Forecasting Product Demand in R
Manuela da Cruz Chadreque
17 de Abril de 2019
Forecasting demand with time series
Importing data
ransform the data into an xts object to help with analysis
bev<-read.csv("C:/Users/maiam/Dropbox/PROFESSIONAL DEVELOPMENT/DATA SCIENCE/01_R/Forecasting Product Demand in R/Bev.csv")
head(bev)## M.hi.p M.lo.p MET.hi.p MET.lo.p MET.sp.p SEC.hi.p SEC.lo.p M.hi M.lo
## 1 59.25 29.19 63.67 26.03 50.09 58.56 29.19 458 1455
## 2 56.26 26.31 60.34 25.54 48.82 54.64 26.31 477 1756
## 3 56.26 26.25 60.79 25.69 48.56 57.90 26.25 539 2296
## 4 49.33 26.15 55.09 26.46 47.74 49.70 26.15 687 3240
## 5 61.34 25.88 65.09 25.72 50.75 63.72 25.88 389 2252
## 6 61.40 27.35 67.91 26.17 52.63 68.38 27.35 399 1901
## MET.hi MET.lo MET.sp SEC.hi SEC.lo
## 1 2037 3437 468 156 544
## 2 1700 3436 464 151 624
## 3 1747 3304 490 178 611
## 4 2371 3864 657 217 646
## 5 1741 3406 439 141 624
## 6 2072 3418 453 149 610# Load xts package
library(xts)## Warning: package 'xts' was built under R version 3.4.4## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.4.4##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric# Create the dates object as an index for your xts object
dates <- seq(as.Date("2014-01-19"), length = 176, by = "weeks")
# Create an xts object called bev_xts
bev_xts <- xts(bev, order.by = dates)
head(bev_xts)## M.hi.p M.lo.p MET.hi.p MET.lo.p MET.sp.p SEC.hi.p SEC.lo.p M.hi
## 2014-01-19 59.25 29.19 63.67 26.03 50.09 58.56 29.19 458
## 2014-01-26 56.26 26.31 60.34 25.54 48.82 54.64 26.31 477
## 2014-02-02 56.26 26.25 60.79 25.69 48.56 57.90 26.25 539
## 2014-02-09 49.33 26.15 55.09 26.46 47.74 49.70 26.15 687
## 2014-02-16 61.34 25.88 65.09 25.72 50.75 63.72 25.88 389
## 2014-02-23 61.40 27.35 67.91 26.17 52.63 68.38 27.35 399
## M.lo MET.hi MET.lo MET.sp SEC.hi SEC.lo
## 2014-01-19 1455 2037 3437 468 156 544
## 2014-01-26 1756 1700 3436 464 151 624
## 2014-02-02 2296 1747 3304 490 178 611
## 2014-02-09 3240 2371 3864 657 217 646
## 2014-02-16 2252 1741 3406 439 141 624
## 2014-02-23 1901 2072 3418 453 149 610Plotting / visualizing data
The column names for the sales of these three products are MET.hi(high end products), MET.lo( low end products), and MET.sp(specialty products)
# Create the individual region sales as their own objects
MET_hi <- bev_xts[,"MET.hi"]
MET_lo <- bev_xts[,"MET.lo"]
MET_sp <- bev_xts[,"MET.sp"]
# Sum the region sales together
MET_t <- MET_hi + MET_lo + MET_sp
# Plot the metropolitan region total sales
plot(MET_t)
library(forecast)## Warning: package 'forecast' was built under R version 3.4.4# Split the data into training and validation
MET_t_train <- MET_t[index(MET_t) < "2017-01-01"]
MET_t_valid <- MET_t[index(MET_t) >= "2017-01-01"]
# Use auto.arima() function for metropolitan sales
MET_t_model<-auto.arima(MET_t_train)
# Forecast the first 22 weeks of 2017
forecast_MET_t <- forecast(MET_t_model, h = 22)
# Plot this forecast #
plot(forecast_MET_t)
# Convert to numeric for ease
for_MET_t <- as.numeric(forecast_MET_t$mean)
v_MET_t <- as.numeric(MET_t_valid)
# Calculate the MAE
MAE <- mean(abs(for_MET_t - v_MET_t))
# Calculate the MAPE
MAPE <- 100*mean(abs(for_MET_t - v_MET_t)/v_MET_t)
