Quantitative methods of market forecasting (commodities ...€¦ · Quantitative methods of market...

National Research University «Higher School of Economics»

“Quantitative methods of market forecasting” – Course syllabus

Bachelor’s program 38.03.05 “Business informatics”

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The Government of the Russian Federation

The Federal State Autonomous Institution of Higher Education “National Research University – Higher School of Economics”

Faculty of Business and Management

School of Business Informatics

Department for Management of Information Systems and Digital Infrastructure

Quantitative methods of market forecasting (commodities and stock

markets)


Author: S.V. Petropavlovsky, associate professor

[email protected]

Approved at the meeting of the

Department for Management of Information Systems and Digital Infrastructure

«___»____________ 2017

Head of Department

_______________ / E.A. Isaev /

Approved by the Academic Council of Business Informatics

«___»____________ 2017

Chairman

_______________/ A.V. Dmitriev

Moscow, 2017

The document cannot be used by other HSE departments as well as other universities and

educational institutions without permission from the course authors

http://www.hse.ru/text/image/4011945.html

mailto:[email protected]




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1. Applicability and Normative References

The program provides the contents of the course and describes the learning outcomes,

competences and practical skills obtained upon completion of the course. It also sets pre-

requisites for taking the course and provides criteria for assessing students’ performance. The

program is designed for instructors teaching the course, teaching assistants and undergraduate

students following educational track 38.03.05 "Business Informatics", Bachelor’s level.

2. Course Objectives

The course provides a theoretical background of financial time series analysis and aims at

developing practical skills of acquisition, processing and interpretation of the financial data.

3. Course Description

"Quantitative methods of market forecasting" is an elective course taken in the 4th

academic year

of the Bachelor’s program. The course focuses on the basic as well as more advanced

econometric models explaining the structure of the financial time series. We start with the

definition of asset returns and review their basic properties. Then we consider the simple linear

models for asset returns such as the autoregressive AR(p) and moving average MA(q) models,

combined ARMA models, the unit-root processes, exponential smoothing and the ARIMA(p,q)

models. For each model, the processes of identification, estimation, verification and forecasting

are described in detail and illustrated by examples. Some additional topics such as handling

seasonality and long-memory effects are also addressed in this section.

A significant attention is paid to the non-linear time series in the context of volatility

modeling. The ARCH/GARCH processes are studied in detail including various extensions of

these models. As an alternative to the ARCH/GARCH paradigm, we introduce and briefly

discuss the stochastic volatility models.

The applications of volatility modeling such as option pricing, term structure of interest

rates and portfolio management are demonstrated. However, the emphasis in the applications is

put on the risk management, more specifically, on the measures of risk such as value at risk

(VaR) and expected shortfall. The course provides a comprehensive description of computing,

interpreting and backtesting the VaR indicator. Among other approaches, we introduce the

extreme value theory to compute the VaR.

A considerable portion of the course is devoted to modeling the high frequency data.

Specifically, we introduce and discuss the models for price changes (ordered probit model and

some others), duration models (the ACD model), and the concept of realized volatility.

As a natural generalization of simple linear models, we discuss the multivariate time

series at the introductory level. We focus on the notion of the cointegrated time series which

provides a theoretical framework for algorithms of statistical arbitrage used in automated trading

systems, in particular, pairs trading.

In the last part of the course some non-econometric methods for classification and

prediction in the financial markets are analyzed. In particular, machine learning algorithms such

as regression trees, support vector machines, neural networks and multivariate adaptive

regression splines are applied for building a prototype of an on-line trading system.

The students are supposed to use the R language for implementing the algorithms

throughout the course (but not limited to), so a brief introduction to R is done at the very

beginning. The duration of the course is one module. The course is taught in English and worth

4 credits.





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4. Learning Outcomes and Competencies

At the end of the course, students should:

Be aware of:

the need, basic concepts and applicability of models used in financial econometrics;

the details of implementing the models of financial econometrics in R.

Be able:

to download and pre-process market data;

to select the model and identify it;

to estimate the parameters of the model;

to make forecasts with the help of the model;

to interpret the results of the forecast and use them in the decision-making process.

