# Space Time AutoRegressive Moving Average (STARMA) modelling for space-time series This package aims to provide all the tools needed to identify, estimate and diagnose STARMA models for space-time series. It follows the three-stage iterative model building procedure developed by (Box and Jenkins, 1970) and extended to space-time modelling by (Pfeifer and Deutsch, 1980). Designed with large datasets in mind, the package has been optimized by integrating C++ code via Rcpp and RcppArmadillo (Eddelbuettel and Sanderson, 2014). Furthermore, the parameter estimation, which is usually computationally very expensive when using common optimization routines, uses a Kalman filter (see Cipra and Motykova, 1987), making it extremely efficient when dealing with large datasets. package ## Details ||| |:--|:--| |Package:|starma| |Type:|Package| |Version:|1.2| |Date:|2015-11-12| |License:|GPL-2| The three stages of the iterative model building procedure are as follow, after centering the space-time series with `stcenter`: - Identification: Using `stacf` and `stpacf`, the user should try to identify which parameters should be estimated. - Estimation: Use `starma` to estimate the parameters. - Diagnostic: Use `stacf`, `stpacf` and `stcor.test` to check whether the residuals of the models are similar to white noise. Refer to (Box and Jenkins, 1970) for details over the three-stage iterative model building procedure. ## Author(s) Felix Cheysson Maintainer: Felix Cheysson ## References - Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden Day. - 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. - Cipra, T., & Motykova, I. (1987). Study on Kalman filter in time series analysis. Commentationes Mathematicae Universitatis Carolinae, 28(3). - Dirk Eddelbuettel, Conrad Sanderson (2014). RcppArmadillo: Accelerating R with high-performance C++ linear algebra. Computational Statistics and Data Analysis, Volume 71, March 2014, pages 1054-1063. URL http://dx.doi.org/10.1016/j.csda.2013.02.005 ## Examples ```r # Load spdep library to easily create weight matrices library(spdep) # Create a 5x5 regular grid which will be our lattice sites <- matrix(0, 25, 2) for (i in 1:5) { for (j in 1:5) sites[(i-1)*5 + j, ] <- c(i, j) - .5 } plot(sites) # Create a uniform first order neighbourhood knb <- dnearneigh(sites, 0, 1) plot(knb, sites) # Lag the neighbourhood to create other order matrices knb <- nblag(knb, 4) klist <- list(order0=diag(25), order1=nb2mat(knb[[1]]), order2=nb2mat(knb[[2]]), order3=nb2mat(knb[[3]]), order4=nb2mat(knb[[4]])) # Simulate a STARMA(2;1) process eps <- matrix(rnorm(200*25), 200, 25) star <- eps for (t in 3:200) { star[t,] <- (.4*klist[[1]] + .25*klist[[2]]) %*% star[t-1,] + (.25*klist[[1]] ) %*% star[t-2,] + ( - .3*klist[[2]]) %*% eps[t-1,] + eps[t, ] } star <- star[101:200,] # Remove first observations star <- stcenter(star) # Center and scale the dataset # Identify the process stacf(star, klist) stpacf(star, klist) # Estimate the process ar <- matrix(c(1, 1, 1, 0), 2, 2) ma <- matrix(c(0, 1), 1, 2) model <- starma(star, klist, ar, ma) model summary(model) # Diagnose the process stcor.test(model$residuals, klist, fitdf=4) stacf(model$residuals, klist) stpacf(model$residuals, klist) ```

starma-package