# Print to see how good your forecast is!
print(MAE)## [1] 898.8403print(MAPE)## [1] 17.10332# Convert your forecast to an xts object
for_dates <- seq(as.Date("2017-01-01"), length = 22, by = "weeks")
for_MET_t_xts <- xts(forecast_MET_t$mean, order.by = for_dates)
# Plot the validation data set
plot(MET_t_valid, main = 'Forecast Comparison', ylim = c(4000, 8500))
# Overlay the forecast of 2017
lines(for_MET_t_xts, col = "blue")
# No wonder our MAPE was over 17% on average!
# Confidence Intervals for Forecast
# Plot the validation data set
plot(MET_t_valid, main = 'Forecast Comparison', ylim = c(4000, 8500))
# Overlay the forecast of 2017
lines(for_MET_t_xts, col = "blue")
# Convert the limits to xts objects
lower <- xts(forecast_MET_t$lower[,2], order.by = for_dates)
upper <- xts(forecast_MET_t$upper[,2], order.by = for_dates)
# Adding confidence intervals of forecast to plot
lines(lower, col = "blue", lty = "dashed")
lines(upper, col = "blue", lty = "dashed")
Although inside the confidence intervals, I bet there are other things that we can include in our model to make our forecasts better!
Calculating price elasticity
bev_xts_train <- bev_xts[index(MET_t) <= "2016-12-25"]
MET_hi<-MET_hi[index(MET_t) <= "2016-12-25"]
# Save the prices of each product
l_MET_hi_p <- as.vector(log(bev_xts_train[,"MET.hi.p"]))
# Save as a data frame
MET_hi_train <- data.frame(as.vector(log(MET_hi)), l_MET_hi_p)
colnames(MET_hi_train) <- c("log_sales", "log_price")
# Calculate the regression
model_MET_hi <- lm(log_sales ~ log_price, data = MET_hi_train)
model_MET_hi##
## Call:
## lm(formula = log_sales ~ log_price, data = MET_hi_train)
##
## Coefficients:
## (Intercept) log_price
## 13.977 -1.517
Looks like our products are rather elastic here. We better be careful if we increase prices too much!
Seasonal / holiday / promotional effects
MET_hi_p<- bev_xts[,"MET.hi.p"]
# Plot the product's sales
plot(MET_hi)
# Plot the product's price
plot(MET_hi_p)
# Create date indices for New Year's week
n.dates <- as.Date(c("2014-12-28", "2015-12-27", "2016-12-25"))
# Create xts objects for New Year's
newyear <- as.xts(rep(1, 3), order.by = n.dates)
# Create date indices for valentines's week
n1.dates <- as.Date(c("2014-02-09", "2015-02-08", "2016-02-07"))
# Create xts objects for valentine's week
valentine <- as.xts(rep(1, 3), order.by = n1.dates)
# Create date indices for christmas's week
n2.dates <- as.Date(c("2014-12-21", "2015-12-20", "2016-12-18"))
# Create xts objects for christmas's
christmas <- as.xts(rep(1, 3), order.by = n2.dates)
# Create date indices for New mother's week
n3.dates <- as.Date(c("2014-05-04", "2015-05-03", "2016-05-01"))
# Create xts objects for mother's
mother <- as.xts(rep(1, 3), order.by = n3.dates)
# Create sequence of dates for merging
dates_train <- seq(as.Date("2014-01-19"), length = 154, by = "weeks")
# Merge training dates into New Year's object
newyear <- merge(newyear, dates_train, fill = 0)
valentine <- merge(valentine, dates_train, fill = 0)
christmas<- merge(christmas, dates_train, fill = 0)
mother<- merge(mother, dates_train, fill = 0)
# Create MET_hi_train_2 by adding newyear
MET_hi_train_2 <- data.frame(MET_hi_train, as.vector(newyear))
