DS 6030 | Spring 2026 | University of Virginia

Homework #8: Forecasting Fatal Crashes

Overview

You work for your home state’s highway safety office. Budget season is approaching and your director needs a forecast of monthly fatal crashes for the next year to plan resource allocation like emergency response staffing, public safety campaigns, and infrastructure improvements. She wants to know: how many crashes should we expect each month, and how confident should we be in those numbers?

Data: The file FARS-monthly.csv (in Canvas/Assignments/HW 8) contains monthly fatal crash counts for every U.S. state from 2012–2023, compiled from the Fatality Analysis Reporting System (FARS).

Your state: Use the state where you were born or first lived in the U.S.

TipCoding Help

This homework introduces new libraries and data structures that you haven’t worked with before. The fpp3 ecosystem (R) and Nixtla ecosystem (python) tools have their own conventions for time series objects, model fitting, and forecasting. The learning curve can be steep on a first encounter.

It’s OK if you get stuck on code, especially for this assignment. Focus on the concepts: decomposing a series, comparing models against baselines, evaluating forecast uncertainty. If a particular function isn’t cooperating, describe what you’re trying to do and show what you attempted. A clear explanation of your approach with partial code is worth more than a polished notebook that skips the hard parts.

As a reminder, homework is graded on a coarse 5-point scale that emphasizes engagement with the learning process rather than correctness or polish. A serious attempt that gets stuck on implementation details will score well.

Some resources that may help:

• R: Forecasting: Principles and Practice
  • uses the fpp3 package ecosystem (tsibble, fable, feasts)
• Python: Forecasting: Principles and Practice, the Pythonic Way
  • uses statsforecast and related libraries from Nixtla
  • AI tools (Claude, ChatGPT, Copilot) are allowed and encouraged for help with syntax and debugging

Problem 1: Explore and Decompose

a. Load and plot

Load the FARS data, filter to your state, and create a time series plot of monthly fatal crashes.

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b. Daily Average Crash Rate

Because months have different numbers of days, model average daily fatal crashes rather than raw monthly counts. Define

\[ \texttt{daily\_avg} = \frac{\texttt{fatal\_crashes}}{\texttt{days\_in\_month}}. \]

Create and use daily_avg as the outcome variable for the remaining problems.

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c. Decomposition

Apply an STL decomposition to your state’s series. Describe what you see:

1. Is there a trend? If so, what direction and are there any notable changes?
2. Is there a seasonal pattern? Which months tend to have the most and fewest crashes?
3. Does the remainder look like noise, or is there leftover structure?

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d. COVID effect

Does your state show a notable change around 2020–2021? Many states saw an increase in fatal crashes despite reduced driving during COVID. Describe what you observe in your state’s data. Does this appear as a shock (temporary) or a changepoint (persistent shift)?

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Problem 2: Baselines

In this problem, use data through December 2021 for model building and model selection. Do not use the 2022–2023 data until Problem 4.

a. Fit baseline models

Fit the following baseline models to the data through December 2021:

1. Naive: \(\hat{y}_{t+h} = y_t\)
2. Seasonal naive: \(\hat{y}_{t+h} = y_{t+h-12}\)
3. Mean: \(\hat{y}_{t+h} = \frac{1}{t}\sum_{s=1}^t y_s\)

Then produce forecasts for January 2022 through December 2023.

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b. Plot and compare baseline forecasts

1. Plot the forecasts for all three baseline models.
2. Based on the plots, which baseline seems most reasonable for your state? Briefly explain.

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Problem 3: Modeling and Model Selection

Our planning target is 12 months ahead, so use \(h = 12\) step-ahead forecasting as the main basis for model comparison.

a. One model beyond the baselines

Fit at least one forecasting model that goes beyond the baselines. Choose one of the following:

1. ETS (exponential smoothing with automatic component selection)
2. ARIMA (automatic specification)
3. Regression with temporal features, such as a linear trend and month indicators

If you choose the regression option, keep the model simple. A good default is a linear trend plus month indicators. More complicated lag-based (autoregressive) models are optional but not required.

For each model you fit, state the model clearly and give a short explanation of why it seems reasonable for your state’s data.

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b. Rolling origin model selection

Compare your model from part (a) to the seasonal naive baseline using rolling origin cross-validation with forecast horizon \(h = 12\). For each fold, evaluate the 12-month-ahead forecast. Do not aggregate performance equally across all horizons 1 through 12. You may use either a growing or sliding window.

1. Briefly justify your choice of growing versus sliding window.
2. Report one or more performance measures at horizon \(h = 12\), such as MAE, RMSE, or MASE.
3. Based on this rolling origin analysis, which model would you choose for 12-month-ahead planning?

Note: this step is for model comparison and selection. Do not use the 2022–2023 data yet.

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Problem 4: Forecasting 2022–2023 and Recommendation

Pretend it is December 2021.

Using the model you selected in Problem 3b, refit it on all data through December 2021. Then use it to forecast January 2022 through December 2023.

a. Forecast plot with prediction intervals

Produce forecasts of average daily fatal crashes for 2022–2023 with 95% prediction intervals. Plot the forecasts and intervals, but do not show the actual 2022–2023 values on this plot.

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b. Recommendation memo

Write a short recommendation (3–5 sentences) to your director. Address the following:

1. About how many fatal crashes per month should the office plan for during 2022–2023?
2. Is there a seasonal pattern that should affect when resources are deployed?
3. How far ahead can the office reasonably trust the forecasts?

Write this as if you are advising the director at the end of 2021, before the actual 2022–2023 outcomes are known.

Note: your model is fit to average daily fatal crashes. If you want to express your recommendations in monthly counts, you may convert back using \[ \widehat{\texttt{fatal\_crashes}} = \widehat{\texttt{daily\_avg}} \times \texttt{days\_in\_month}. \]

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c. Final evaluation

Now compare your forecasts from part (a) to the actual 2022–2023 values.

1. Plot the forecasts together with the observed values for 2022–2023.
2. Report one or two error measures for the held-out period.
3. Did the model perform about as well as you expected based on the rolling origin results at \(h = 12\)? Briefly explain.

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