\r\n\r\ny <- cbind(c(1030.829,893.551,1084.09,1278.436,936.708,915.322,885.713,2364.399,774.88,977.506,831.616,813.656,1569.956,967.925,806.146,1063.117,1123.787,906.686,996.498,1088.464,977.414,1128.328,896.594,1007.172,1046.379,1514.648,1626.115,2959.558,838.506,949.377,1433.307,805.048,1218.907,872.43,1730.103,865.734,1845.713,919.291,1003.363,1102.969,847.38,1965.26,809.673,953.193,1066.089,991.352,1115.694,1003.333,1090.48,930.749,1006.184,1239.068,873.707,728.583,881.316,1302.468,997.442,3481.118,841.042,997.601,1830.194,909.693,2358.406,2573.673,777.08,773.781,945.424,968.646,1074.589,1046.22,1155.559,990.627,931.943,786.285,2297.025,628.166,889.238,937.631,1113.925,870.384,1018.375,799.458,1542.328,1879.587,750.307,1087.948,1247.803,1052.352,883.899,793.126,913.736,1082.142,968.823,2099.176,841.224,964.227,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA))\r\nx <- cbind(c(0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0),\r\n c(0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0),\r\n c(0,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,1,1,0,0))\r\ny <- y[!is.na(y)]\r\ny <- ts(y,frequency=12)\r\n\r\n<\/pre>\n

This toy set includes sales of a heavily promoted item, with three different promotion. Let’s visualise what we have:<\/p>\n

\r\n\r\nplot(y)\r\ncmp <- brewer.pal(3,"Set1")\r\nfor (i in 1:3){\r\n  points(time(y)[which(x[,i]==1)],y[which(x[,i]==1)],col=cmp[i],pch=i,cex=1.5)\r\n}\r\nlegend("topright",c("Promo1","Promo2","Promo3"),col=cmp,pch=1:3)\r\n\r\n<\/pre>\n<\/a><\/p>\n
Now let’s fit a MAPA and MAPAx and produce forecasts. I am modelling the sales in logs to capture the multiplicative promotional effects. For other types of applications this is not needed.<\/p>\n
\r\nlibrary(MAPA)\r\nmapafit.x <- mapaest(log(y),type="es",display=1,outplot=1,xreg=x)\r\nmapafit <- mapaest(log(y),type="es",outplot=1)\r\n\r\nfrc.x <- mapafor(log(y),mapafit.x,ifh=13,fh=13,xreg=x,conf.lvl=c(0.8,0.9,0.95),comb="w.mean")\r\nfrc <- mapafor(log(y),mapafit,ifh=13,fh=13,conf.lvl=c(0.8,0.9,0.95),comb="w.mean")\r\n\r\n<\/pre>\nLet’s plot the results<\/p>\n\r\n\r\npar(mfrow=c(1,2))\r\nplot(1:96, y, type="l",xlim=c(1,109),xaxs="i",main="MAPA",xlab="Period",ylab="Sales")\r\nfor (i in 1:96){\r\n  lines(i:(12+i),exp(frc$infor[,i]),col="red")\r\n}\r\ncmp <- brewer.pal(9,"Reds")[4:2]\r\nfor (i in 1:3){\r\n  polygon(c(97:109,109:97),exp(c(frc$PI[i,],rev(frc$PI[7-i,]))),col=cmp[i],border=NA)\r\n}\r\nlines(97:109,exp(frc$outfor),col="red")\r\n\r\nplot(1:96, y, type="l",xlim=c(1,109),xaxs="i",main="MAPAx",xlab="Period",ylab="Sales")\r\nfor (i in 1:96){\r\n  lines(i:(12+i),exp(frc.x$infor[,i]),col="red")\r\n}\r\ncmp <- brewer.pal(9,"Reds")[4:2]\r\nfor (i in 1:3){\r\n  polygon(c(97:109,109:97),exp(c(frc.x$PI[i,],rev(frc.x$PI[7-i,]))),col=cmp[i],border=NA)\r\n}\r\nlines(97:109,exp(frc.x$outfor),col="red")\r\n\r\n<\/pre>\n<\/a><\/p>\n
As you can see, MAPA provides a flat forecast. This is “correct” in the sense that apart from promotions this time series contains like information that could be captured by exponential smoothing. On the other hand, MAPAx is provided with the promotional information and makes use of it.<\/p>\n
Related Posts<\/H3>Special issue on innovations in hierarchical forecasting<\/a><\/li>\n
Elucidate structure in intermittent demand time series<\/a><\/li>\n
Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption<\/a><\/li>\n<\/ul><\/div>","protected":false},"excerpt":{"rendered":"I have been asked a few time to provide an example how to use MAPAx, from the MAPA package for R, so I prepared this blog post. I admit the documentation could be better, so I put together this example from a retailing case – the original setting MAPAx was developed for (see paper here).\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[41],"tags":[45,38,33,39,36],"_links":{"self":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts\/1449"}],"collection":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/comments?post=1449"}],"version-history":[{"count":5,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts\/1449\/revisions"}],"predecessor-version":[{"id":1460,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/posts\/1449\/revisions\/1460"}],"wp:attachment":[{"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/media?parent=1449"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/categories?post=1449"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kourentzes.com\/forecasting\/wp-json\/wp\/v2\/tags?post=1449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}