2026 Price Forecasting
Lucas Libero
2025-12-01
# Bring in Libraries
library(tidyr)
library(dplyr)
library(ggplot2)
library(gridExtra)
library(forecast)
library(tsibble)
library(lubridate)
library(tseries)
library(zoo)
library(kableExtra)
library(urca)
library(knitr)Data from proprietary source (not included)
## Clean data
# rename rows
rownames(occ) = rownames(hwe) = occ[,1]
# change OCC from wide format to long
occ = occ %>%
pivot_longer(cols = -YEAR, # remove year
names_to = "month", # create month column
values_to = "price" #create price column
) %>%
mutate(month = match(substr(month, 1, 3), month.abb),
# match month names to month abbreviations
date = as.Date(paste(YEAR, month, "01", sep = "-"))
# create a date column of the month and year separated by -
) %>%
arrange(date) # arrange by date
# change HWE from wide format to long
hwe = hwe %>%
pivot_longer(cols = -YEAR, # remove year
names_to = "month", # create month column
values_to = "price" #create price column
) %>%
mutate(month = match(substr(month, 1, 3), month.abb),
# match string of month names to month abbreviations
date = as.Date(paste(YEAR, month, "01", sep = "-"))
# create a date column of the month and year separated by -
) %>%
arrange(date) # arrange by date## Find useful measures
max_hwe = hwe %>% filter(price == max(hwe$price, na.rm = TRUE))
min_hwe = hwe %>% filter(price == min(hwe$price, na.rm = TRUE))
max_occ = occ %>% filter(price == max(occ$price, na.rm = TRUE))
min_occ = occ %>% filter(price == min(occ$price, na.rm = TRUE))
## Set desired horizon
h = 12Visualizing Paper Prices Since 2018
Here is a broad overview of both prices side by side:
## Create HWE plot
hwe.plot = ggplot(aes(date, price), data = hwe) +
geom_point(color = "black") +
geom_line(color = "gray") +
labs(title = "HWE Prices Since 2018", y = "Price ($)", x = "Year") +
# force each year on x-axis
scale_x_date(breaks = seq(min(hwe$date), max(hwe$date), by = "1 year"),
date_labels = "%Y") +
# add max point
geom_segment(data = max_hwe,
aes(x = date, xend = date,
y = price + 25, yend = price + 5),
arrow = arrow(length = unit(0.25, "cm")),
color = "black",
linewidth = 0.7) +
# add text
geom_text(data = max_hwe[2,],
aes(x = date - 10, y = price + 30,
label = paste0("Max: $", price)),
color = "black") +
# add min point
geom_segment(data = min_hwe,
aes(x = date - 100, xend = date,
y = price - 25, yend = price - 5),
arrow = arrow(length = unit(0.25, "cm")),
color = "black",
linewidth = 0.7) +
# add text
geom_text(data = min_hwe[1,],
aes(x = date - 175, y = price - 30,
label = paste0("Min: $", price)),
color = "black")
## Create OCC plot
occ.plot = ggplot(aes(date, price), data = occ) +
geom_point(color = "brown2") +
geom_line(color = "brown4") +
labs(title = "OCC Prices Since 2018", y = "Price ($)", x = "Year") +
# force each year on x-axis
scale_x_date(breaks = seq(min(occ$date), max(occ$date), by = "1 year"),
date_labels = "%Y") +
# add max point
geom_segment(data = max_occ,
aes(x = date, xend = date,
y = price + 25, yend = price + 5),
arrow = arrow(length = unit(0.25, "cm")),
color = "black",
linewidth = 0.7) +
# add text
geom_text(data = max_occ[1,],
aes(x = date, y = price + 30,
label = paste0("Max: $", price)),
color = "black") +
# add min point
geom_segment(data = min_occ,
aes(x = date, xend = date,
y = price - 25, yend = price - 5),
arrow = arrow(length = unit(0.25, "cm")),
color = "black",
linewidth = 0.7) +
# add text
geom_text(data = min_occ[c(4,11),],
aes(x = date, y = price - 30,
label = paste0("Min: $", price)),
color = "black")
## Arrange both on a grid
grid.arrange(hwe.plot, occ.plot, ncol = 2)
HWE: There was a 3 month max at $465 from August 2022 through
October 2022. We are currently at the minimum price of $260 through
December 2025.
