import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.holtwinters import ExponentialSmoothing
import warnings
warnings.filterwarnings('ignore')
from pathlib import Path
def data_path(name):
"""Find the processed data file whether you render from the repo root or from
this file's own folder."""
for base in (Path.cwd(), *Path.cwd().parents):
p = base / "data" / "processed" / name
if p.exists():
return p
raise FileNotFoundError(
f"Could not find data/processed/{name}. "
"Run `python scripts/prep_m5.py` from the repository root first."
)
weekly = pd.read_csv(data_path("m5_weekly.csv"), parse_dates=["week_start"])
# Store CA_1, FOODS category, for the univariate models in Part 1
ca1 = (weekly[(weekly.store_id == "CA_1") & (weekly.cat_id == "FOODS")]
.set_index("week_start")["units"]
.sort_index())
print(f"CA_1 FOODS: {len(ca1)} weekly observations "
f"from {ca1.index.min().date()} to {ca1.index.max().date()}")15 Homework 1, Part 1: Exponential Smoothing
16 Overview
Homework 1 comes in two parts. Part 1 (this document) covers exponential smoothing and is due before class in Week 2 — it uses only material from Lecture 1. Part 2 covers ARIMA, VAR, and method comparison, and is due before class in Week 3, after Lecture 2.
Each part has its own context prompt, its own prompt budget, and its own submission. Do not start Part 2 until Part 1 is submitted.
Exponential smoothing is a workhorse of operational forecasting in retail and supply chain: interpretable, cheap to fit, and hard to beat at scale. Working through real store-level sales data, you will see how the choice of smoothing model and the rigor of evaluation translate directly into business decisions.
Learning objectives. By the end of Part 1 you will be able to:
- Read a retail time series plot for trend, seasonality, and business-driven irregularity
- Apply Simple Exponential Smoothing, Holt’s linear trend model, and Holt-Winters to seasonal weekly data
- Interpret the smoothing parameter \(\alpha\) in business terms
- Compare competing models on a held-out test set using RMSE and MAE, against a benchmark
17 Dataset
This course runs on the M5 / Walmart dataset — the spine described in ECON8310_Datasets.md. It covers daily unit sales for Walmart stores across California, Texas, and Wisconsin from 29 January 2011 to 22 May 2016, and it was the data for the M5 forecasting competition.
You will work with the prepared weekly file, data/processed/m5_weekly.csv: 30 series (10 stores × 3 product categories), 277 weeks each, with average price, SNAP benefit days, and event-day counts alongside the unit sales.
If the file does not exist, run python scripts/prep_m5.py once first — it will tell you where to get the raw download.
18 Initial Prompt for Your AI Assistant
Any assistant works — ChatGPT, Claude, Gemini, or Copilot, in an editor or in a browser tab. Paste the block below as your first message, before you ask anything else.
Important
Your numbers will not match mine, and that is fine
Every result in this course depends on a random seed, and often also on your library versions, your hardware, and how many CPU threads your machine uses. Two people running identical, correct code will get different numbers — sometimes noticeably different.
What is graded is that you used the right model and the right procedure, and that your interpretation follows from the numbers you actually obtained. Quote your own output.
What is not graded is matching any particular value. Do not tune your way toward a number you saw on a slide or heard from a classmate — that is the one way to turn this into a wrong answer.
One caveat worth knowing. The broad ordering of models usually survives this variation. If yours comes out backwards from what the lecture found, say so in a sentence and offer a reason: either you have found something real about your run, or there is a bug worth hunting. Both are worth more marks than quietly reporting a number you do not believe.
18.1 Initial Prompt for Your AI Assistant
Paste the block below as the very first message in your assistant session before sending any questions. This sets the context that all subsequent prompts build on and does not count against your prompt budget.
I am working on Homework 1, Part 1 for ECON 8310: Business Forecasting at the University of Nebraska at Omaha.
Dataset: M5 / Walmart weekly sales, prepared at `data/processed/m5_weekly.csv`. Columns: store_id (10 Walmart stores across CA, TX, WI), cat_id (FOODS, HOBBIES, HOUSEHOLD), state_id, week_start, units, avg_price, snap_days, event_days, and lag features (units_lag1 through units_lag52). There are 30 store-category series, each with 277 weekly observations covering January 2011 to May 2016.
Part 1 covers exponential smoothing only (SES, Holt, Holt-Winters) using Python and statsmodels, on the CA_1 FOODS series. ARIMA and VAR come in Part 2 — do not introduce them here. I will ask you questions one at a time. For each:
1. Write clean, well-commented Python code that runs end-to-end
2. Explain what the output means so that I understand it — but do NOT draft the written
answers I submit. The interpretation and business-recommendation sections are mine to
write, in my own words.