MET_hi_train_2 <- data.frame(MET_hi_train_2, as.vector(valentine))
MET_hi_train_2 <- data.frame(MET_hi_train_2, as.vector(christmas))
MET_hi_train_2 <- data.frame(MET_hi_train_2, as.vector(mother))
colnames(MET_hi_train_2)[3:6] <- c("newyear","valentine","christmas","mother")
head(MET_hi_train_2)## log_sales log_price newyear valentine christmas mother
## 1 7.619233 4.153713 0 0 0 0
## 2 7.438384 4.099995 0 0 0 0
## 3 7.465655 4.107425 0 0 0 0
## 4 7.771067 4.008968 0 1 0 0
## 5 7.462215 4.175771 0 0 0 0
## 6 7.636270 4.218183 0 0 0 0# Build regressions for the product
model_MET_hi_full <- lm(log_sales ~log_price + newyear+valentine+christmas+mother, data = MET_hi_train_2)
summary(model_MET_hi_full)##
## Call:
## lm(formula = log_sales ~ log_price + newyear + valentine + christmas +
## mother, data = MET_hi_train_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.83099 -0.23266 0.00558 0.23651 0.64194
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.17872 1.56327 8.430 2.83e-14 ***
## log_price -1.32544 0.38423 -3.450 0.000731 ***
## newyear 0.35624 0.19716 1.807 0.072818 .
## valentine 0.30424 0.19443 1.565 0.119773
## christmas 0.38218 0.19434 1.967 0.051102 .
## mother -0.09371 0.19428 -0.482 0.630287
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3327 on 148 degrees of freedom
## Multiple R-squared: 0.1475, Adjusted R-squared: 0.1187
## F-statistic: 5.122 on 5 and 148 DF, p-value: 0.0002316
For a level of significance of 5%, we can say that the Valentine’s Day and Mother’s Day promotion the doesn’t lead to a significant increase in sales.
Forecasting with regression
bev_xts_valid<-bev_xts[index(MET_t) >="2017-01-01"]
# Subset the validation prices
l_MET_hi_p_valid <- as.vector(log(bev_xts_valid[,"MET.hi.p"]))
# Create a validation data frame
MET_hi_valid <- data.frame(l_MET_hi_p_valid)
colnames(MET_hi_valid) <- "log_price"
model_MET_hi<-lm(formula = log_sales ~ log_price, data = MET_hi_train)
# Predict the log of sales for your high end product
pred_MET_hi <- predict(model_MET_hi, MET_hi_valid)
# Convert predictions out of log scale
pred_MET_hi <- exp(pred_MET_hi)
# Convert to an xts object
dates_valid <- seq(as.Date("2017-01-01"), length = 22, by = "weeks")
pred_MET_hi_xts <- xts(pred_MET_hi, order.by = dates_valid)
# Plot the forecast
plot(pred_MET_hi_xts)
# Calculate and print the MAPE
MET_hi_v <- bev_xts_valid[,"MET.hi"]
MAPE <- 100*mean(abs((pred_MET_hi_xts - MET_hi_v)/MET_hi_v))
print(MAPE)## [1] 29.57455Calculating residuals from regression
# Calculate the residuals from the model
MET_hi_full_res <- residuals(model_MET_hi_full)
# Convert the residuals to an xts object
MET_hi_full_res <- xts(MET_hi_full_res, order.by = dates_train)
# Plot the histogram of the residuals
par(mfrow=c(2,1))
hist(MET_hi_full_res)
# Plot the residuals over time
plot(MET_hi_full_res)
#Forecasting residuals
#Build an ARIMA model on the residuals: MET_hi_arima
MET_hi_arima<-auto.arima(MET_hi_full_res)
# Look at a summary of the model
summary(MET_hi_arima)## Series: MET_hi_full_res
