*Conducted in terms:*2020L, 2021L

*Erasmus code:*14.3

*ISCED code:*0311

*ECTS credits:*3

*Language:*Polish

*Organized by:*Faculty of Economic Sciences

*Related to study programmes:*

# Time Series Analysis 2400-IiE3ASC

Lecture 1

• Introduction, organizational issues.

1. Definition of time series.

Bibliography:

Pawełek, Wanat and Zeliaś (2003/2013), chapter 1

Lecture 2

2. Forecasts and measures of forecast precision.

• Lag operator, differential operator.

Bibliography:

Pawełek, Wanat and Zeliaś (2003/2013), chapter 2

Enders (2014), chapter 1.2

Lecture 3

3. Decomposition of time series:

• classic methods of time series decomposition in additive and multiplicative form into trend, seasonal component, cyclic component and purely stochastic component;

• introduction to programs X-12, TRAMO-SEATS in Demetra or Eviews.

Bibliography:

Gomez V. and A. Maravall (1997), Programs TRAMO and SEATS - Instructions for the User, Banco de Espana

X-12 ARIMA Reference Manual (2011), U.S. Census Bureau

Lecture 4

4. Extrapolative models part 1:

• moving average;

• exponential smoothing.

Bibliography:

Pawełek, Wanat and Zeliaś (2003/2013), chapter 4

Lecture 5

4. Extrapolative models part 2:

• seasonal smoothing;

• Holt and Holt-Winters models.

Bibliography:

Pawełek, Wanat and Zeliaś (2003/2013), chapter 4

Lecture 6

5. Univariate time series – modeling and forecasting part 1:

• stochastic process, deterministic process and time series – definitions,

• weak and strong stationarity of time series;

• white noise.

Bibliography:

Enders (2014), chapter 4.1-4.2

Lecture 7

5. Univariate time series – modeling and forecasting part 2:

• autoregressive process AR(p) and its features;

• moving average process MA(q) and its characteristics;

• autocorrelation and partial autocorrelation functions, correlograms (ACF, PACF).

Bibliography:

Enders (2014), chapter 2.1, 2.2, 2.3

Lecture 8

5. Univariate time series – modeling and forecasting part 3:

• random walk (with/without drift),

• integrated series, integration level, differentiation of series;

• stationarity testing, unit root tests: DF.

Bibliography:

Enders (2014), chapter 4.3-4.7

Lecture 9

5. Univariate time series – modeling and forecasting part 4:

• stationarity testing, unit root tests part II: ADF test, KPSS test.

Bibliography:

Enders (2014), chapter 4.3-4.7

Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, Y. Shin (1992): Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics, 54, pp. 159-178.

Lecture 10

5. Univariate time series – modeling and forecasting part 5:

• ARMA(p,q) models / ARIMA(p,d,q) models;

• stationarity conditions;

• Box-Jenkins procedure;

• information criteria AIC, SBC (BIC).

Bibliography:

Enders (2014), chapter 2.4, 2.5, 2.6.

Lecture 11

5. Univariate time series – modeling and forecasting part 6:

• parameter estimation and model diagnostics;

• Portmanteau test, Box-Pierce and Ljung-Box tests, Jarque-Berra test;

• forecasting in ARMA/ARIMA models.

Bibliography:

Enders (2014), chapter 2.7 – 2.8

Lecture 12

5. Univariate time series – modeling and forecasting part 7:

• stochastic seasonality, deterministic seasonality;

• testing the presence of seasonality (Dickey-Hasza-Fuller test).

Bibliography:

Ghysels E., Osborn D.R., The econometric analysis of seasonal time series, Cambridge University Press, Cambridge 2001., chapter 2, chapter 3

Dickey, D. A., H. P. Hasza, and W. A. Fuller (1984), “Testing for unit roots in seasonal time series,” JASA, 79, 355-367.

H. P. Hasza, and W. A. Fuller (1982),”Testing for nonstationary parameter specifications in seasonal time series models”, The Annals of Statistics 1982, Vol.10, No. 4, 1209-1216

Lecture 13

5. Univariate time series – modeling and forecasting part 8:

• seasonal SARIMA models;

• forecasting seasonal SARIMA models.

Bibliography:

Enders (2014), chapter 2.11

Lecture 14

6. Multivariate time series models part 1:

• long-term relationships;

• cointegration – definition and testing.

Bibliography:

Enders (2014), chapter 6.1-6.2

Engle, R.F. and C.W. J. Granger (1987), “Co-integration and Error Correction: Representation, Estimation, and Testing”, Econometrica, 55, 251-276.

