Forecasting monthly LMS access sessions with exponential smoothing

Exponential Smoothing (ETS) for Education and Learning

Field: Education and LearningLevel: Undergraduate thesis (S1)Method: Exponential Smoothing (ETS)

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Forecasting monthly LMS sessions with exponential smoothing (ETS) capturing trend and seasonality, illustrated with synthetic data. Exponential Smoothing (ETS) forecasts a time series by gradually updating level, trend and seasonal components and selects the best error, trend and seasonal combination by AICc. It suits theses on monthly forecasting such as sales, demand, tax revenue or visits.

Forecasting monthly LMS access sessions with exponential smoothing: result sheet

Project info

Field of studyEducation and Learning
LevelUndergraduate thesis (S1)
Method typeTime Series
Estimated build time± 3 working days
Toolsforecast::ets, forecast::forecast, forecast::accuracy, forecast::snaive, stats::Box.test, ggplot2
PriceUS$16 - US$106

Research goal

Forecasting monthly LMS sessions with exponential smoothing (ETS) capturing trend and seasonality, illustrated with synthetic data.

Variables

Role	Variable	Unit
Main	Monthly LMS sessions	sessions
Supporting 1	Active users	persons
Supporting 2	Assignments posted	count

Example result

2.484MAPE ETS (test, %)
4.12MAPE SNaive (test, %)
1.571RMSE ETS (test)
0.006Alpha (level)
0.001Ljung-Box p-value
49.275Next-month forecast

The selected ETS(M,A,M) model for Monthly LMS sessions reaches a MAPE of 2.48% on the 12-month test set, beating seasonal naive (MAPE 4.12%). The smoothing parameter alpha = 0.006 shows how fast the level adapts, and the Ljung-Box test (p = 0.001) flags remaining autocorrelation. The next-month forecast is 49.28.

Computed from illustrative synthetic data, not from a real study.

About Exponential Smoothing (ETS)

Exponential Smoothing (ETS) forecasts a time series by gradually updating level, trend and seasonal components and selects the best error, trend and seasonal combination by AICc. It suits theses on monthly forecasting such as sales, demand, tax revenue or visits.

Steps

1Convert the data to a monthly ts object and plot the pattern
2Split the data into training and a 12-month test set
3Select an ETS model automatically with forecast::ets
4Forecast 12 months with 80% and 95% prediction intervals
5Evaluate accuracy (RMSE, MAE, MAPE) and compare with the seasonal naive method
6Inspect the level, slope and seasonal components and run the Ljung-Box test on residuals

Assumptions to check

Past trend and seasonal patterns are expected to continue into the forecast period
Residuals are not autocorrelated (white noise)
The series is long enough, at least two to three seasonal cycles

Reading and reporting the results

State the selected ETS model, for example ETS(M,A,M) meaning multiplicative error, additive trend and multiplicative seasonality, with its smoothing parameters. Report test-set MAPE and RMSE against seasonal naive, the Ljung-Box result and the forecasts with their prediction intervals.