Learn how to:

search for, select and download market data for the subsequent prediction;

process market data using modern software;

make predictions regarding the risk and returns of assets

present the results of the analysis.

Pre-requisites:

Programming (R is a plus but not essential), mathematics (algebra and calculus), probability

theory and statistics. Good command of English.

Competencies:

Competencies

Code

accord- ing to

Federal

standard/HSE

Descriptors – basic signs of

mastering (indicators of

achieving a result)

Ways and methods of

teaching leading to

formation and development

of the competencies

Being able to explicate the scientific essence of problems in the professional field

СК-1 Mastering and using Lectures, practice in computer labs, preparation of class and home assignments

Being able to solve problems in the professional field on the basis of analysis and synthesis

СК-Б4 Mastering and using Lectures, practice in computer labs, preparation of class and home assignments





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Being able to realize scientific and practical activities in international environment

СК-Б11

Mastering and using Lectures, practice in computer labs, preparation of class and home

assignments

Being able to control and develop the content of an enterprise and Internet- resources, to control the processes of creating and using information services

ПК-13 Mastering and using Lectures, practice in computer labs, preparation of class and home assignments

Consulting with respect to the rational choice of methods and tools for con- trolling the IT-infrastructure of an enterprise


Being able to use the relevant mathematical and technical tools for processing, analysis and systematization of data on the topic of research


Being able to prepare scientific reports and presentations


5. Role of the course in the curriculum The course is a part of major (professional) block of disciplines. It is an elective course. The

course is based on a number of preceding disciplines:

Calculus;

Linear Algebra;





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Micro- and Macroeconomics, Financial Management;

Probability Theory and Statistics;

Modeling of processes and systems

The concepts and methods provided by the current course may be helpful in studying the

subsequent courses such as:

Analysis of business processes;

Fractal analysis of market data;

Semantic informational systems;

6. Course Structure and Contents

6.1. Course Structure

№ Topic

In-class hours

Self-

study Total

Lectures

Practice

in

computer

labs

Total

1st module

1. Introduction to R 2 2 4 5 9

2. Properties of Asset Returns 2 2 4 10 14

3. Linear Models for Financial Time

Series 6 6 12 10 22

4. Multivariate Linear Time Series 4 4 8 10 18

5. Volatility Models 4 4 8 10 18

6. Applications of Volatility Models 4 4 8 5 13

7. High Frequency Financial Data

4 4 8 10 18

8. Value at Risk 2 2 4 10 14

9. Machine Learning Algorithms in

Finance 4 4 8 10 18

Total 32 32 64 80 144

6.2. Syllabus

Topic 1. Introduction to R.

Data objects in R, installing and using packages. Loading data from local files and on-line

databases. Plotting data in R. Advanced graphics. Time series objects. Overview of basic

statistics in R. Major programming constructs: conditional operators, loops, functions.

Reading:

1. Core Text: [2]

2. Further Reading: [5]





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Topic 2. Properties of Asset Returns

The time value of money: future value, present value, multiple compounding periods, eff ective

annual rate. Asset return calculations. Portfolio returns. Average returns. Continuously

compounded returns.

Reading:

1. Core Text: [2]


Topic 3. Linear Models for Financial Time Series

Stationarity of a time series. Correlation and autocorrelation functions. White noise and linear

time series.

Autoregressive (AR) models. Properties of AR models. Identifying AR models in practice.

Goodness of fit. Forecasting under AR models.

Moving average (MA) models. Properties of MA models. Identifying MA models in practice.

Estimation. Forecasting using MA models.

Mixed ARMA models. Properties of the ARMA(1,1) models. General ARMA models.

Identifying ARMA models. Forecasting under the ARMA models. Different representations of

the ARMA model.

Unit-root non-stationarity. Random walks. Trend-stationary time series. General unit-root non-

stationary models. Unit-root test.

Exponential smoothing.

Seasonal models. Seasonal differencing. Multiplicative seasonal model. Seasonal dummy

variable.

Regression models with time series errors. Long-memory models.