OCC: There was a 2 month max at $195 from September 2021
through October 2021. The minimum price for OCC of $35 has been reached
twice. Each time the price was stable for several months. The first time
was from July 2019 through January 2020. The second time was from
November 2022 through March 2023.
Here are both of the prices plotted for each month:
plot1 = ggplot(aes(hwe$price, occ$price), data = hwe) +
geom_point(color = "black") +
labs(title = "Paper Price Since 2018", y = "HWE Price", x = "OCC Price")
plot1
There seems to be very little association with each other and the
correlation is very small. (\(\tau =
0.183\)). It does not seem like when one peaks/falls so does the
other.
HWE
# Create time series object
ts_hwe = ts(data = hwe$price,
start = c(year(min(hwe$date)),
month(min(hwe$date))),
end = c(2025, 12),
frequency = 12)
# Find recommended lambda
lambda_hwe = BoxCox.lambda(ts_hwe)
# Transform with recommended lambda
ts_hwe = BoxCox(ts_hwe, lambda= lambda_hwe)Visualizations
Here is the trend line above just for HWE:
hwe.plotThe data has extreme changes in price from Dec 2018 to Dec 2019. It
then trended up and peaked in mid 2022 but has been in decline since. To
this day, prices have risen only twice since the peak in 2022. HWE
prices are now at an all-time low of 260.
Here is a plot of the prices through the years:
This is a breakdown of the prices by year. There doesn’t seem to be a
strong relationship. There are years where prices decreased throughout
the year (2019, 2023), years where prices increased then stabilized
(2018, 2021, 2022), and years where prices were stable (2024, 2025).
Only one year (2020) had the prices peak in the spring/summer then
decrease again.
Model(s) Selected
## Fit the benchmark model
# Naive
hwe_naive = naive(ts_hwe, bootstrap = TRUE, h = h)
## Fit the tested models
# Fit Auto ARIMA
hwe_arima = auto.arima(ts_hwe, seasonal = FALSE,
stepwise = FALSE, approximation = FALSE,
ic = "aicc")
# Fit ETS Model
hwe_ets = ets(ts_hwe, damped = TRUE) #no trace = true because it is too large
# Fit Holt model
hwe_holt = holt(ts_hwe, damped = TRUE, h = h)
# Fit Neural Network
hwe_nnet = nnetar(ts_hwe)## Create functions for CV to find errors that will be the base of the weights
# Create Naive forecast function (with bootstrapped residuals)
naive.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = naive(y,
bootstrap = TRUE,
h = h)
return(fit)
}
# Create Drift forecast function
drift.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = rwf(y, drift = TRUE,
bootstrap = TRUE,
h = h)
return(fit)
}
# Create ARIMA forecast function
arima.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = auto.arima(y, seasonal = FALSE,
stepwise = FALSE, approximation = FALSE,
ic = "aicc")
fc = forecast(fit, h)
return(fc)
}
# Create ETS forecast functions
ets.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = ets(y, damped = TRUE)
fc = forecast(fit, h = h)
return(fc)
}
# Create Holt forecast functions
holt.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = holt(y, damped = TRUE, h = h)
fc = forecast(fit, h = h)
return(fc)
}
# Create Neural Net forecast functions
nnet.fun = function(y, h) {
# leave out first year
if(length(y) < 12) {
return(structure(list(mean = ts(rep(NA, h))), class = "forecast"))
}
# finish function
fit = nnetar(y)
fc = forecast(fit, h = h)
return(fc)
}
## Find CV error & RMSE for all models
set.seed(1120)
hwe_naive_er = tsCV(ts_hwe, naive.fun, h = h)
hwe_naive_rmse = sqrt(mean(hwe_naive_er^2, na.rm = TRUE))
hwe_arima_er = tsCV(ts_hwe, arima.fun, h = h)
hwe_arima_rmse = sqrt(mean(hwe_arima_er^2, na.rm = TRUE))
hwe_ets_er = tsCV(ts_hwe, ets.fun, h = h)
hwe_ets_rmse = sqrt(mean(hwe_ets_er^2, na.rm = TRUE))
hwe_holt_er = tsCV(ts_hwe, holt.fun, h = h)
hwe_holt_rmse = sqrt(mean(hwe_holt_er^2, na.rm = TRUE))
hwe_nnet_er = tsCV(ts_hwe, nnet.fun, h = h)
hwe_nnet_rmse = sqrt(mean(hwe_nnet_er^2, na.rm = TRUE))Essentially, some of the models are better at predicting short-term forecasts (first 3 months) while some models are better in the long-term. I combined the models and found they predicted better than any of the models individually.