Example R code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

Show code

# Contoh kode R: Exponential Smoothing (ETS)
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(forecast)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis: deret bulanan 8 tahun dengan tren dan musiman ----
bulan <- seq(as.Date("2017-01-01"), by = "month", length.out = 96)
tt <- seq_along(bulan)
tumbuh <- runif(1, 0.15, 0.5)                                # pertumbuhan total selama 8 tahun
level <- 1 + tumbuh * tt / 96 + cumsum(rnorm(96, 0, 0.004))   # level dengan sedikit pergeseran acak
pola <- c(-1, -0.8, -0.2, 0.1, 0.3, 0.6, 0.9, 0.7, 0.2, -0.1, 0.3, 1.2)   # pola musiman dasar
geser <- sample(0:11, 1)
musim <- 1 + runif(1, 0.06, 0.14) * pola[((tt - 1 + geser) %% 12) + 1] / sd(pola)
galat <- exp(rnorm(96, 0, runif(1, 0.025, 0.045)))
d <- data.frame(bulan = bulan, monthly_lms_sessions = round(max(100, 1) * level * musim * galat, 3))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Analisis: ETS otomatis (pemilihan error-tren-musiman berbasis AICc) ----
y <- ts(d$monthly_lms_sessions, start = c(2017, 1), frequency = 12)
latih <- window(y, end = c(2023, 12))
uji <- window(y, start = c(2024, 1))
fit <- ets(latih)                                  # model ETS(E,T,S) dipilih otomatis
print(summary(fit))
fc <- forecast(fit, h = length(uji), level = c(80, 95))
ak <- accuracy(fc, uji)
print(ak)
# pembanding: naive musiman (nilai bulan yang sama tahun lalu)
sn <- snaive(latih, h = length(uji))
ak_sn <- accuracy(sn, uji)
print(ak_sn)
n_par <- sum(names(fit$par) %in% c("alpha", "beta", "gamma", "phi"))
lb <- Box.test(residuals(fit), lag = 24, type = "Ljung-Box", fitdf = n_par)
print(lb)
fit_all <- ets(y, model = fit, use.initial.values = FALSE)    # struktur model yang sama, data lengkap
fc12 <- forecast(fit_all, h = 12)
alpha_hat <- unname(fit$par["alpha"])


# ---- Grafik ----
# 1) ramalan ETS dengan interval 80% dan 95% vs data uji
waktu <- function(x) as.numeric(time(x))
dh <- data.frame(t = waktu(latih), y = as.numeric(latih))
dh <- dh[dh$t >= 2021, ]                           # tampilkan 3 tahun terakhir data latih
du <- data.frame(t = waktu(uji), y = as.numeric(uji))
df <- data.frame(t = waktu(fc$mean), m = as.numeric(fc$mean),
                 lo80 = as.numeric(fc$lower[, 1]), hi80 = as.numeric(fc$upper[, 1]),
                 lo95 = as.numeric(fc$lower[, 2]), hi95 = as.numeric(fc$upper[, 2]))
p1 <- ggplot() +
  geom_ribbon(data = df, aes(t, ymin = lo95, ymax = hi95), fill = pal[2], alpha = 0.15) +
  geom_ribbon(data = df, aes(t, ymin = lo80, ymax = hi80), fill = pal[2], alpha = 0.3) +
  geom_line(data = dh, aes(t, y), colour = pal[1], linewidth = 0.7) +
  geom_line(data = df, aes(t, m), colour = pal[2], linewidth = 1) +
  geom_point(data = du, aes(t, y), colour = warna$teks, size = 1.8) +
  scale_x_continuous(breaks = 2021:2025) +
  labs(title = paste(fit$method, "forecast, 80/95% PI (dots = test)"), x = "Year", y = "monthly_lms_sessions")
# 2) komponen state ETS: level, slope, musiman
st <- fit$states[-1, , drop = FALSE]
kom <- data.frame(t = waktu(latih), Level = st[, "l"])
if ("b" %in% colnames(st)) kom$Slope <- st[, "b"]
if ("s1" %in% colnames(st)) kom$Season <- st[, "s1"]
kom$Error <- as.numeric(residuals(fit))
dk <- do.call(rbind, lapply(names(kom)[-1], function(k) data.frame(t = kom$t, komponen = k, nilai = kom[[k]])))
dk$komponen <- factor(dk$komponen, levels = names(kom)[-1])
p2 <- ggplot(dk, aes(t, nilai)) +
  geom_line(colour = pal[3], linewidth = 0.7) +
  facet_wrap(~komponen, ncol = 1, scales = "free_y", strip.position = "right") +
  theme(axis.text.y = element_text(size = rel(0.65))) +
  labs(title = "ETS components", x = "Year", y = NULL)
# 3) galat absolut per bulan uji: ETS vs naive musiman
dg <- rbind(data.frame(t = format(time(uji)), bln = month.abb[cycle(uji)], g = abs(as.numeric(uji - fc$mean)), model = "ETS"),
            data.frame(t = format(time(uji)), bln = month.abb[cycle(uji)], g = abs(as.numeric(uji - sn$mean)), model = "Seasonal naive"))
dg$bln <- factor(dg$bln, levels = month.abb[cycle(uji)])
p3 <- ggplot(dg, aes(bln, g, fill = model)) +
  geom_col(position = position_dodge(0.8), width = 0.75) +
  scale_fill_manual(values = c(ETS = pal[2], "Seasonal naive" = pal[4]), name = NULL) +
  theme(axis.text.x = element_text(size = rel(0.7))) +
  labs(title = "Absolute error by test month", x = "2024", y = "|Error|")
p_hasil <- if (tata == 1) ((p1 / p3) | p2) + plot_layout(widths = c(1.5, 1)) else (p2 | (p1 / p3)) + plot_layout(widths = c(1, 1.5))