Model comparison and averaging. In-sample and out-of-sample comparison.

Reading:

1. Core Text: [2]


Topic 4. Multivariate Linear Time Series

Review of univariate analysis of stationary time series. AR(p) time series process. MA(q) time

series process. ARMA(p, q) time series process.

Multivariate analysis of stationary time series characteristics. Vector autoregressive model.

Specification, assumptions and estimation. Diagnostic tests, causality analysis. Forecasting.





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Structural vector autoregressive model. Specification, assumptions and estimation. Forecast error

variance decomposition. Non-stationary time series. Unit root processes. Long-memory

processes.

Cointegration and common trends. Spurious regression. Concept of cointegration and error-

correction models. Systems of cointegrated variables. Granger's representation theorem.

Statistical inference for cointegrated systems. Statistical arbitrage. Formation of cointegration

pairs. Trading with cointegration pairs.

Reading:

1. Core Text: [3]


Topic 5. Volatility Models.

Characteristics of volatility. Structure of a model. Testing for ARCH effect.

The ARCH Model. Properties of the ARCH models. Building and using an ARCH model.

Examples.

The GARCH Model. Forecasting evaluation. A two-pass estimation method. The integrated

GARCH model. The GARCH-M model. The exponential GARCH model. The threshold

GARCH model. Asymmetric power ARCH model. Non-symmetric GARCH model.

The stochastic volatility model.

Reading:

1. Core Text: [2]


Topic 6. Applications of Volatility Models

GARCH volatility term structure. Option pricing and hedging. Time dependent correlations and

betas. Minimum variance portfolios.

Reading:

1. Core Text: [2]

2. Further Reading: [4,5]





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Topic 7. High Frequency Financial Data

Nonsynchronous trading. Bid–ask spread of trading price. Empirical characteristics of high

frequency trading data.

Models for price changes. Ordered probit model, decomposition model.

Duration models. Diurnal component, the ACD model.

Realized volatility. Handling microstructure noises.

Reading:

1. Core Text: [2]


Topic 8. Value at Risk

Risk measure and coherence: Value at Risk (VaR), expected shortfall. JP Morgan’s Riskmetrics,

multiple positions. Econometric approach. Quantile estimation, quantile and order statistics.

Quantile regression. Extreme value theory, application to asset returns. An extreme value

approach to VaR. Multiperiod VaR. Peaks over thresholds: statistical theory, mean excess

function, estimation. The stationary loss processes.

Reading:

1. Core Text: [2]


Topic 9. Machine Learning Algorithms in Finance

Types of machine learning algorithms. The limits of machine learning.

Classification using Nearest Neighbors algorithm: measuring similarity with distance, choosing

an appropriate number of neighbors, preparing data for use with k-NN. Examples of k-NN

algorithm.

Probabilistic learning using Naive Bayes approach: the basic idea, the Laplace estimator,

numerical features of the Naive Bayes approach. Examples (filtering out spam, etc).

Classification using decision trees and rules. Divide and conquer algorithm. The 1R algorithm.

The RIPPER algorithm. Boosting the accuracy of decision trees, pruning the trees. Bagging

classification. Random forests. The Gini index. Advantages and disadvantages of trees.

Black box methods. Neural networks. Activation functions. Network topology. Training a model

on the data. Evaluating and improving model performance. Support vector machines.





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Classification with hyperplanes (linearly and non-linearly separable data). Using kernels for non-

linear spaces.

Reading:

1. Core Text: [5]

2. Further Reading: [1-3]

7. Reading List

A. Core Texts

1. J. Verzani, Using R for Introductory Statistics, Second Edition, Chapman & Hall/CRC The

R Series, Taylor & Francis, 2014. URL https://books.google.ru/books?id=O86uAwAAQBAJ

2. R. Tsay, An Introduction to Analysis of Financial Data with R, John Wiley & Sons, Inc.,

2013.

3. R. Tsay, Multivariate Time Series Analysis With R and Financial Applications, John Wiley &

Sons, Inc., 2014.