## Forecast the models
# ARIMA
hwe_fc_arima = forecast(hwe_arima, h = h)
# ETS
hwe_fc_ets = forecast(hwe_ets, h = h)
# Holt
hwe_fc_holt = forecast(hwe_holt, h = h)
# Neural Net
hwe_fc_nnet = forecast(hwe_nnet, h = h)## Create function to find rmse per block
rmse_block = function(e, cols) {
sqrt(mean(e[, cols]^2, na.rm = TRUE))
}
## Create RMSE df to find RMSEs for each block
hwe.rmse.df = data.frame(
Model = c("Naive", "ARIMA", "ETS", "Holt", "NNet"),
Block1 = c(
rmse_block(hwe_naive_er, 1:3),
rmse_block(hwe_arima_er, 1:3),
rmse_block(hwe_ets_er, 1:3),
rmse_block(hwe_holt_er, 1:3),
rmse_block(hwe_nnet_er, 1:3)
),
Block2 = c(
rmse_block(hwe_naive_er, 4:9),
rmse_block(hwe_arima_er, 4:9),
rmse_block(hwe_ets_er, 4:9),
rmse_block(hwe_holt_er, 4:9),
rmse_block(hwe_nnet_er, 4:9)
),
Block3 = c(
rmse_block(hwe_naive_er, 10:12),
rmse_block(hwe_arima_er, 10:12),
rmse_block(hwe_ets_er, 10:12),
rmse_block(hwe_holt_er, 10:12),
rmse_block(hwe_nnet_er, 10:12)
)
)
## Create a function that finds weights
wghts = function(x){
w = 1/x
w / sum(w)
}
## Create weights df
hwe.wghts.df = data.frame(
Model = hwe.rmse.df$Model,
wblock1 = wghts(hwe.rmse.df$Block1),
wblock2 = wghts(hwe.rmse.df$Block2),
wblock3 = wghts(hwe.rmse.df$Block3)
)## Create the combination forecast
# create the object
fc_hwe = numeric(12)
# months 1 - 3
fc_hwe[1:3] =
hwe.wghts.df$wblock1[1] * hwe_naive$mean[1:3] +
hwe.wghts.df$wblock1[2] * hwe_fc_arima$mean[1:3] +
hwe.wghts.df$wblock1[3] * hwe_fc_ets$mean[1:3] +
hwe.wghts.df$wblock1[4] * hwe_fc_holt$mean[1:3] +
hwe.wghts.df$wblock1[5] * hwe_fc_nnet$mean[1:3]
# months 4-9
fc_hwe[4:9] =
hwe.wghts.df$wblock1[1] * hwe_naive$mean[4:9] +
hwe.wghts.df$wblock1[2] * hwe_fc_arima$mean[4:9] +
hwe.wghts.df$wblock1[3] * hwe_fc_ets$mean[4:9] +
hwe.wghts.df$wblock1[4] * hwe_fc_holt$mean[4:9] +
hwe.wghts.df$wblock1[5] * hwe_fc_nnet$mean[4:9]
# months 4-9
fc_hwe[10:12] =
hwe.wghts.df$wblock1[1] * hwe_naive$mean[10:12] +
hwe.wghts.df$wblock1[2] * hwe_fc_arima$mean[10:12] +
hwe.wghts.df$wblock1[3] * hwe_fc_ets$mean[10:12] +
hwe.wghts.df$wblock1[4] * hwe_fc_holt$mean[10:12] +
hwe.wghts.df$wblock1[5] * hwe_fc_nnet$mean[10:12]
## Make forecast a time series object
fc_hwe = ts(fc_hwe, start = 2026, frequency = 12)
## Inverse them back into original units, then round them to nearest 5 dollars
# Inverse Box-Cox
fc_hwe = InvBoxCox(fc_hwe, lambda = lambda_hwe)
ts_hwe = InvBoxCox(ts_hwe, lambda = lambda_hwe)
hwe_naive = InvBoxCox(hwe_naive$mean, lambda = lambda_hwe)
hwe_fc_arima = InvBoxCox(hwe_fc_arima$mean, lambda = lambda_hwe)
hwe_fc_ets = InvBoxCox(hwe_fc_ets$mean, lambda = lambda_hwe)
hwe_fc_holt = InvBoxCox(hwe_fc_holt$mean, lambda = lambda_hwe)
hwe_fc_nnet = InvBoxCox(hwe_fc_nnet$mean, lambda = lambda_hwe)
# Round to nearest 5 dollars
fc_hwe = round((fc_hwe/5))*5Here are the forecasts for the combination models:
autoplot(ts_hwe) +
autolayer(hwe_naive, series="Naive", PI=FALSE) +
autolayer(hwe_fc_arima, series="ARIMA", PI=FALSE) +
autolayer(hwe_fc_ets, series="ETS", PI=FALSE) +
