St. Edward's Teaching Hub

Our Journey So Far

Each week builds on the last. You are not starting over — you are adding tools.

📈

Week 1

Regression

Linear model

Assumptions

Interpretation

“What drives Y?”

🧮

Week 2

Nonlinear

Quadratic

Log models

Elasticity

“Is it curved?”

🔀

Week 3

Logistic

Odds

Sigmoid

Confusion

“Yes or no?”

🎯

Week 4

kNN + Naive Bayes

Distance

Probabilities

Lift · ROC

“Which class?”

🌲

Week 5

Tree Models

Splits

Forests

Ensembles

“Which split?”

The Learning Loop

Every predictive model you build follows this same cycle.

🎯

Definethe ask

▼

🔍

Explorethe data

▼

⚙️

Prepareto model

▼

🧠

Modeland train

▼

📊

Evaluateand decide

🔄 iterate

↑

↓

The steps stay the same — your tools get sharper

Session A · The Bridge

From Static Data to Data That Moves

In earlier weeks, row order usually did not matter. In time series analysis, order is the story.

Cross-sectional thinking

Rows describe different people, firms, or products at one moment in time.

Shuffling rows usually changes nothing important.

Time-series thinking

Rows describe the same process unfolding over time.

Shuffling rows destroys the signal we want to forecast.

Session A · Definition

What Is Time Series Data?

Time series data are observations collected sequentially over time.

“Forecasting is about predicting the future as accurately as possible, given all of the information available.”

— Rob Hyndman, Forecasting: Principles and Practice

🌍

Quarterly GDP

📉

Daily stock prices

⚡

Monthly demand

👥

Annual population

❗

Key Rule

The defining feature of time series data is simple: order matters.

Session A · Forecastability

What Makes a Series Forecastable?

Some series are much easier to predict than others.

Structure

Clear patterns are easier to project.

History

More data gives us better evidence.

Stability

Forecasting breaks down when the process changes too much.

Session A · Components

The Three Major Components

When homework asks for three components, this is the answer students should know.

Trend-Cycle

Long-run direction plus slower wave-like movement.

Seasonal

Patterns that repeat on a fixed calendar rhythm.

Remainder

Noise and unexplained movement left after removing structure.

OBSERVED DATA │ ├── Trend-Cycle ├── Seasonal └── Remainder

💡

Clarification

Textbooks sometimes list four pieces, but in practice trend and cycle are combined because standard methods cannot reliably separate them.

Session A · Homework Prep

GDP Per Capita in `global_economy`

Students need this because GDP per capita is not a built-in column. They must compute it.

R — GDP per capita

r

head(global_economy)

global_economy %>%
mutate(GDP_per_capita = GDP / Population) %>%
autoplot(GDP_per_capita) +
theme(legend.position = "none") +
labs(
  title = "GDP Per Capita by Country Over Time",
  y = "$US"
)

global_economy %>%
mutate(GDP_per_capita = GDP / Population) %>%
filter(GDP_per_capita == max(GDP_per_capita, na.rm = TRUE))

global_economy %>%
filter(Country == "United States") %>%
mutate(GDP_per_capita = GDP / Population) %>%
autoplot(GDP_per_capita) +
labs(title = "US GDP Per Capita Over Time", y = "$US")

Session A · Additive vs Multiplicative

Additive vs. Multiplicative Decomposition

Students should learn to diagnose this visually before touching code.

Additive

Seasonal swings stay roughly the same size over time.

y(t) = Trend + Seasonal + Remainder

Multiplicative

Seasonal swings grow as the series level grows.

y(t) = Trend × Seasonal × Remainder

❗

Rule of Thumb

If the wiggles stay the same size, think additive. If the wiggles get larger as the series grows, think multiplicative.

Session A · Classical Decomposition

Classical Decomposition Step by Step

This is the logic behind many official seasonal-adjustment systems.

Step 1: Estimate Trend-Cycle using a moving average Step 2: De-trend the data Step 3: Estimate Seasonal by averaging each seasonal period Step 4: Compute Remainder as whatever is left

For multiplicative decomposition, we divide by the trend and seasonal pieces.

For additive decomposition, we subtract the trend and seasonal pieces.

Session A · R Lab

Classical Decomposition in R

This code is suitable for homework preparation and lecture demonstration.

