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Applied Time Series Analysis STA457
创建日期：2024-05-02 11:38:29
所属分类：统计学statistics
标签： STA457
Applied Time Series Analysis

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Applied Time Series Analysis

STA457H5 S LEC9101
Course Project
Time Series Analysis of Monthly VIX Index
Several metrics exist to quantify market volatility; however, the most well-known and followed metrics are
realized and implied volatility. The realized volatility gauges the fluctuations of underlying securities or indices
by measuring price changes over predetermined periods, while implied volatility is a forward-looking metric
representing future expectations of the market’s uncertainty. The most important member of the latter family is
the Chicago Board Options Exchange’s (CBOE) VIX index which can be considered as an estimator of the equity
market’s implied volatility. In this project, you will construct a time series model to forecast the future behaviour
of the VIX index.
As you may have already noticed from our ongoing discussions during the semester, the real-world time series
often possess very intricate nature, which renders their analysis rather a difficult task. As a time series analyst, the
first and foremost difficulty that you will encounter pertains to the fact that no significant source of external help
and guidance would be available to assist you on your path towards analysis of the given time series. For this
reason, many analysts eventually embark upon learning vast majority of the necessary aspects of the domain
knowledge on their own. As a result, this would require the time series analysts to have already acquired and
developed a multi-faceted approach for scientific thinking, which would enable them to gather know-how of any
given problem, regardless of its domain of applications, in the shortest amount of time and in the most effective
manner.
Yet, this would only count towards completing the first step of the time series analysis (gathering the required
elements of the domain knowledge). Thereafter, it is most likely for the analyst to find himself/herself in a situation
where his/her familiar time series models would deem inapplicable for analyzing the problem in hand. Thus, it
often becomes a vital step for the analyst to develop a relatively novel methodology which is only tailored to solve
that particular problem. Also, it goes without saying that there are other types of challenges that the analyst has to
overcome, mainly by relying on his/her knowledge, insight and set of skills. Hence, one can see the importance of
becoming an independent researcher, thinker and problem solver in the field of time series analysis. That being
said, one of the main goals of this project is to give you an opportunity to experience similar types of challenges
that a time series analyst confronts in the real-world situations.
Further, this project is designed in a way that it can potentially help you obtain the ability to think and make
decisions independently (at least to some extent), and more importantly, learn how to validate the outcomes of
your analysis in lack of any external source for verification. In regard to these points, I have decided not to provide
you with a detailed explanation of the project since this a unique opportunity for you to amalgamate all of your
time series knowledge and apply it to a real problem, and I would rather let you experience every step of this
journey on your own; of course, I will be available during the office hours (general and one-on-one) to provide
you with guidance.
Outline of the Written Project
1. Jupyter Notebook: You are required to prepare your report using the Jupyter notebook and submit a pdf
or html version of the final report on Crowdmark. Please try to organize your report in different sections
and use various available headings and typesetting to embellish on your work.
2. Title and Abstract: Please choose an appropriate title and provide an abstract (in a very high level)
summarizing the entire project, its main points and the most significant findings. You may aim for
maximum 200 words.
3. Introduction: This part introduces the reader to the dataset and to the area to which it pertains. You should
describe why this is an important problem to investigate and give the reader a review of pertinent
background information about the underlying problem. Basically, introduce the reader to the problem and
why it is meritorious of investigation. The introduction should be written at a very basic level (i.e., no
mathematics or notation), and remember that your reader may not know anything about the area in which
you are writing. You may aim for 1-2 pages (1000 words maximum) here. In the introduction, you will
also need to come up with a set of critical questions and try to answer them to the best of your capability.
For instance, you may address the following questions (these are just a few examples and the list is not
exhaustive):
1. Is it possible to forecast the monthly VIX index? What are the reasons in favour or against such
possibility (you may even skim through several articles to see what the experts think about this
problem, but eventually you need to draw your own conclusion).
2. Are the provided past data sufficient to help construct a predictive model for forecasting the VIX
trend?
3. Are there other factors influencing the value of VIX index at every month? If so, is it possible to
omit these additional elements from our analysis and simplify the problem to studying only the
univariate time series of the VIX observations? What would be the main drawbacks of such
simplification?
.
.
.
4. Model Specification: In this section, you want to describe, in clear detail, the data analysis used to specify
your candidate models. Pretend as if you are taking the reader by the hand and leading him/her through
your thought process which leads to your model selections. In doing this, however, try not to overdo the
first-person writing. It can sound less professional and less authoritative if you continually write things
like, “I tried this, and then I tried that ...”
5. Fitting and Diagnostics: This part of the project should describe the model fitting and diagnostics
techniques you used, with the goal of identifying a “final” model for forecasting. Identify also what
possible deficiencies your final model has. Remember, no model is perfect. You will also need to be very
detailed and use your critical thinking to come up and answer questions related to the possible obstacles.
For instance, you may address the following questions (these are just a few examples and the list is not
exhaustive):
1. If the residuals of a model do not follow a white noise, is it still possible to consider the constructed
model as a potential candidate?
2. If the residuals of a model do not follow a normal distribution, is it still possible to consider the
constructed model as a potential candidate? If so, would the estimates of the parameters provided
by the maximum likelihood method still be reliable?
3. Is the Shapiro-Wilk test the only hypothesis test available for investigating the normality of the
residuals? Or, based on the sample size and skewness of the residuals, there might exist more
powerful tests, providing rather different results as compared to the results of Shapiro-Wilk test.
If so, is it worthwhile to employ them within your analytic framework?
.
.
.
6. Forecasting: This section should describe the techniques you used to forecast future observations. Why
is forecasting important? What impacts and implications could your forecasts have?
7. Discussion: Here you want to offer a summary of what you did in the project and draw your main
conclusions. Also, it is a good idea to discuss here other issues related to the data analysis. For example,
does your analysis have any shortcomings or lack of generalization? What were the main problems you
encountered? It is OK if your final model is not picture-perfect as real-life data analysis is often more
difficult than textbook problems.
8. Bibliography: Cite all the references carefully.

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