Adding exogeneous regressor to the forecast using fable

General
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1

Hi All,

Please see the below code where I have two variables- Net.Production.Qty which is my regressor variable and Shipment Qty is my dependent variable.

Below is the process steps I intend to follow

  1. Split the Train and test data
  2. Use the training data set of Net.Production.Qty variable and fit the model using ARIMA with Fourier terms(using fourier as regressor) and forecast the Net.Production.Qty for 30 steps and store into Final.Net.Prod variable
  3. Use the training data set of Shipment variable along with the training data set of Net.Production.Qty and fourier terms of Shipment as two regressor variables to the ARIMA and fit the model for predicting Shipment variable.
    4.Final step would be forecasting the Shipment variable for 30 steps using the fitted model from step 3 but in this case instead of using the training data set of Net.Production.Qty, I'm trying to use the forecasted Net.Production.Qty from step 2 along with the fourier terms of Shipment variable.

I'm not sure how to proceed(Step 4) using the Forecasted Net.Production.Qty and fourier terms as two regressors while forecasting the Shipment variable.

Could you please help me with this.
Thank you

library(dplyr)
library(tsibble)
library(fpp3)
library(forecast)
library(fable)
library(tidyverse)
library(ISOweek)

Original.df <- structure(list(YearWeek = c("201901", "201902", "201903", "201904", 
"201905", "201906", "201907", "201908", "201909", "201910", "201911", 
"201912", "201913", "201914", "201915", "201916", "201917", "201918", 
"201919", "201920", "201921", "201922", "201923", "201924", "201925", 
"201926", "201927", "201928", "201929", "201930", "201931", "201932", 
"201933", "201934", "201935", "201936", "201937", "201938", "201939", 
"201940", "201941", "201942", "201943", "201944", "201945", "201946", 
"201947", "201948", "201949", "201950", "201951", "201952", "202001", 
"202002", "202003", "202004", "202005", "202006", "202007", "202008", 
"202009", "202010", "202011", "202012", "202013", "202014", "202015", 
"202016", "202017", "202018", "202019", "202020", "202021", "202022", 
"202023", "202024", "202025", "202026", "202027", "202028", "202029", 
"202030", "202031", "202032", "202033", "202034", "202035", "202036", 
"202037", "202038", "202039", "202040", "202041", "202042", "202043", 
"202044", "202045", "202046", "202047", "202048", "202049", "202050", 
"202051", "202052", "202053", "202101", "202102", "202103", "202104", 
"202105", "202106", "202107", "202108", "202109", "202110", "202111", 
"202112", "202113", "202114", "202115", "202116", "202117", "202118", 
"202119", "202120", "202121", "202122", "202123", "202124", "202125", 
"202126", "202127", "202128", "202129", "202130", "202131", "202132", 
"202133", "202134", "202135", "202136", "202137", "202138", "202139", 
"202140", "202141", "202142", "202143"), Shipment = c(418, 1442, 
1115, 1203, 1192, 1353, 1191, 1411, 933, 1384, 1362, 1353, 1739, 
1751, 1595, 1380, 1711, 2058, 1843, 1602, 2195, 2159, 2009, 1812, 
2195, 1763, 821, 1892, 1781, 2071, 1789, 1789, 1732, 1384, 1435, 
1247, 1839, 2034, 1963, 1599, 1596, 1548, 1084, 1350, 1856, 1882, 
1979, 1021, 1311, 2031, 1547, 591, 724, 1535, 1268, 1021, 1269, 
1763, 1275, 1411, 1847, 1379, 1606, 1473, 1180, 926, 800, 840, 
1375, 1755, 1902, 1921, 1743, 1275, 1425, 1088, 1416, 1168, 842, 
1185, 1570, 1435, 1209, 1470, 1368, 1926, 1233, 1189, 1245, 1465, 
1226, 887, 1489, 1369, 1358, 1179, 1200, 1226, 1066, 823, 1913, 
2308, 1842, 910, 794, 1098, 1557, 1417, 1851, 1876, 1010, 160, 
1803, 1607, 1185, 1347, 1700, 981, 1191, 1058, 1464, 1513, 1333, 
1169, 1294, 978, 962, 1254, 987, 1290, 758, 436, 579, 636, 614, 
906, 982, 649, 564, 502, 274, 473, 506, 902, 639, 810, 398, 488
), Production = c(0, 198, 1436, 1055, 1396, 1330, 1460, 1628, 
1513, 1673, 1737, 1274, 1726, 1591, 2094, 1411, 2009, 1909, 1759, 
1693, 1748, 1455, 2078, 1717, 1737, 1886, 862, 1382, 1779, 1423, 
1460, 1454, 1347, 1409, 1203, 1235, 1397, 1563, 1411, 1455, 1706, 
688, 1446, 1336, 1618, 1404, 1759, 746, 1560, 1665, 1317, 0, 
441, 1390, 1392, 1180, 1477, 1265, 1485, 1495, 1543, 1584, 1575, 
1609, 1233, 1420, 908, 1008, 1586, 1392, 1385, 1259, 1010, 973, 
1053, 905, 1101, 1196, 891, 1033, 925, 889, 1136, 1058, 1179, 
1047, 967, 900, 904, 986, 1014, 945, 1030, 1066, 1191, 1143, 
1292, 574, 1174, 515, 1296, 1315, 1241, 0, 0, 1182, 1052, 1107, 
1207, 1254, 1055, 258, 1471, 1344, 1353, 1265, 1444, 791, 1397, 
1186, 1264, 1032, 949, 1059, 954, 798, 956, 1074, 1136, 1209, 
975, 833, 994, 1127, 1153, 1202, 1234, 1336, 1484, 1515, 1151, 
1175, 976, 1135, 1272, 869, 1900, 1173), Net.Production.Qty = c(22, 
188, 1428, 1031, 1382, 1368, 1456, 1578, 1463, 1583, 1699, 1318, 
1582, 1537, 2118, 1567, 1961, 1897, 1767, 1603, 1666, 1419, 2186, 
1621, 1677, 1840, 698, 1290, 1411, 927, 1754, 1222, 1411, 1549, 
1491, 1359, 1179, 1945, 1463, 1465, 1764, 764, 810, 1308, 1830, 
1542, 1695, 544, 1482, 1673, 1659, 0, 445, 1358, 1364, 1224, 
1417, 1239, 1387, 1595, 1469, 1624, 1643, 1763, 1217, 1456, 568, 
1290, 1666, 1428, 1327, 773, 1118, 1231, 1143, 921, 1083, 1124, 
935, 903, 937, 849, 1132, 1032, 1143, 1081, 891, 886, 880, 1002, 
1072, 969, 1000, 996, 1243, 1183, 1306, 650, 1226, 553, 1306, 
1379, 1359, 0, 0, 1182, 988, 1099, 1173, 1244, 1039, 254, 1425, 
1318, 1385, 1221, 1364, 739, 1397, 1112, 1160, 924, 971, 1015, 
978, 828, 868, 994, 1090, 1165, 783, 887, 934, 1023, 1045, 1114, 
1052, 1186, 1456, 1401, 1249, 779, 430, 1625, 1498, 883, 1860, 
1101)), row.names = c(NA, 148L), class = "data.frame")

