the space-time partial correlation function of spatial order λ.

References

Box, G. E.P. et al. (1994). Time Series Analysis: Forecasting and Control. New Jersey: Prentice-Hall.

Pfeifer, P. E. and Deutsch, S. J. (1980a). A three-stage iterative procedure for space-time modelling. Technometrics, volume 22, pg. 35-47.

Pfeifer, P. E. and Deutsch, S. J. (1980b). Identification and interpretation of first order space-time ARMA models. Technometrics, volume 22, pg. 397-408.

Pfeifer P. E. and Deutsch, S. J. (1981). Seasonal space-time ARMA modelling. Geographical Analysis, volume 13, pg. 117-133.

See Also

stcor website

Examples

## The package contains dataset named palay. Run ?palay
## to get help about the data. The data has 6 regions that
## can be assigned into the following weights matrices
## using the equal weighting of spatial order.

# First spatial order weights matrix
W1 <- rbind(c(0, 1/2, 1/2, 0, 0, 0),
            c(1/2, 0, 1/2, 0, 0, 0),
            c(1/3, 1/3, 0, 1/3, 0, 0),
            c(0, 0, 1/2, 0, 1/2, 0),
            c(0, 0, 0, 1/2, 0, 1/2),
            c(0, 0, 0, 1/2, 1/2, 0))

# Second spatial order weights matrix
W2 <- rbind(c(0, 0, 0, 1, 0, 0),
            c(0, 0, 0, 1, 0, 0),
            c(0, 0, 0, 0, 1, 0),
            c(0, 0, 0, 0, 0, 1),
            c(0, 0, 1, 0, 0, 0),
            c(0, 0, 1, 0, 0, 0))

# Third spatial order weights matrix
W3 <- rbind(c(0, 0, 0, 0, 1, 0),
            c(0, 0, 0, 0, 1/2, 1/2),
            c(0, 0, 0, 0, 0, 1),
            c(1, 0, 0, 0, 0, 0),
            c(1/2, 1/2, 0, 0, 0, 0),
            c(0, 1, 0, 0, 0, 0))

## It is required to centralize the data to its mean for
## STARIMA modeling, but before doing so, the Year column
## of the data must be removed since we do not have to
## centralize this,
palay1 <- subset(palay, select = -c(Year))

## Now, centralize the data
palay.cen <- stcenter(palay1)

## Finally, Compute the STACF and STPACF
stacf(data = palay.cen, wmatrices = list(NULL, W1, W2, W3))
stpacf(data = palay.cen, wmatrices = list(NULL, W1, W2, W3))

alstat/stcor documentation built on May 11, 2019, 11:29 p.m.