import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.api import VAR
from statsmodels.tsa.stattools import adfuller, grangercausalitytests
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
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"])
ca1 = (weekly[(weekly.store_id == "CA_1") & (weekly.cat_id == "FOODS")]
.set_index("week_start")["units"].sort_index())
N_TEST = 52 # identical to Part 1
train, test = ca1.iloc[:-N_TEST], ca1.iloc[-N_TEST:]
print(f"train: {len(train)} weeks test: {len(test)} weeks")16 Homework 1, Part 2: ARIMA, VAR & Method Comparison
17 Overview
This is Part 2 of Homework 1, due before class in Week 3. It assumes you have submitted Part 1 (exponential smoothing) and that you have your Part 1 accuracy table available — Q5 asks you to compare against it.
Part 2 covers ARIMA-based models and their multivariate extension, Vector Autoregression. Where exponential smoothing summarizes the past through a smoothed level, ARIMA models the correlation structure of the series directly, and VAR lets two series inform each other.
Learning objectives. By the end of Part 2 you will be able to:
- Diagnose stationarity with the Augmented Dickey-Fuller test and difference a series appropriately
- Identify a plausible ARIMA(\(p,d,q\)) order from ACF and PACF plots
- Evaluate a model with walk-forward cross-validation rather than a single train/test split
- Fit a VAR, run a Granger causality test, and state precisely what the result does and does not license you to claim
18 Dataset and Split
Same M5 weekly panel as Part 1, and the same train/test split, so your Part 2 numbers are directly comparable to Part 1.
19 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.
19.1 Initial Prompt for Your AI Assistant
Start a new assistant session for Part 2 and paste the block below as the very first message. It does not count against your Part 2 budget.
I am working on Homework 1, Part 2 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. There are 30 store-category series, each with 277 weekly observations covering January 2011 to May 2016.
Part 2 covers ARIMA, walk-forward cross-validation, VAR, and Granger causality using Python and statsmodels, on the CA_1 and CA_3 FOODS series. I already completed exponential smoothing in Part 1 and will compare against those results. The train/test split is fixed: the final 52 weeks are the test set. For each question:
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 2 is 8 (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_part2_<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_part2 prompt <prompt_id>: <short summary>`
- If a prompt would take me past my budget of 8, 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: HW01P2_CONTEXT_ACKSubmit this text as INITIAL_PROMPT.md in your Part 2 submission folder.
20 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.
20.1 Q3 — ARIMA
(Suggested prompts: 3)
Work through the following steps for the CA_1 FOODS series.
(a) Run the Augmented Dickey-Fuller test. Report the test statistic, p-value, and your conclusion about stationarity. If differencing is needed, apply it and re-test.
This one is not clean, and that is the point
The ADF result on this series depends on how many augmenting lags you use. adfuller picks a lag order automatically by default, but you can set maxlag yourself — and short lag orders and long ones do not agree here.
Do not just report whatever the default returns. Run it at two or three different lag settings, report what you find, and commit to a conclusion with a reason. Then carry that conclusion into (b), (c), and Q4.
Real series are frequently borderline. Learning to defend a judgment call is the skill; a clean p-value would have taught you nothing.
(b) Plot the ACF and PACF of the (possibly differenced) series. Based on the plots, propose an ARIMA(\(p, d, q\)) order and explain your reasoning. Compare what you see against the four reference patterns from Lecture 2 — which one does this series most resemble?
(c) Fit your chosen ARIMA model on train. Report the AIC and compute the forecast RMSE on test.
(d) Implement walk-forward cross-validation: use an expanding window with a minimum training length of 104 weeks, re-fit your ARIMA at each step, and produce a 1-step-ahead forecast. Report the mean RMSE across all steps.
# (a) ADF test
# (b) ACF and PACF plots
# (c) Fit ARIMA on train, report AIC, compute RMSE on test
# (d) Walk-forward CV, expanding window, min 104 weeks, 1-step-aheadYour response: Compare the ARIMA walk-forward RMSE to the best exponential smoothing model from Part 1. Which method would you recommend for a weekly store-category forecast and why — consider accuracy, interpretability, and what it costs to maintain across 30 series. Then note whether the walk-forward RMSE in (d) differs much from the single-split RMSE in (c), and say which number you would trust and why.
20.2 Q4 — VAR and Granger Causality
(Suggested prompts: 3)
This question extends the analysis to two stores in the same state: CA_1 and CA_3, both FOODS.
(a) Test whether CA_3 FOODS Granger-causes CA_1 FOODS at lag 4 using grangercausalitytests. Report the F-statistic and p-value for that lag.
Use the transformation you justified in Q3(a) — levels if you concluded the series is stationary, differences if you concluded it has a unit root. State which you used and why. Lecture 2 covered both hazards: regressing non-stationary series gives you spurious results, and differencing an already-stationary series induces autocorrelation you then have to model away.
(b) Fit a VAR(4) on the training window of both series — same transformation as in (a) — using statsmodels.tsa.api.VAR. Forecast the next 4 weeks. Plot actual versus forecast for CA_1 only.
(c) Report the contemporaneous correlation between the two series’ weekly changes.
ca3 = (weekly[(weekly.store_id == "CA_3") & (weekly.cat_id == "FOODS")]
.set_index("week_start")["units"].sort_index())
# (a) Granger causality at lag 4, using the transformation you justified in Q3(a)
# (b) VAR(4) on the training window, forecast 4 weeks, plot CA_1
# (c) contemporaneous correlation of the weekly changesYour response: Answer in three parts.
First, state what Granger causality means in your own words, and what it does not mean.
Second, report what you actually found — the F-statistic, the p-value, and the contemporaneous correlation from (c). You will likely find both a strong contemporaneous correlation and a significant Granger test.
Third, and this is the important one: explain what that combination does and does not establish. Two Walmart stores 40 miles apart share regional promotions, weather, holidays, and local economic conditions. Does CA_3’s sales cause CA_1’s? If not, what is generating both the correlation and the predictive relationship — and what would a demand planner be entitled to do with this result? Be specific about the difference between “CA_3 helps me forecast CA_1” and “CA_3 drives CA_1.”
20.3 Q5 — Method Comparison
(Suggested prompts: 0 — write yourself)
No code required for this question. Write your answer directly below in 150–200 words.
You are a demand planner at Walmart responsible for producing 52-week store-category sales forecasts, updated monthly, across all 30 series in this dataset. Drawing on your results from Part 1 and from Q3–Q4, answer the following:
Which of the methods from this homework (SES, Holt, Holt-Winters, ARIMA, VAR) would you recommend for production use at scale, and which would you retain as a benchmark? Justify your choice based on forecast accuracy, the operational realities of refitting 30 series every month, the cost of model maintenance, and interpretability to non-technical stakeholders.
Your response: (150–200 words)
21 Submission Checklist
Before submitting Part 2, confirm each item below.
Not graded, but worth doing: commit locally once per prompt, hw01_part2 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. - [ ] REPORT.md included with a final business recommendation (3–5 sentences) addressed to a non-technical manager, drawing on both parts of Homework 1