R — classical decomposition

r

Gas <- tail(aus_production, 5 * 4) %>%
select(Quarter, Gas)

autoplot(Gas, Gas) +
labs(
  title = "Australian Gas Production (Last 5 Years)",
  y = "Petajoules"
)

Gas %>%
model(
  classical_decomposition(Gas, type = "multiplicative")
) %>%
components() %>%
autoplot() +
labs(title = "Classical Multiplicative Decomposition of Gas Production")

Session A · Seasonal Adjustment

Seasonally Adjusted Data

Removing seasonal effects helps reveal the underlying movement that decision-makers care about.

R — seasonally adjusted gas production

r

dcmp <- Gas %>%
model(
  classical_decomposition(Gas, type = "multiplicative")
)

components(dcmp) %>%
as_tsibble() %>%
autoplot(Gas, colour = "gray") +
geom_line(aes(y = season_adjust), colour = "blue", linewidth = 1) +
labs(
  title = "Seasonally Adjusted Gas Production",
  y = "Petajoules"
)

💡

Classroom Translation

When news reports say a number is seasonally adjusted, they are removing the predictable calendar pattern so we can see the real trend more clearly.

Session A · Outlier Sensitivity

How Outliers Distort Classical Decomposition

Classical decomposition is simple, but it is not robust.

R — inject outliers safely

r

Gas_clean <- tail(aus_production, 5 * 4) %>%
select(Quarter, Gas)

Gas_mid_outlier <- Gas_clean %>%
mutate(Gas = if_else(row_number() == 10, Gas + 300, Gas))

dcmp_mid <- Gas_mid_outlier %>%
model(
  classical_decomposition(Gas, type = "multiplicative")
)

components(dcmp_mid) %>%
as_tsibble() %>%
autoplot(Gas, colour = "gray") +
geom_line(aes(y = season_adjust), colour = "red", linewidth = 1) +
labs(title = "Seasonally Adjusted — Outlier in Middle")

Session A · STL

STL vs. Classical Decomposition

STL is more flexible and more robust than classical decomposition.

Why STL is powerful

• Handles evolving seasonality
• Estimates endpoints better
• Can be made robust to outliers

Limitations

• Natively additive
• Does not directly handle all calendar effects
• Requires tuning choices

R — STL decomposition

r

us_retail_employment <- us_employment %>%
filter(year(Month) >= 1990, Title == "Retail Trade") %>%
select(-Series_ID)

dcmp <- us_retail_employment %>%
model(stl = STL(Employed))

components(dcmp) %>% autoplot()

us_retail_employment %>%
model(
  STL(Employed ~ trend(window = 7) +
        season(window = "periodic"),
      robust = TRUE)
) %>%
components() %>%
autoplot()

Session A · Official Methods

Methods Used by Statistical Agencies

Official seasonal adjustment systems are built on the same core decomposition ideas, but with stronger endpoint and robustness handling.

Major methods to recognize

Students should know the names and big ideas.

Click to flip

Session B · Benchmark Methods

Why Benchmark Methods Matter

Simple forecasting methods are not bad models. They are the baseline every complex model must beat.

The four benchmark methods

These are the standard baselines students should recognize instantly.

Click to flip

Session B · Visual Intuition

What Each Benchmark Predicts

Students often understand these methods much faster when they see the forecast shape rather than just the formula.

Mean: flat at the historical average Naive: flat at the last observed value Seasonal Naive: repeats the most recent seasonal pattern Drift: extends the average historical slope

Session B · R Lab

Fit All Benchmark Methods at Once

This is a great example of how model() can fit multiple forecasting methods in one clean pipeline.

R — beer production benchmarks

r

train <- aus_production %>%
filter_index("1992 Q1" ~ "2006 Q4")

beer_fit <- train %>%
model(
  Mean = MEAN(Beer),
  Naive = NAIVE(Beer),
  Seasonal_naive = SNAIVE(Beer),
  Drift = RW(Beer ~ drift())
)

beer_fc <- beer_fit %>% forecast(h = 14)

beer_fc %>%
autoplot(train, level = NULL) +
autolayer(
  filter_index(aus_production, "2007 Q1" ~ .),
  colour = "black"
) +
labs(
  y = "Megalitres",
  title = "Forecasts for quarterly beer production"
) +
guides(colour = guide_legend(title = "Forecast"))

Session B · Drift Method

The Drift Method in Practice

The drift method is especially teachable because it matches a simple geometric idea.

❗

Interpretation

The drift method is like drawing a straight line from the first observation to the last observation and extending it forward.