Lecture 15

6. Multivariate time series models part 2:

• cointegration – definition and testing, estimation of cointegrating vector, error correction mechanism models (ECM).

Bibliography:

Enders (2014), chapter 6.3-6.6

Engle, R.F. and C.W. J. Granger (1987), “Co-integration and Error Correction: Representation, Estimation, and Testing”, Econometrica, 55, 251-276.

## Type of course

## Prerequisites (description)

## Course coordinators

Term 2020L: | Term 2021L: |

## Mode

## Learning outcomes

A) Knowledge

The student has knowledge of basic concepts and tools used in the analysis and forecasting of time series.

1. The student knows and understands the concepts of stochastic and deterministic processes as well as time series.

2. The student knows and understands the methods of time series decomposition.

3. The student knows the methods of smoothing using moving averages and exponential smoothing.

4. The student knows and understands the need to smooth seasonal time series.

5. The student knows and understands the concept of seasonality.

6. The student knows basic ARIMA X-12 and TRAMO / SEATS programs.

7. The student knows the concepts of strong and weak stationary.

8. The student knows and understands the basic stochastic processes: autoregressive (AR), moving average (MA) and ARIMA models.

9. The student knows and understands the concept of integration of a time series.

10. The student knows and understands the concept of cointegration and error correction mechanism (ECM).

B) Skills

The student has the ability to independently conduct an econometric study: preparation of time series data, estimation and verification of the model, conducting diagnostic tests and forecasting.

1. The student is able to decompose a time series into elementary components.

2. The student has the ability to generate forecasts for time series and is able to assess their quality.

3. The student can perform stationary tests of a time series and interpret their results.

4. The student has the ability to interpret autocorrelation function (ACF) and partial autocorrelation (PACF)

5. The student is able to use formal statistical tests to assess the integration of a time series.

6. The student has the ability to estimate the parameters of ARIMA class model and obtain forecasts from this model.

7. The student is able to estimate the parameters of a model with cointegration and determine whether the cointegration taking place has economic justification.

C) Social competences

The student is aware of the necessity to verify economic theories by means of empirical data using statistical tests. The student is aware of the continuous increase in the set of possible methods for verification of hypotheses.

1. The student is aware that economic theories are controversial and that it is necessary to confront them with empirical data using the tools listed above.

2. The student is able to analyze basic economic phenomena on the basis of available or collected empirical data and verify the hypotheses associated with them. He can draw conclusions about important social and economic issues from them, predict the behavior of these phenomena.

3. The student is aware that the analysis of time series has wide application in economics.

KW01, KW02, KW03, KU01, KU02, KW03, KK01, KK02, KK03

## Assessment criteria

- the absence limit is 3

- performance of an empirical written assignment involving the analysis of real time series data (50%),

- passing a written exam (50%),

- an additional condition is obtaining at least 50% of points from the empirical written assignment and at least 50% of points from the exam

The empirical written assignment should be submitted::

a) electronic version no later than on 23:59 the day preceding the last day of classes for the subject

and

b) paper version during the last class.

The empirical written assignment should be submitted for retake session:

a) electronic version and paper version until the first day of the retake session.

Failure to meet the above deadlines results in the inability to pass the subject.

## Bibliography

Enders W. (2014), Applied Econometric Time Series, Wiley.

Ghysels E., Osborn D.R. (2001), The econometric analysis of seasonal time series, Cambridge University Press.

Gomez V. and A. Maravall (1997), Programs TRAMO and SEATS - Instructions for the User, Banco de Espana.

X-12 ARIMA Reference Manual (2011), U.S. Census Bureau.

Pawełek B., Wanat S., Zeliaś A. (2003/2013), Prognozowanie ekonomiczne – Teoria, przykłady, zadania, PWN.

Articles:

Dickey, D. A., H. P. Hasza, and W. A. Fuller (1984), “Testing for unit roots in seasonal time series,” JASA, 79, 355-367.

Engle, R.F. and C.W. J. Granger (1987), “Co-integration and Error Correction: Representation, Estimation, and Testing”, Econometrica, 55, 251-276.

H. P. Hasza, and W. A. Fuller (1982),”Testing for nonstationary parameter specifications in seasonal time series models”, The Annals of Statistics 1982, Vol.10, No. 4, 1209-1216.

Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, Y. Shin (1992): Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics, 54, pp. 159-178.

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
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