autolayer(hwe_fc_holt, series="Holt", PI=FALSE) +
autolayer(hwe_fc_nnet, series="Neural Net", PI=FALSE) +
autolayer(fc_hwe, series="Combined Models") +
xlab("Year") + ylab("Transformed Price") +
ggtitle("HWE Price Forecasts")
Here is at table of the predicted prices:
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2026 260 260 260 260 265 265 265 265 265 265 265 265According to the model, the price of HWE is projected to stay the same at $260 and then maintain through April of 2026. After that, there will be an increase in May to $265 that is expected to maintain until the prices go back down to $260 in November.
OCC
# Create time series object
ts_occ = ts(data = occ$price,
start = c(year(min(occ$date)),
month(min(occ$date))),
end = c(2025, 12),
frequency = 12)
# Clean with tsclean() command
ts_occ = tsclean(ts_occ)
# Find recommended lambda
lambda_occ = BoxCox.lambda(ts_occ)
# Transform with recommended lambda
ts_occ = BoxCox(ts_occ, lambda = lambda_occ)Visualizations
Here is the trend line above just for OCC:
occ.plotThe data has extreme changes in price from Nov 2020 to mid 2021 It
then fell consistently until 2023. OCC prices peaked in mid 2024 but has
been in decline since. Right now, prices currently sit at $60 which is
below the median, but not at an all time low.
Here is a plot plotting all the years:
This is a breakdown of the prices by year. There doesn’t seem to be a
strong relationship. The largest takeway is that OCC prices seem less
volatile than HWE prices. In this graph there aren’t many peaks or
extreme jumps up.
Model(s) Selected
## Fit the benchmark model
# Naive
occ_naive = naive(ts_occ, bootstrap = TRUE, h = h)
## Fit the tested models
# Fit Auto ARIMA
occ_arima = auto.arima(ts_occ, seasonal = FALSE,
stepwise = FALSE, approximation = FALSE,
ic = "aicc",
trace = TRUE)##
## ARIMA(0,0,0) with zero mean : 573.6837
## ARIMA(0,0,0) with non-zero mean : 156.7202
## ARIMA(0,0,1) with zero mean : Inf
## ARIMA(0,0,1) with non-zero mean : 55.19845
## ARIMA(0,0,2) with zero mean : Inf
## ARIMA(0,0,2) with non-zero mean : -21.51933
## ARIMA(0,0,3) with zero mean : Inf
## ARIMA(0,0,3) with non-zero mean : -61.74933
## ARIMA(0,0,4) with zero mean : Inf
## ARIMA(0,0,4) with non-zero mean : -84.86529
## ARIMA(0,0,5) with zero mean : Inf
## ARIMA(0,0,5) with non-zero mean : -92.99843
## ARIMA(1,0,0) with zero mean : Inf
## ARIMA(1,0,0) with non-zero mean : -81.44967
## ARIMA(1,0,1) with zero mean : Inf
## ARIMA(1,0,1) with non-zero mean : -99.84382
## ARIMA(1,0,2) with zero mean : Inf
## ARIMA(1,0,2) with non-zero mean : -118.7397
## ARIMA(1,0,3) with zero mean : Inf
## ARIMA(1,0,3) with non-zero mean : -117.1684
## ARIMA(1,0,4) with zero mean : Inf
## ARIMA(1,0,4) with non-zero mean : -115.9116
## ARIMA(2,0,0) with zero mean : Inf
## ARIMA(2,0,0) with non-zero mean : -116.169
## ARIMA(2,0,1) with zero mean : Inf
## ARIMA(2,0,1) with non-zero mean : -117.67
## ARIMA(2,0,2) with zero mean : Inf
## ARIMA(2,0,2) with non-zero mean : -117.7332
## ARIMA(2,0,3) with zero