R — drift with Facebook stock

r

fb_stock <- gafa_stock %>%
filter(Symbol == "FB") %>%
mutate(trading_day = row_number()) %>%
update_tsibble(index = trading_day, regular = TRUE)

fb_stock %>%
autoplot(Close) +
labs(title = "Facebook Daily Closing Stock Price", y = "$US")

fb_fit <- fb_stock %>%
model(Drift = RW(Close ~ drift()))

fb_fit %>%
forecast(h = 30) %>%
autoplot(fb_stock) +
labs(title = "Drift Forecast for Facebook Stock Price", y = "$US")

Session A · Real Dataset Walkthrough

Example: US Retail Employment

This is a strong lecture dataset because it has long-run movement, seasonality, and a familiar business context.

R — inspect US employment data

r

head(us_employment)
tail(us_employment)

str(us_employment)
glimpse(us_employment)
dim(us_employment)
nrow(us_employment)
ncol(us_employment)

names(us_employment)
colnames(us_employment)

summary(us_employment$Employed)

us_retail_employment <- us_employment %>%
filter(year(Month) >= 1990, Title == "Retail Trade")

us_retail_employment <- us_retail_employment[, 
names(us_retail_employment) != "Series_ID"
]

head(us_retail_employment)

Session A · Visual Diagnostics

Plotting Trend, Seasonality, and Cycles

A big part of time-series work is learning to read the pattern before choosing the model.

R — retail employment plots

r

plot <- autoplot(us_retail_employment, Employed) +
labs(
  y = "Persons (thousands)",
  title = "Total employment in US retail"
)

print(plot)

gg_season(us_retail_employment, Employed) +
labs(title = "Seasonal Plot: US Retail Employment", y = "Persons (thousands)")

gg_subseries(us_retail_employment, Employed) +
labs(title = "Month Plot: US Retail Employment", y = "Persons (thousands)")

us_retail_quarterly <- us_retail_employment %>%
index_by(Quarter = yearquarter(Month)) %>%
summarise(Employed = mean(Employed))

gg_subseries(us_retail_quarterly, Employed) +
labs(title = "Quarterly Plot: US Retail Employment", y = "Persons (thousands)")

gg_season(us_retail_employment, Employed, polar = TRUE) +
labs(title = "Polar Seasonal Plot: US Retail Employment", y = "Persons (thousands)")

Session A · Smoothing

Moving Average Smoothing

Moving averages are one of the clearest ways to explain smoothing before formal forecasting models.

R — moving averages

r

us_retail_employment %>%
mutate(
  `3-Month MA` = slider::slide_dbl(Employed, mean, .before = 1, .after = 1, .complete = TRUE),
  `5-Month MA` = slider::slide_dbl(Employed, mean, .before = 2, .after = 2, .complete = TRUE)
) %>%
tidyr::pivot_longer(
  cols = c(Employed, `3-Month MA`, `5-Month MA`),
  names_to = "Series",
  values_to = "Value"
) %>%
ggplot(aes(x = Month, y = Value, color = Series)) +
geom_line() +
labs(
  title = "US Retail Employment with Moving Averages",
  y = "Persons (thousands)",
  x = "Month"
)

Session A · Exponential Smoothing

Exponential Smoothing in Practice

ETS gives a more formal smoothing framework than moving averages.

R — exponential smoothing

r

fit_ets <- us_retail_employment %>%
model(ETS(Employed))

report(fit_ets)

components(fit_ets) %>%
autoplot() +
labs(
  title = "Exponential Smoothing Decomposition: US Retail Employment",
  y = "Persons (thousands)"
)

Session B · Measuring Performance

Google Stock: Forecast Accuracy Example

This example shows how to split time-ordered data into training and test sets and compare multiple simple models.

R — Google forecasting accuracy

r

google_data <- gafa_stock %>%
filter(Symbol == "GOOG") %>%
select(Date, Close) %>%
as_tsibble(index = Date)

google_train <- google_data %>%
filter(row_number() <= 200)

google_test <- google_data %>%
filter(row_number() > 200)

models_google <- google_train %>%
model(
  Naive = NAIVE(Close),
  Drift = RW(Close ~ drift()),
  Mean = MEAN(Close)
)

google_fc <- models_google %>%
forecast(new_data = google_test)

google_acc <- google_fc %>%
accuracy(google_data) %>%
mutate(
  MSE = RMSE^2,
  MAD = MAE
)

google_acc %>%
select(.model, MSE, MAD, MAPE)

Session B · Cross-Validation

Time Series Cross-Validation

Unlike ordinary cross-validation, time-series cross-validation respects temporal order.

