analyze and forecast a time series
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STAT 153 Project
The main goal of this class is to be able to analyze and forecast a time series. Thus, your project is
to analyze and forecast a time series of your choice! Broadly speaking, your task is to
1. Form groups of 3-5 students to work on the project.
2. Find a dataset in an interesting field and to analyze.
3. Complete a detailed analysis of the dataset.
• Exploratory data analysis
• Pursue stationarity two different ways (two signal models)
• Model the plausibly-stationary noise from the two signal models, in two different ways each,
resulting in four total models.
• Appropriately select the model (and you should discuss how you define “best”).
• Using this best model, forecast the next 10 time points.
4. Write up results in a report (5-10 pages). Include the name and SID of your group members. Each
group will submit a single pdf file.
5. This document is not intended to give you a step-by-step instruction on how to do the analysis. It
only helps you with Latex and shows you some general aspect you should take care about in your
report.
Summary:
In the beginning of your report, write a short summary. You should summarize in a few
sentences which data set you analyzed, which model you used to make predictions, and
briefly describe the public impact of your analysis and prediction.
1 Introduction
Here you can discuss the background of the question you will explore and describe your data resources.
2 Exploratory Data Analysis
Here you will explore the data. Naturally, the first plot you should make is the data itself. You should
point out any visible features, e.g. heteroscedasticity, seasonality, trend.
3 Models Considered
Here I would put a brief introductory statement. First, include details on your pursuit of stationarity:
removing trends and seasonalities, stabilizing the variance, and any other operation that makes sense
for your dataset. You should do this in two different ways (e.g., model A and model B). Then, second,
describe your ARMA model selections: provide convincing justification why a particular ARMA (or
SARIMA, etc.) is suitable. You should do this in two different ways for each stationary series, resulting
in four different models (e.g. models A1, A2, B1, B2). For example, the models could be.
1
• polynomial trend + ARMA(1,1)
• polynomial trend + SARIMA(p = 0, q = 0, P = 1, Q = 2, S = 12)
• ARIMA(p = 1, d = 2, q = 3) (second differences with ARMA(1,3))
• SARIMA(p = 0, d = 2, q = 0, P = 1, S = 12).
How to begin this section is up to you, but I suggest individual model details be broken up into subsections
below.
3.1 Signal Model 1 (but you won’t call it “signal model 1”, perhaps “Para-
metric model: quadratic polynomial of time with monthly indicators”)
Here I describe the first method of pursuing stationarity. It’d probably be good to show the fitted values
and the stationary-looking residuals. I would also describe why I made these modeling decisions, but it
should NOT be a travel log of all the different models I tried before landing on this one.
3.1.1 Signal Model 1 + ARMA version 1
Describe what the ARMA choice is and why it was made. ACF and PACF plots should show up
somewhere, and perhaps the full SARIMA diagnostics if that makes sense.