# Converting the df to accomodate leap year for weekly observations
Original.df <- Original.df %>%
  mutate(
    isoweek =stringr::str_replace(YearWeek, "^(\\d{4})(\\d{2})$", "\\1-W\\2-1"),
    date = ISOweek::ISOweek2date(isoweek)
  )

View(Original.df)

# creating test and train data
Original.train.df <- Original.df %>%
  filter(date >= "2018-12-31", date <= "2021-03-29")
Original.test.df <- Original.df %>%
  filter(date >= "2021-04-05", date <= "2021-10-25")

# splitting the original train data with multiple variables to have only one variable(univariate time series)

Total.train.df<-Original.train.df %>%
  mutate(Week.1 = yearweek(ISOweek::ISOweek(date))) %>%
  select(-YearWeek, -Production, -date,-isoweek) %>%
  as_tsibble(index = Week.1)

Total.train.df

#Fitting forecast model(Arima errors) to Net.Production.qty 

fit_all_models <- list()

for(K in seq(25)){
  fit <- Total.train.df %>% 
    model(ARIMA(Net.Production.Qty ~ fourier(K = K), approximation = FALSE))
  names(fit) <- paste0("arima_", K)
  
  fit_all_models <- bind_cols(fit_all_models, fit)
}


glance(fit_all_models) %>% arrange(AICc) %>% select(.model:BIC)

best_model <- glance(fit_all_models) %>% 
  filter(AICc == min(AICc)) %>% 
  select(.model) %>% 
  as.character

#Forecasting Net.Production.Qty for 30 steps using ARIMA with fourier terms
Forecast.Net.Prod<-fit_all_models %>% 
  select(best_model) %>% 
  forecast(h = 30)

Final.Net.Prod<-Forecast.Net.Prod$.mean

#Fitting forecast model(Arima errors) to Shipment Qty

fit_all_models <- list()

for(K in seq(25)){
  fit <- Total.train.df %>% 
    model(ARIMA(Shipment ~ Net.Production.Qty + fourier(K = K), approximation = FALSE))
  names(fit) <- paste0("arima_", K)
  
  fit_all_models <- bind_cols(fit_all_models, fit)
}

glance(fit_all_models) %>% arrange(AICc) %>% select(.model:BIC)

best_model <- glance(fit_all_models) %>% 
  filter(AICc == min(AICc)) %>% 
  select(.model) %>% 
  as.character

#Forecasting Shipment Qty using Forecasted Net.Production.Qty and Fourier terms of
#Shipment variable as regressors

Forecast.Shipment<-fit_all_models %>% 
  select(best_model) %>% 
  forecast(Total.train.df$Shipment ~ Final.Net.Prod + fourier(K=K),approximation = FALSE,h=30)
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