My prompt budget for Part 1 is 4 (this context prompt is excluded). I will label each question before asking.
Repository rules — these apply to every prompt in this thread:
- If you cannot write files or run git — a browser chat cannot — then the file and commit
rules below are mine to carry out, not yours. Tell me what to write and what to commit,
and I will do it. Everything else in this list still applies to you.
- My submission folder is `submissions/hw01_part1_<my_name>/`. Put everything there.
- Keep a `PROMPT_LOG.md` in that folder. For every prompt I send, append a block:
### Prompt <n> — YYYY-MM-DD HH:MM
<my prompt, verbatim>
Numbered from 1, in order. Never edit or delete an earlier entry. If your tool cannot write
files, I will paste them in myself.
- After finishing the work for each prompt, make exactly one git commit:
`hw01_part1 prompt <prompt_id>: <short summary>`
- If a prompt would take me past my budget of 4, do not do the work. Reply exactly
PROMPT_LIMIT_REACHED, and still log that prompt.
- Never modify `AGENTS.md`, anything in `assignments/`, or anything in `policy/`.
Confirm by responding with: HW01P1_CONTEXT_ACKSubmit this text as INITIAL_PROMPT.md in your Part 1 submission folder.
19 Questions
How the code cells work
A cell that is empty except for a comment is where you write. The comment states the task; your code goes underneath it.
Some cells already contain setup code — a train/test split, a rename, a cutoff date — and end with a comment marking where your part begins. Leave the setup as it is and write below the comment. It is there so that everyone’s results are computed on the same basis.
Every cell runs as the document stands, so you can render at any point, finished or not. Doing that early and often is how you avoid finding a problem at the deadline.
The Your response blocks are written answers, not code. They are yours to write, in your own words — your assistant explains output to you, it does not draft these.
19.1 Q1 — Exploratory Plot
(Suggested prompts: 1)
Plot CA_1 FOODS weekly unit sales over the full 277-week window. After examining the plot, answer the written questions below.
# Plot CA_1 FOODS weekly units over timeYour response: Describe what you see. Is there a trend, and roughly how large is it over the five years? Is there a repeating annual pattern, and where do the peaks fall? Identify at least one irregular spike or dip and propose a business explanation — the dataset includes SNAP benefit days and event flags, and Walmart food sales respond to both.
19.2 Q2 — Exponential Smoothing Models
(Suggested prompts: 2)
Hold out the final 52 weeks as a test set. Fit the three models below on the training portion, forecast across the test period, and compute RMSE and MAE for each.
- Simple Exponential Smoothing (SES)
- Holt’s linear trend model
- Holt-Winters (additive seasonality, period = 52)
Also compute the same two metrics for a seasonal naive benchmark — this week last year — so you can tell whether any of the three models is earning its complexity. Present all four rows in one summary table.
Why a 52-week test set works here
Holt-Winters must estimate a seasonal index for each of the 52 weeks in a year, and it needs at least two complete cycles — \(2m = 104\) observations — before it can initialize them. This is the \(2m\) rule from Lecture 1.
Each series has 277 weeks. Holding out 52 still leaves 225 for training, comfortably above the threshold, and a one-year holdout is the horizon a demand planner actually cares about. The assertion below makes the constraint explicit rather than letting it fail deep inside statsmodels.
N_TEST = 52 # final year held out
train, test = ca1.iloc[:-N_TEST], ca1.iloc[-N_TEST:]
SEASONAL_PERIOD = 52
assert len(train) >= 2 * SEASONAL_PERIOD, (
f"Training set has {len(train)} weeks but Holt-Winters with period "
f"{SEASONAL_PERIOD} needs at least {2 * SEASONAL_PERIOD}. "
f"Reduce N_TEST."
)
print(f"train: {len(train)} weeks test: {len(test)} weeks")
# Fit SES, Holt, and Holt-Winters; add a seasonal naive benchmark;
# compute RMSE and MAE for all fourYour response: Which model performs best, and does it beat the seasonal naive benchmark? This series trends upward over the sample — explain what that implies for SES specifically, given that SES produces a flat forecast. Then interpret the estimated \(\alpha\): what does its value say about how quickly CA_1 food sales respond to recent weeks, and what would you tell a demand planner who wanted to know how much weight the model puts on last week?
20 Submission Checklist
Before submitting Part 1, confirm each item below.
Not graded, but worth doing: commit locally once per prompt, hw01_part1 prompt <id>: <summary>. Nobody sees these — they are your own record of which prompt produced what, and they make it far easier to retrace your steps when something breaks.
Part 2 is due before class in Week 3 and carries its own prompt budget. The business recommendation REPORT.md is submitted with Part 2, once you have results from all five questions.