mean : Inf
## ARIMA(2,0,3) with non-zero mean : Inf
## ARIMA(3,0,0) with zero mean : Inf
## ARIMA(3,0,0) with non-zero mean : -119.1532
## ARIMA(3,0,1) with zero mean : Inf
## ARIMA(3,0,1) with non-zero mean : -119.11
## ARIMA(3,0,2) with zero mean : Inf
## ARIMA(3,0,2) with non-zero mean : -117.3318
## ARIMA(4,0,0) with zero mean : Inf
## ARIMA(4,0,0) with non-zero mean : -118.6221
## ARIMA(4,0,1) with zero mean : Inf
## ARIMA(4,0,1) with non-zero mean : -117.0096
## ARIMA(5,0,0) with zero mean : Inf
## ARIMA(5,0,0) with non-zero mean : -118.2044
##
##
##
## Best model: ARIMA(3,0,0) with non-zero mean # Fit ETS Model
occ_ets = ets(ts_occ, damped = TRUE) #no trace = true because it is too large
# Fit Holt model
occ_holt = holt(ts_occ, damped = TRUE, h = h)
# Fit Neural Network
occ_nnet = nnetar(ts_occ)## Find CV error & RMSE for all models
set.seed(1120)
occ_naive_er = tsCV(ts_occ, naive.fun, h = h)
occ_naive_rmse = sqrt(mean(occ_naive_er^2, na.rm = TRUE))
occ_arima_er = tsCV(ts_occ, arima.fun, h = h)
occ_arima_rmse = sqrt(mean(occ_arima_er^2, na.rm = TRUE))
occ_ets_er = tsCV(ts_occ, ets.fun, h = h)
occ_ets_rmse = sqrt(mean(occ_ets_er^2, na.rm = TRUE))
occ_holt_er = tsCV(ts_occ, holt.fun, h = h)
occ_holt_rmse = sqrt(mean(occ_holt_er^2, na.rm = TRUE))
occ_nnet_er = tsCV(ts_occ, nnet.fun, h = h)
occ_nnet_rmse = sqrt(mean(occ_nnet_er^2, na.rm = TRUE))Again, some of the models are better at predicting short term forecasts (first 3 months) while other models better at medium term, and one model is better at long-term. I tried a combination of these models but that did not improve the models compared to the baseline of using last month’s prices as the predicted price.
## Forecast the models
# ARIMA
occ_fc_arima = forecast(occ_arima, h = h)
# ETS
occ_fc_ets = forecast(occ_ets, h = h)
# Holt
occ_fc_holt = forecast(occ_holt, h = h)
# Neural Net
occ_fc_nnet = forecast(occ_nnet, h = h)## Create RMSE df to find RMSEs for each block
occ.rmse.df = data.frame(
Model = c("Naive", "ARIMA", "ETS", "Holt", "NNet"),
Block1 = c(
rmse_block(occ_naive_er, 1:3),
rmse_block(occ_arima_er, 1:3),
rmse_block(occ_ets_er, 1:3),
rmse_block(occ_holt_er, 1:3),
rmse_block(occ_nnet_er, 1:3)
),
Block2 = c(
rmse_block(occ_naive_er, 4:9),
rmse_block(occ_arima_er, 4:9),
rmse_block(occ_ets_er, 4:9),
rmse_block(occ_holt_er, 4:9),
rmse_block(occ_nnet_er, 4:9)
),
Block3 = c(
rmse_block(occ_naive_er, 10:12),
rmse_block(occ_arima_er, 10:12),
rmse_block(occ_ets_er, 10:12),
rmse_block(occ_holt_er, 10:12),
rmse_block(occ_nnet_er, 10:12)
)
)
## Create weights df
occ.wghts.df = data.frame(
Model = occ.rmse.df$Model,
wblock1 = wghts(occ.rmse.df$Block1),
wblock2 = wghts(occ.rmse.df$Block2),
wblock3 = wghts(occ.rmse.df$Block3)
)## Create the combination forecast
# create the object
fc_occ = numeric(12)
# months 1 - 3
fc_occ[1:3] =
occ.wghts.df$wblock1[1] * occ_naive$mean[1:3] +
occ.wghts.df$wblock1[2] * occ_fc_arima$mean[1:3] +
occ.wghts.df$wblock1[3] * occ_fc_ets$mean[1:3] +
occ.wghts.df$wblock1[4] * occ_fc_holt$mean[1:3] +