4. Brett Lantz, Machine Learning with R, Second Edition, Packt Publishing, 2015.

B. Further reading

1. J. Ross Quinlan. Induction of decision trees. Machine learning, 1(1): 81–106, 1986.

2. Anthony, M. & Bartlet, P. Neural Network Learning: Theoretical Foundations,

Cambridge University Press, 1999.

3. Barber, D. Bayesian reasoning and machine learning, Cambridge University

Press, 2012.

4.Bernhard Pfaff, Analysis of Integrated and Cointegrated Time Series with R, Springer, 2008.

5. N. Chan, Time Series Applications to Finance with R and S-Plus, Second Edition, John Wiley

& Sons, Inc., Hoboken, New Jersey, 2010.

8. Assessment of student’s performance

Type of

assessment

Means of assessment 3 year

1 2 3 4

Pre-exam test

(last week of

module 1)

Computer-based

assignment

*

Final Exam *


https://books.google.ru/books?id=O86uAwAAQBAJ




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8.1. Criteria of assessment

To successfully pass the pre-exam test, the students should be able to solve the problems that

were discussed in class. To pass the final exam, the students should demonstrate the knowledge

of basic concepts of financial econometrics and ability to implement them in practice.

8.2. Topics suggested for the pre-exam test

Computer-based assignments on Topics 1-9.

8.3. Sample concept questions for final exam

1. Basic properties of the AR models. Identification, estimation and forecasting under the AR

model.

2. Basic properties of the MA models. Identification, estimation and forecasting under the MA

model.

3. Basic properties of the ARMA models. Identification, estimation and forecasting under the

ARMA model..

4. Unit-root process.

5. Basic properties of the ARIMA models. Identification, estimation and forecasting under the

ARIMA model.

6. Handling seasonality under the linear models.

7. Handling long-memory effects under the linear models.

8. The idea of exponential smoothing.

9. Vector autoregressive models: specification, assumptions and estimation.

10. Vector autoregressive models: diagnostic tests, causality analysis.

11. Vector autoregressive models: forecasting.

12. Structural vector autoregressive models: specification, assumptions and estimation.

13. Structural vector autoregressive models: forecast error variance decomposition.

14. Unit root processes.

15. Cointegration and common trends.

16. Statistical arbitrage. Trading with cointegration pairs.

17. Properties of the ARCH model.

18. Properties of the GARCH model.

19. Extensions of the GARCH model.

20. Models for intraday price changes.

21. Duration models for high frequency trading.

22. Computation and backtesting of VaR.

23. Nearest Neighbors algorithm for classification and its use in financial modeling.

24. Probabilistic learning: naive Bayes approach.

25. Decision trees and their use in financial modeling.

26. Basic concepts of neural networks and their use in financial modeling.

27. Support vector machine algorithms.

The final exam is computer based and lasts for 90 minutes. The assignment consists of two

concept questions and two practical tasks.





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8.3. Sample practice assignments for final exam

Problem 1 .

1 . Use getSymbols command of quantmod package to download data on some

commodity such as oil, gold, wheat, etc from Federal Reserve Economic Data cite

( http://research.stlouisfed.org/fred2/ ) .

2. Clearly state in your report what kind of data you are using (daily, monthly etc) .

3. Check for the missing data and remove the respective entries from the dataset, if any. You

may use the following script as an example: getSymbols ( ` GOLDAMGBD228NLBM ' , src= ' FRED ' )

idx < - c ( 1 : nrow (GOLD) ) [i s . na (GOLD) ]

GOLD <- GOLD [- idx]

If you did find the missing data, make a comment on this in your report.

4. Compute and plot the log price xt and the log return rt (in the same figure). Comment on

the two plots (how volatile the data are, volatility clustering, outliers etc).

5. Compute and plot the first 12 lags of ACF of xt. Comment on the plot. Based on the ACF,

is there a unit root in xt dataset? Why?

6. Consider the time series for rt. Perform the Ljung-Box test for m = 12. Make a conclusion

and back it with the statistical language, i.e. , in terms of critical region or p-value.