## ARIMA(2,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.5950 -0.7972 -0.6845 0.1836
## s.e. 0.0829 0.0663 0.1156 0.0949
##
## sigma^2 estimated as 0.02829: log likelihood=57.16
## AIC=-104.33 AICc=-103.92 BIC=-89.14
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.00027865 0.1659916 0.1230188 -0.2910207 184.4528 0.4569681
## ACF1
## Training set -0.0007572244# Forecast 22 weeks with your model: for_MET_hi_arima
for_MET_hi_arima<-forecast(MET_hi_arima,h=22)
# Print first 10 observations
head(for_MET_hi_arima, n = 10)## $method
## [1] "ARIMA(2,0,2) with zero mean"
##
## $model
## Series: MET_hi_full_res
## ARIMA(2,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 1.5950 -0.7972 -0.6845 0.1836
## s.e. 0.0829 0.0663 0.1156 0.0949
##
## sigma^2 estimated as 0.02829: log likelihood=57.16
## AIC=-104.33 AICc=-103.92 BIC=-89.14
##
## $level
## [1] 80 95
##
## $mean
## Time Series:
## Start = 1079
## End = 1226
## Frequency = 0.142857142857143
## [1] -0.127128510 -0.101823382 -0.061062154 -0.016220804 0.022806701
## [6] 0.049308342 0.060465882 0.057135049 0.042927466 0.022921523
## [11] 0.002338127 -0.014543832 -0.025061591 -0.028379171 -0.025285937
## [16] -0.017707390 -0.008085441 0.001220042 0.008391748 0.012412335
## [21] 0.013107902 0.011012105
##
## $lower
## Time Series:
## Start = 1079
## End = 1226
## Frequency = 0.142857142857143
## 80% 95%
## 1079 -0.3426730 -0.4567753
## 1086 -0.3933350 -0.5476520
## 1093 -0.4040771 -0.5856583
## 1100 -0.3837139 -0.5782530
## 1107 -0.3506071 -0.5482804
## 1114 -0.3241058 -0.5217793
## 1121 -0.3165505 -0.5161309
## 1128 -0.3289811 -0.5333787
## 1135 -0.3538749 -0.5639294
## 1142 -0.3817586 -0.5959833
## 1149 -0.4059052 -0.6220161
## 1156 -0.4234066 -0.6398455
## 1163 -0.4339846 -0.6504554
## 1170 -0.4383387 -0.6553582
## 1177 -0.4372779 -0.6553732
## 1184 -0.4318311 -0.6510550
## 1191 -0.4236315 -0.6436084
## 1198 -0.4148735 -0.6351402
## 1205 -0.4077549 -0.6280497
## 1212 -0.4037837 -0.6241045
## 1219 -0.4033773 -0.6238513
## 1226 -0.4059362 -0.6266553
##
## $upper
## Time Series:
## Start = 1079
## End = 1226
## Frequency = 0.142857142857143
## 80% 95%
## 1079 0.08841594 0.2025183
## 1086 0.18968826 0.3440052
## 1093 0.28195280 0.4635339
## 1100 0.35127231 0.5458114
## 1107 0.39622047 0.5938938
## 1114 0.42272245 0.6203959
## 1121 0.43748225 0.6370627
## 1128 0.44325124 0.6476488
## 1135 0.43972986 0.6497844
## 1142 0.42760160 0.6418263
## 1149 0.41058142 0.6266924
## 1156 0.39431894 0.6107578
## 1163 0.38386145 0.6003322
## 1170 0.38158038 0.5985999
## 1177 0.38670599 0.6048013
## 1184 0.39641634 0.6156402
## 1191 0.40746066 0.6274375
## 1198 0.41731361 0.6375802
## 1205 0.42453841 0.6448331
## 1212 0.42860832 0.6489292
## 1219 0.42959314 0.6500671
## 1226 0.42796043 0.6486795
##
## $x
## Time Series:
## Start = 1
## End = 1072
## Frequency = 0.142857142857143
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## [151] 0.161431255 -0.005883972 -0.137035112 -0.113308647
##
## $series
## [1] "MET_hi_full_res"
##
## $fitted
## Time Series:
## Start = 1
## End = 1072
## Frequency = 0.142857142857143
## [1] -0.026150923 -0.074952460 -0.309190081 -0.251437022 -0.313101802
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## [56] 0.093945354 -0.066487517 -0.428502459 -0.400708997 -0.224726355