occ.wghts.df$wblock1[5] * occ_fc_nnet$mean[1:3]
# months 4-9
fc_occ[4:9] =
occ.wghts.df$wblock1[1] * occ_naive$mean[4:9] +
occ.wghts.df$wblock1[2] * occ_fc_arima$mean[4:9] +
occ.wghts.df$wblock1[3] * occ_fc_ets$mean[4:9] +
occ.wghts.df$wblock1[4] * occ_fc_holt$mean[4:9] +
occ.wghts.df$wblock1[5] * occ_fc_nnet$mean[4:9]
# months 4-9
fc_occ[10:12] =
occ.wghts.df$wblock1[1] * occ_naive$mean[10:12] +
occ.wghts.df$wblock1[2] * occ_fc_arima$mean[10:12] +
occ.wghts.df$wblock1[3] * occ_fc_ets$mean[10:12] +
occ.wghts.df$wblock1[4] * occ_fc_holt$mean[10:12] +
occ.wghts.df$wblock1[5] * occ_fc_nnet$mean[10:12]
## Make forecast a time series object
fc_occ = ts(fc_occ, start = 2026, frequency = 12)
## Inverse them back into original units, then round them to nearest 5 dollars
# Inverse Box-Cox
fc_occ = InvBoxCox(fc_occ, lambda = lambda_occ)
ts_occ = InvBoxCox(ts_occ, lambda = lambda_occ)
occ_naive = InvBoxCox(occ_naive$mean, lambda = lambda_occ)
occ_fc_arima = InvBoxCox(occ_fc_arima$mean, lambda = lambda_occ)
occ_fc_ets = InvBoxCox(occ_fc_ets$mean, lambda = lambda_occ)
occ_fc_holt = InvBoxCox(occ_fc_holt$mean, lambda = lambda_occ)
occ_fc_nnet = InvBoxCox(occ_fc_nnet$mean, lambda = lambda_occ)
# Round to nearest 5 dollars
fc_occ = round((fc_occ/5))*5Here are the forecasts for the combination models:
autoplot(ts_occ) +
autolayer(occ_naive, series="Naive", PI=FALSE) +
autolayer(occ_fc_arima, series="ARIMA", PI=FALSE) +
autolayer(occ_fc_ets, series="ETS", PI=FALSE) +
autolayer(occ_fc_holt, series="Holt", PI=FALSE) +
autolayer(occ_fc_nnet, series="Neural Net", PI=FALSE) +
autolayer(fc_occ, series="Combined Models") +
xlab("Year") + ylab("Transformed Price") +
ggtitle("occ Price Forecasts")## Warning in ggplot2::geom_line(ggplot2::aes(x = .data[["timeVal"]], y = .data[["seriesVal"]], : Ignoring unknown parameters: `PI`
## Ignoring unknown parameters: `PI`
## Ignoring unknown parameters: `PI`
## Ignoring unknown parameters: `PI`
## Ignoring unknown parameters: `PI`
Here is at table of the predicted prices:
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2026 60 60 60 60 65 65 65 65 70 70 70 70According to the model, the price of OCC is projected to stay the same at $60 and then increase to $65 in April of 2026. After that, there will be an increase in August to $70 that is expected to maintain until another increase in December to $75.
Takeaways/Futher Steps:
The data is very noisy, with extreme jumps that are hard to predict.
HWE prices were predicted with a combination of models that seem to be better than any one individual model.
The combined model predicted the price of HWE will largely stay the same.
OCC prices did not move in any predictable pattern. The best overall model was the “naive” model that only used the last price as its prediction.
However, a combination was almost as good, and that is what I included above. The combinations predict price increase to $75 in the year 2026.
Other potential variables should be considered for prediction of paper prices.