7. Use the command ar (rt , method=”mle” , order . max=20) to specify the

order of an

AR model for rt. State clearly the criterion you are using. Compare your selection with the

analysis of partial ACF. Use pacf (rt,lag= 12) command.

8. Build an AR model for rt. Check the model analyzing the ACF and the Ljung-Box statistics

of the residuals. Plot the time series of the residuals, ACF and p-values of the Ljung-Box. Is

the model adequate? Why? Refine the model by eliminating all estimates with t-ratio less

than 1.645 and check the new model as described above. Is the new model adequate? Why?

Write down the final model.

9. Does the model imply existence of a cycle? Why? If the cycles are present, compute the

average length of these cycles.

10. Use the fitted AR model to compute 1-step to 4-step ahead forecasts of rt at the forecast

origin corresponding to the last date of the time series. Also, compute the corresponding

95% interval forecasts. Plot these results.

9. Grading

The formula for the final grade finO

fin accm exam0.7 0.3O O O

is comprised of the grade accmO accumulated over the module and the grade examO for the final

exam. The accumulated grade accmO is calculated as follows:

accm HA MT0.6 0.4O O O

where HAO and MTO are the grades for the home assignments and the pre-exam test,

respectively.


http://research.stlouisfed.org/fred2/




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10. Software and Technical Tools

R, RStudio, Python, Matlab, Microsoft Excel

11. Recommendations for instructors In general, lectures should give insight into the concepts and ideas underlying the topic under

review. The theoretical core of presentation should be preceded and followed up by clear

examples. The lecture slides may contain pieces of (quasi) code illustrating implementation of

the algorithms in some programming language (presumably, in R). It is highly recommended to

provide students with the lecture slides prior to the lecture so that they could familiarize

themselves with the material in advance and prepare some questions. The lecturer should refer

the students for technicalities to the recommended textbooks, reviews and papers as needed

throughout the presentation.

Practice classes play the key role in providing the course. The instructor should focus on the

implementation of data analysis algorithms on computers. The difficult tasks should be

discussed and worked out together with students. The tasks being discussed should be close to

those of home assignment so as students could solve similar problems on their own. The students

are supposed to prepare a report on a particular home assignment and submit it to the instructor

electronically or in paper form. Some requirements for these reports may be set, e.g.:

The questions should be addressed in the same order they appear in the assignment. The

text of the question must be retained and placed before each answer. The working

language is English.

The answer to a particular question may take a form of a plot, formula etc followed by a

brief explanation and a conclusion. All conclusions must be justified numerically, i.e., by

some computed quantities, plots, etc. The answers do not need to be lengthy but they

must be convincing in mathematical and statistical sense, i.e., in terms of some

quantitative measures.

Each student must use a unique data set. It is the student’s responsibility to make sure that

no one else is using the same data. To facilitate the distribution of datasets among the

students, the instructor can create an editable shared check-in list on Google Drive or

some other cloud resource.

The deadlines for the reports should be clearly specified.

The instructor should notify the students about the penalties for late submission of the

reports.

The solutions should normally contain code in R or some other language.

It is good practice to suggest the students some datasets for the home assignments. For example,

a great amount of market data can be found at Yahoo Finance, Google Finance, Federal Reserve

Economic Data repository http://research.stlouisfed.org/fred2/ and so on. Other possible data

sources include the JSE archive http://ww2.amstat.org/publications/jse/jse_data_archive.htm, a

huge repository at https://www.data.gov/ and a list of freely available sources at

http://guides.emich.edu/data/free-data. Remarkably, most of these data can be downloaded in R

directly by using the respective functions which should be pointed out to students.


http://research.stlouisfed.org/fred2/

https://www.data.gov/




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12. Recommendations for students

When completing homework assignments, first read the lecture slides and the recommended

textbook. Then think a little and try some problems and then read and think some more. This

procedure should be iterated until the problem becomes clear. You should not spend much time

on pure reading with no practice but, at the same time, you should not tackle a problem without

understanding of the underlying theory. Plan your timetable so that to do the homework shortly

after the lecture and/or practice class so as to keep the basic ideas fresh in your mind.

Author of the program:

Associate professor Sergey V. Petropavlovsky


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