stcor: Correlograms of Space-Time ARIMA

r, arima, space-time, time series, package

Description

The stcor package provides functions for correlograms of the advanced time series model, the Space-Time Autoregressive Integrated Moving Average (STARIMA). These functions are the Space-Time Autocorrelation Function (stacf) and Space-Time Partial Autocorrelation Function (stpacf). Including function for centralizing (stcenter) the data to its mean.

Installation

This package is not yet on CRAN, and still under development on github. Run the following to install the latest development:

if (!require("devtools"))
  install.packages("devtools")
devtools::install_github("stcor", "alstat")

Functions

  1. stacf - estimates the autocorrelation function of the space-time series.

    stacf(data, max.timelag = 15, wmatrices = list(NULL, ...), conf.level = 0.95)
    • data - the space-time data;
    • max.timelag - the maximum timelag of the STACF (default is set to 15);
    • wmatrices - weights matrices of the space-time series for the spatial orders. The entries is enumerated in a list function, where the first entry NULL designates the spatial lag 0, and (. . .) for higher order weights matrices. Note that, NULL should not be omitted, otherwise, the function will treat the first weights matrix as entries for spatial lag 0; and
    • conf.level - is the confidence level for significant spikes of the correlogram (default is set to 95%).

  2. stpacf - estimates the partial autocorrelation function of the space-time series.

    stpacf(data, max.timelag = 15, wmatrices = list(NULL, ...), conf.level = 0.95)
    • The same descriptions of parameters as the stacf function.

  3. stcenter - centralizes the space-time data to its mean.

    stcenter(data)
    • data - the space-time data.

Dataset

  1. palay - A dataset containing the volume of palay production in Cordillera Administrative Region (CAR) of the Philippines, from 1994 - 2013 quarterly.
    • Format - a data frame with 79 rows and 7 columns
    • Details
      • Year - the time variable in quarterly;
      • Apayao - spatial location 1;
      • Abra - spatial location 2;
      • Kalinga - spatial location 3;
      • Mt.Province - spatial location 4;
      • Ifugao - spatial location 5;
      • Benguet - spatial location 6.

Quick Reference

The package contains dataset named palay which is the volume of the rice production from the Cordillera Administrative Region (CAR) of the Philippines. Run ?palay to get more details about the data. There are 6 regions in the dataset that can be assigned into the following weights matrices using the equal weighting of spatial order.

It is required to centralize the data to its mean for STARIMA modeling, but before doing so, the Year column 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))

      Spatial Lag 0 Spatial Lag 1 Spatial Lag 2 Spatial Lag 3
 [1,]    -0.4992931    -0.3768003   0.103059733    0.07686560
 [2,]     0.6379861     0.6286114   0.013944315   -0.02638101
 [3,]    -0.4907843    -0.3636884   0.046419684    0.07925981
 [4,]     0.9050261     0.5807629   0.019897096    0.09256568
 [5,]    -0.4804457    -0.3743855   0.094946729    0.06465131
 [6,]     0.5895664     0.5862548   0.007210034   -0.02778151
 [7,]    -0.4769501    -0.3559720   0.041717828    0.06999287
 [8,]     0.8321032     0.5432305   0.015287949    0.08079311
 [9,]    -0.4626080    -0.3692359   0.089099718    0.05182974
[10,]     0.5400462     0.5396841  -0.001916337   -0.03069186
[11,]    -0.4607559    -0.3461168   0.041789698    0.06116461
[12,]     0.7589304     0.5078718   0.008028795    0.07026631
[13,]    -0.4446532    -0.3634106   0.081175576    0.03902433
[14,]     0.5030049     0.5120928  -0.003504128   -0.02963862
[15,]    -0.4451392    -0.3396895   0.037675321    0.05017871

Space-Time ACF Plot

stpacf(data = palay.cen, wmatrices = list(NULL, W1, W2, W3))