## [61] -0.033349556 0.144399793 0.234737673 0.488483245 0.567964317
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## [126] 0.342390503 0.384140396 0.416031273 0.264429750 0.294320645
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## [151] 0.027242440 0.087415795 -0.049586700 -0.171153312
##
## $residuals
## Time Series:
## Start = 1
## End = 1072
## Frequency = 0.142857142857143
## [1] -0.0278208633 -0.2310697648 0.0402877770 -0.1467944705 0.1313474354
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## [16] 0.1124329508 0.1272847540 -0.1188932639 -0.1104446322 -0.1208997582
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## [36] -0.0441424287 0.1600883137 0.0117488508 0.0154454393 -0.0180672241
## [41] -0.0405125356 0.0130440397 -0.1891854061 0.0694253374 0.1377410966
## [46] 0.0618211739 0.1810418064 0.0318558761 -0.2302574126 -0.1177011026
## [51] 0.4150018682 -0.1029032300 0.1634911861 0.0623661949 -0.0136886030
## [56] -0.0889475860 -0.3318235555 0.0287001186 0.0992994522 0.0731195761
## [61] 0.0695282210 0.0225105503 0.2668748135 0.1534530664 -0.0656016408
## [66] 0.0717287257 0.0789901523 -0.0123579150 0.2149421572 -0.4913714273
## [71] 0.1502123884 0.1174251564 0.2115146297 -0.1138182153 0.0262565254
## [76] -0.1927120149 -0.1553341605 -0.0226421323 -0.0015047839 -0.0020394046
## [81] 0.1051810941 0.0814004989 -0.2902840115 -0.2749363000 -0.0781957469
## [86] -0.0465594256 -0.1102522154 -0.0433844830 0.0120172608 -0.1242640839
## [91] 0.4481499144 0.0889484084 0.0122900886 -0.2141501322 0.0090162759
## [96] 0.0002871234 -0.0030322918 -0.2395063838 0.0134947234 -0.0554287700
## [101] 0.4014869907 -0.0148693304 -0.1176341942 0.1334167564 0.2590759072
## [106] 0.0766458961 0.1823663286 -0.0165301377 -0.2121103826 -0.1019510939
## [111] -0.0287604492 -0.0362684574 0.2617212508 0.0357188002 0.1631727738
## [116] 0.0312103909 -0.0341580861 0.1127532568 -0.1144557401 -0.0725413406
## [121] 0.5552028962 -0.6698650591 0.1985017149 0.3352955778 0.2420536158
## [126] 0.0426272256 0.1124983623 -0.0262184066 0.2066059648 0.2631635933
## [131] 0.0659556414 -0.0345260818 0.0413430073 -0.1052261700 0.0010246860
## [136] -0.1776873171 -0.2287243827 -0.2221077717 -0.2347879129 -0.1095515830
## [141] 0.0087779538 -0.2016168470 -0.0102908528 -0.1027724349 -0.1981652758
## [146] -0.0268195995 0.0897486893 0.1441223409 -0.0623727159 -0.0466069362
## [151] 0.1341888152 -0.0932997675 -0.0874484122 0.0578446648# Convert your forecasts into an xts object
dates_valid <- seq(as.Date("2017-01-01"), length = 22, by = "weeks")
for_MET_hi_arima <- xts(for_MET_hi_arima$mean , order.by = dates_valid)
# Plot the forecast
plot(for_MET_hi_arima)
# Convert your residual forecast to the exponential version
for_MET_hi_arima <- exp(for_MET_hi_arima)
# Multiply your forecasts together!
for_MET_hi_final <- pred_MET_hi_xts * for_MET_hi_arima
# Plot the final forecast - don't touch the options!
plot(for_MET_hi_final, ylim = c(1000, 4300))
# Overlay the validation data set
lines(MET_hi_v, col = "blue")
# Transfer functions & ensembling