R — rolling origin cross-validation

r

google_stretch <- google_data %>%
stretch_tsibble(.init = 40, .step = 5)

cv_models <- google_stretch %>%
model(
  Naive = NAIVE(Close),
  Drift = RW(Close ~ drift()),
  Mean = MEAN(Close)
)

cv_fc <- cv_models %>%
forecast(new_data = google_data)

cv_fc %>%
accuracy(google_data)

Session B · Diagnostics

Trends, Outliers, and Volatility

Forecasting is not only about fitting models. It is also about inspecting the process for dependence, outliers, and structural changes.

R — diagnostics on Google prices

r

google_data %>%
ACF(Close) %>%
autoplot() +
labs(title = "Autocorrelation of Google Closing Prices")

google_data %>%
ggplot(aes(x = Date, y = Close)) +
geom_line() +
geom_point(
  data = google_data %>% filter(abs(scale(Close)) > 2),
  aes(x = Date, y = Close),
  size = 2
) +
labs(title = "Potential Outliers in Google Closing Prices", y = "Close Price")

google_data %>%
mutate(Return = difference(log(Close))) %>%
ggplot(aes(x = Date, y = Return)) +
geom_line() +
labs(title = "Google Daily Log Returns", y = "Log Return")

Session B · Advanced Model

ARIMA Forecast for Australian Bricks

This gives students a first look at a more flexible time-series model after the benchmark methods.

R — ARIMA on bricks

r

bricks_train <- aus_production %>%
filter(year(Quarter) >= 1970, year(Quarter) <= 2004) %>%
select(Quarter, Bricks)

bricks_arima <- bricks_train %>%
model(ARIMA = ARIMA(Bricks))

report(bricks_arima)

fc_arima <- bricks_arima %>%
forecast(h = "2 years")

autoplot(bricks_train, Bricks) +
autolayer(fc_arima, level = NULL) +
labs(
  title = "ARIMA Forecast: Australian Clay Bricks",
  y = "Million Bricks"
)

gg_tsresiduals(bricks_arima)

Session B · Evaluation

How Do We Compare Forecasts?

A forecast is only useful if we know how well it performs on data it did not see during training.

MAE

Average absolute error

RMSE

Penalizes large mistakes more heavily

MAPE

Percent error, when meaningful

Session B · Accuracy in R

Accuracy on Recent Production Data

This version explicitly defines the evaluation set before calling accuracy().

R — define recent data before accuracy()

r

recent_production <- aus_production %>%
filter_index("2007 Q1" ~ .)

accuracy(beer_fc, recent_production)

Session B · External Data

Pulling Time Series Data from FRED

Students often want to know how to fetch real economic data directly from a public source.

R — quantmod and FRED

r

library(quantmod)
library(ggfortify)

getSymbols("TRP6001", src = "FRED")

autoplot(TRP6001) +
labs(title = "Real Personal Consumption Expenditures", y = "Index")

# Fallback if autoplot methods are unavailable
plot(TRP6001, main = "Real Personal Consumption Expenditures")

Week 6 · Takeaways

Time Series Analysis in One Page

If students remember these ideas, they will be ready for forecasting work and the homework set.

Five ideas to remember

These are the concepts that matter most from Week 6.

Click to flip

Our Journey So Far

Regression

Nonlinear

Logistic

kNN + Naive Bayes

Tree Models

The Learning Loop

From Static Data to Data That Moves

Cross-sectional thinking

Time-series thinking

What Is Time Series Data?

What Makes a Series Forecastable?

Structure

History

Stability

The Three Major Components

Trend-Cycle

Seasonal

Remainder

GDP Per Capita in global_economy

Additive vs. Multiplicative Decomposition

Additive

Multiplicative

Classical Decomposition Step by Step

Classical Decomposition in R

Seasonally Adjusted Data

How Outliers Distort Classical Decomposition

STL vs. Classical Decomposition

Why STL is powerful

Limitations

Methods Used by Statistical Agencies

Why Benchmark Methods Matter

What Each Benchmark Predicts

Fit All Benchmark Methods at Once

The Drift Method in Practice

Example: US Retail Employment

Plotting Trend, Seasonality, and Cycles

Moving Average Smoothing

Exponential Smoothing in Practice

Google Stock: Forecast Accuracy Example

Time Series Cross-Validation

Trends, Outliers, and Volatility

ARIMA Forecast for Australian Bricks

How Do We Compare Forecasts?

MAE

RMSE

MAPE

Accuracy on Recent Production Data

Pulling Time Series Data from FRED

Time Series Analysis in One Page

GDP Per Capita in `global_economy`