In christophsax/x13story: Interactive Stories on Seasonal Adjustment with X-13ARIMA-SEATS

Introduction: the data

Let us first investigate the series we will be dealing with. The hobby, toy and game store retail sales are collected during the Census Bureau's economic census. This perticular series features large spikes in the month of December.

library(x13story)  # this will also load seasonal

x <- structure(c(620L, 585L, 643L, 706L, 660L, 721L, 678L, 653L, 638L, 
                 789L, 1332L, 3226L, 598L, 576L, 683L, 735L, 685L, 722L, 745L, 
                 682L, 671L, 799L, 1480L, 3275L, 618L, 637L, 819L, 782L, 742L, 
                 758L, 778L, 801L, 806L, 987L, 1677L, 3445L, 683L, 665L, 823L, 
                 867L, 821L, 873L, 851L, 846L, 846L, 993L, 1830L, 3616L, 705L, 
                 737L, 890L, 862L, 669L, 849L, 877L, 874L, 870L, 1094L, 2002L, 
                 4073L, 730L, 791L, 1032L, 896L, 947L, 940L, 963L, 958L, 971L, 
                 1141L, 2009L, 3643L, 858L, 883L, 987L, 1022L, 986L, 1016L, 1042L, 
                 1025L, 1005L, 1197L, 2011L, 3801L, 933L, 966L, 1135L, 1076L, 
                 1061L, 1101L, 1083L, 1101L, 1111L, 1277L, 2096L, 3711L, 893L, 
                 1002L, 1106L, 1136L, 1072L, 1098L, 1124L, 1132L, 1175L, 1285L, 
                 2161L, 3763L, 880L, 971L, 1176L, 1063L, 1038L, 1107L, 1094L, 
                 1065L, 1050L, 1303L, 2445L, 3628L, 896L, 966L, 1186L, 1014L, 
                 1078L, 1065L, 1103L, 1087L, 1048L, 1347L, 2468L, 3651L, 910L, 
                 940L, 1111L, 1139L, 1088L, 1064L, 1094L, 1087L, 1095L, 1286L, 
                 2223L, 3545L, 962L, 1045L, 1125L, 1082L, 974L, 1024L, 1086L, 
                 1016L, 1051L, 1311L, 2187L, 3451L, 950L, 980L, 1173L, 1098L, 
                 1061L, 1049L, 1077L, 1028L, 1019L, 1229L, 2120L, 3471L, 1063L, 
                 1022L, 1117L, 1094L, 1040L, 1048L, 1070L, 1043L, 1086L, 1205L, 
                 1933L, 3299L, 948L, 974L, 1188L, 1064L, 1050L, 1096L, 1102L, 
                 1084L, 1102L, 1275L, 2208L, 3253L, 1043L, 1077L, 1183L, 1080L, 
                 1131L, 1044L, 1097L, 1065L, 1061L, 1218L, 1959L, 3117L, 1031L, 
                 1009L, 1095L, 1086L, 1064L, 1020L, 1058L, 1007L, 1063L, 1194L, 
                 1842L, 2999L, 953L, 1000L, 1155L, 1059L, 1030L, 1024L, 1070L, 
                 1039L, 1074L, 1254L, 1990L, 3064L, 967L, 1023L, 1193L, 1184L, 
                 1065L, 1061L, 1082L, 1067L, 1143L, 1243L, 1951L, 3033L, 1063L, 
                 1182L, 1259L, 1146L, 1175L, 1120L, 1113L, 1117L, 1148L, 1263L, 
                 1929L, 2963L, 1019L, 1068L, 1239L, 1107L, 1116L, 1057L, 1106L, 
                 1145L, 1161L, 1338L, 2134L, 3263L, 1012L, 1084L, 1213L, 1195L, 
                 1170L, 1084L, 1183L, 1185L, 1253L, 1360L, 2140L, 3511L, 1157L, 
                 1190L, 1360L, 1260L, 1274L, 1196L), 
                 .Tsp = c(1992, 2015.4166666666, 12), class = "ts")

prettify(plot(x, ylab = "retail sales"))

A first attemp at prior adjustment and model fitting

We investigate if we should be taking a log transform (and performing multiplicative seasonal adjustment) or possibly using no transform (and performing additive seasonal adjustment). If a log transform is used then two additive outliers (AOs) are detected in May 1996 and December 1996. However, when no transform is performed 5 additional AO's are identified. All AO's are shown in Figure 2 with vertical dashed lines.

mA <- seas(x, transform.function="log", 
             x11.seasonalma = "s3x5",
             forecast.maxlead = "12",
             outlier.types = "AO",
             regression.aictest = "td")

summary(mA)

mB <- seas(x, transform.function="none", 
             x11.seasonalma = "s3x5",
             forecast.maxlead = "12",
             outlier.types = "AO",
             regression.aictest = "td")

summary(mB)

plot(x)
abline(v = c(1996 + 4/12,
             1996 + 11/12), col="red", lty="dotted")
abline(v = c(1996 + 4/12 + .01,
             1996 + 11/12 + .01,
             2001 + 10/12, 
             2002 + 10/12,
             2007 + 10/12, 
             2013 + 11/12,
             2014 + 11/12), col = "blue", lty = "dotted")
legend("topleft", 
       legend = c("log and no transform","no transform"), 
       lty="dotted", 
       col=c("red", "blue"))

Easter Regressors

An obvious question to be answered for a toy and game store series is does Easter have a significant effect? i.e. should we include a regressor for the date of easter.

mAE <- seas(x, transform.function="log", 
               x11.seasonalma = "s3x5",
               forecast.maxlead = "12",
               outlier.types = "AO",
               regression.aictest = "td, easter")
mBE <- seas(x, transform.function="none", 
               x11.seasonalma = "s3x5",
               forecast.maxlead = "12",
               outlier.types = "AO",
               regression.aictest = "td, easter")

The location March 1997 is the largest change in final SA value when including the easter regressor; a difference of 67.94.

prettify(plot(window(x, start=c(1995, 1), end=c(1999, 12)), ylab="value"))
lines(window(final(mAE), start=c(1995, 1), end=c(1999, 12)), col="red")
lines(window(final(mA), start=c(1995, 1), end=c(1999, 12)), col="blue")
legend("topleft", 
       legend = c("without Easter reg", "with Easter reg"), 
       lty = c(1, 1), 
       col = c("blue", "red"))

christophsax/x13story documentation built on May 13, 2019, 7:06 p.m.