      Spatial Lag 0 Spatial Lag 1 Spatial Lag 2 Spatial Lag 3
 [1,]   -0.14304647   0.511218868    0.55682738    0.19981610
 [2,]   -0.25539678   0.473270591    0.14747855    0.10362970
 [3,]   -0.10146576   0.359960022   -0.37010962    0.17611802
 [4,]    0.38601724   0.035951653    0.06345174    0.11231104
 [5,]   -0.07615717  -0.209693181   -0.09118031   -0.01877791
 [6,]    0.25073879  -0.166778338   -0.03325437   -0.07793400
 [7,]    0.08483755  -0.096729707   -0.05191220   -0.10225812
 [8,]    0.20206063   0.005777546   -0.01424020   -0.03562691
 [9,]    0.14492995  -0.285797604   -0.09654800   -0.09723394
[10,]    0.18184525  -0.576182623   -0.13934442   -0.16191452
[11,]    0.15801674  -0.074907370    0.09285817   -0.01390365
[12,]    0.22796914  -0.048807113   -0.09257688   -0.04854238
[13,]    0.12255899  -0.130296912   -0.17546381   -0.10870668
[14,]   -0.05799165   0.313754236    0.06080497    0.07436464
[15,]   -0.09576009  -0.238561758    0.13853781   -0.06222810

Space-Time PACF Plot

The findings suggest that the STACF is decaying spatially but not temporally, and as observed, the spikes with high magnitude repeats every four lags, which is the seasonal lag since the data is quarterly. Hence, first order seasonal differencing is needed for transformation,

palay.dif <- diff(as.ts(palay.cen), lag = 4)

lag=4 since the data is quarterly; then we compute again the STACF and STPACF for the differenced series,

stacf(palay.dif, wmatrices = list(NULL, W1, W2, W3))

      Spatial Lag 0 Spatial Lag 1 Spatial Lag 2 Spatial Lag 3
 [1,]  -0.102909427   0.025653689   0.082953522  0.0539520289
 [2,]   0.176881582   0.117139152   0.013167676  0.0115715456
 [3,]   0.042544299   0.039321092   0.007792355  0.0554658845
 [4,]  -0.175689995   0.033860939   0.007619782  0.0068130653
 [5,]   0.002817186  -0.028309614  -0.036774801  0.0259092901
 [6,]   0.075060958   0.088457609   0.034410303  0.0135122268
 [7,]   0.044036252   0.023091860  -0.024324734  0.0232175233
 [8,]   0.015816331   0.004172408   0.043260335 -0.0127784432
 [9,]   0.030520792   0.013617616   0.028537045  0.0190366262
[10,]  -0.038435104  -0.120098561  -0.044183399 -0.0241420075
[11,]  -0.008104361   0.061734994   0.053531660  0.0148140566
[12,]   0.002133791   0.013137359  -0.054519301 -0.0190006145
[13,]   0.082231615   0.033276088  -0.005586549 -0.0004980636
[14,]  -0.015698510   0.161005222   0.004396902  0.0289685701
[15,]   0.125114476   0.024381011  -0.010967296  0.0043345931

Space-Time ACF Plot of the Differenced Series

stpacf(palay.dif, wmatrices = list(NULL, W1, W2, W3))

      Spatial Lag 0 Spatial Lag 1 Spatial Lag 2 Spatial Lag 3
 [1,]  -0.146421601   0.032487793  0.0853739625   0.088825947
 [2,]   0.227574617   0.265251476  0.0086875911   0.022379860
 [3,]   0.013884996   0.234501046  0.0017332333   0.087121251
 [4,]  -0.374341579  -0.007449137  0.0367435307   0.055216997
 [5,]  -0.148779101  -0.137998111  0.0327572108   0.064802169
 [6,]   0.144623030   0.218952875 -0.0008164024   0.030398092
 [7,]   0.093971255   0.287856390 -0.0136972967   0.045549415
 [8,]  -0.148459047   0.003528043  0.0666503281  -0.009344122
 [9,]  -0.110767128  -0.218838986  0.0363238989   0.029674330
[10,]  -0.027504504  -0.071234693 -0.0560620268  -0.020184495
[11,]   0.041945574   0.265583483  0.0341692277   0.027824812
[12,]  -0.006097138   0.095614525  0.0095997826  -0.039610927
[13,]   0.022523005  -0.100266088 -0.0116048518  -0.008237559
[14,]  -0.094342410   0.199611218 -0.0280317015   0.050161727
[15,]   0.066798455   0.139086023  0.0203601170   0.003121897

Space-Time PACF Plot of the Differenced Series

The space-time ACF decays both in time and space; and the space-time PACF is significant in time lag 2 and cuts off at spatial lag 1. This is characterized by the space-time AR factor. Hence, we can consider our tentative model to be Seasonal STARIMA$(2_1,0,0)(0,1,0)_4$.