print(p_hasil)

The project file you can download

The original project file is available. It is not just the picture above: you get the working R project. It can be downloaded after payment, and we send it by WhatsApp or email.

ZIP: analisis.R + data_contoh.csv + BACA-DULU.txt

What is inside the ZIP

The complete analysis script (analisis.R), commented step by step, ready to run in RStudio.
A sample dataset (data_contoh.csv) so the script runs straight away.
A short guide (BACA-DULU.txt): which packages to install, how to run it and how to swap in your own data.

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

Package 1

Code and Explanation

US$16

excl. 11% VAT

Duration: 3 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for Exponential Smoothing (ETS)
Example data and step-by-step run instructions
Ready-to-use result figures and metrics table
Short explanation of the method, its assumptions and how to read the results

Choose Package 1

Package 2 · most chosen

Your Data Analysis + Interpretation

US$50

excl. 11% VAT

Duration: 7 working days

Output: Code + analysis + interpretation notes

Includes all of Package 1, plus

Adapting the code to your own research dataset (CSV or Excel)
Assumption checks, result validation and data cleaning
Tables and figures formatted for your manuscript
Interpretation notes for the methods and discussion sections, for you to write up in your own words

Choose Package 2

Package 3

Full Guidance

US$106

excl. 11% VAT

Duration: 12-15 working days

Output: Code + analysis + guidance until ready to present

Includes all of Packages 1 & 2, plus

Comparison against one alternative method with the reasoning for the choice
Two 60-minute online coaching sessions so you fully understand the code and results
Revisions following your supervisor feedback (up to 3 rounds)
Practice Q&A to prepare for your seminar and defence
Full documentation (README, R package list (sessionInfo)) so the results can be reproduced

Choose Package 3

Payment: 50% down payment before work starts, balance after the deliverables are handed over
Tax: Prices exclude 11% VAT
Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions

Do I get the real project file?

Yes. The original project file is a ZIP containing the complete analisis.R script, a data_contoh.csv sample dataset and a BACA-DULU.txt guide. It can be downloaded after payment, and we send it by WhatsApp or email. For your own data (Package 2 and 3) the script is adapted to your dataset.

Is this suitable for a Undergraduate thesis (S1)?

Yes. Exponential Smoothing (ETS) is commonly used at this level in Education and Learning. We adapt the analysis to your research question, your own data and your supervisor's requirements.

Is the result sheet real data?

No. The sheet is computed from illustrative synthetic data so you can see the kind of output R Studio gives. For your order we run the same method on your own data.

Will I understand the code?

That is the point of the packages. Every script is commented, and Package 3 includes two coaching sessions plus practice questions so you can explain the method and the results at your seminar and defence.

How is the price decided?

Each project has three packages: Package 1 (code and explanation) US$16, Package 2 (your data analysis and interpretation) US$50 and Package 3 (full guidance) US$106, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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