STAT3011 Lecture Notes - Lecture 1: Estimation Theory, Final Examination, Scion Tc
23 Jun 2018
School
Department
Course
Professor
STAT3011/3911 - Stochastic Processes and Time Series - 2018, Semester 1
Section I - Time Series Analysis: Weeks 1-6
Section I - Time Series Analysis: Weeks 1-6
Lecturer: Associate Professor Shelton Peiris, Carslaw 819 - Ext 15764
General Information for Time Series Analysis - Section I
•In 2018, lectures on Time Series Analysis section (Section I of STAT3013/3913) will begin in
Week 1. Therefore, the first lecture will be given on Monday, 5 March.
•The weekly tutorials and practicals will begin on Friday, 16 March in Week2 and end on Friday
20 Apri in Week6. Practical examination will be held on Friday 27 April in week7.
•Classes are in common for both STAT3011 and STAT3911.
Objectives: Establish some methods of modelling and analysing of time series data (ie. data
containing serially dependence structure). We consider a number of standard procedures on iden-
tification, estimation, dignostic model checking decision making and prediction. Some real world
applications will be discussed. The R statistical package will be used to analyse time series data.
Outcomes: Successful completion of this unit, students will be able to:
(1) Identify a time series and its various components,
(2) Apply standard transformations to smooth a time series,
(3) Identify Stationary and homogeneous non-stationary time series,
(4) Understand autocorrelation and partial autocorrelation functions,
(5) Identify suitable ARMA and ARIMA models for given time series data,
(6) Estimate all relevant aarameter of a proposed model,
(7) Understand diagnostic checking procedures and forecasting methodology,
(8) Apply the statistical package R to model and forecast time series data in practice.
1
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Approximate Outline for the Time Series Component
Weeks Topics
1 Time series data, components of a time series.
Filtering to remove trends and seasonal components.
2 Stationarity time series.
Sample autocorrelations and partial autocorrelations.
Probability models for stationary time series.
Moving Average (MA) models and properties.
3 Invertibility of MA models.
Autoregressive (AR) models and their properties.
Stationarity of AR models.
Mixed Autoregressive Moving Average (ARMA) models and their properties.
4Homogeneous nonstationary time series (HNTS). Simple moedls for HNTS.
Autoregressive Integrated Moving Average (ARIMA) models and related results.
Review of theoretical patterns of ACF and PACF for AR, MA and ARMA processes.
Identification of possible AR, MA, ARMA and ARIMA models for a set of time series data.
5Estimation and fitting ARIMA models via MM and MLE methods.
Hypothesis testing, diagnostic checking and goodness-of-fit tests. AIC for ARIMA models.
Forecating methods for ARIMA models.
6Minimum mean square error (mmse) forecasting and its properties.
Derivation of l-step ahead mmse forecast function. Forecast updates.
Forecast errors, related results and applications.
Assessment
Section I - Time Series Analysis - 50% as given below:
1 tutorial quiz (Wednesday, 18 April) 10%
4 Computer practicals (weeks 2-6) 5%
(4% (active class participation)+ 1% (submission by 23.59 same day ))
1 Computer exam (week 7) 5%
Final examination in June 30%
References
Chatfield, C. (1996) The Analysis of Time Series: An Introduction. (5th Ed) Chapman and Hall,
London.
Box, G.E.P. ¯and Jenkins, G.M. (1976). Time Series Analysis, Forecasting and Control.
Holden-Day, Oakland.
Brockwell, P.J. and Davis, R.A. (1996). Introduction to Time Series and Forecasting. Springer, New
York.
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STAT3011/3911 - Stochastic Processes and Time Series Analysis
Section I - TIME SERIES ANALYSIS
Preliminary notes from TIME SERIES CONCEPTS & METHODS - M.S.Peiris (2013) c
1 Basic Concepts in Time Series
A time series is a set of observations taken sequentially at specified times.
Examples of time series occur in variety of fields ranging from economics to engineering.
Examples:
(1) Monthly Australian red wine sales: January 1980 - July 1995.
(2) Sales of a Company in successive 4-week periods. 1967-1970. Chatfield, 2nd ed., (1980).
(3) IBM common stock closing prices: daily, 29th June 1959 to 30th June 1960 (N=255). Box & Jenkins
(1976).
The above data are given below:
(1)
464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565
1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722
832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753 2258 1208
1241 1265 1828 809 997 1164 1205 1538 1513 1378 2083 1357 1536 1526 1376 779 1005 1193 1522
1539 1546 2116 2326 1596 1356 1553 1613 814 1150 1225 1691 1759 1754 2100 2062 2012 1897 1964
2186 966 1549 1538 1612 2078 2137 2907 2249 1883 1739 1828 1868 1138 1430 1809 1763 2200 2067
2503 2141 2103 1972 2181 2344 970 1199 1718 1683 2025 2051 2439 2353 2230 1852 2147 2286 1007
1665 1642 1518 1831 2207 2822 2393 2306 1785 2047 2171 1212 1335 2011 1860 1954 2152 2835 2224
2182 1992 2389 2724 891 1247 2017 2257 2255 2255 3057 3330 1896 2096 2374 2535 1041 1728 2201
2455 2204 2660 3670 2665 2639 2226 2586 2684 1185 1749 2459 2618 2585 3310 3923
(2)
153 189 221 215 302 223 201 173 121 106 86 87 108 133 177 241 228 283 255 238 164 128 108 87 74
95 145 200 187 201 292 220 233 172 119 81 65 76 74 111 170 243 178 248 202 163 139 120 96 95 53 94
(3)
445 448 450 447 451 453 454 454 459 440 446 443 443 440 439 435 435 436 435 435 435 433 429 428
425 427 425 422 409 407 423 422 417 421 424 414 419 429 426 425 424 425 425 424 425 421 414 410
411 406 406 413 411 410 405 409 410 405 401 401 401 414 419 425 423 411 414 420 412 415 412 412
411 412 409 407 408 415 413 413 410 405 410 412 413 411 411 409 406 407 410 408 408 409 410 409
405 406 405 407 409 407 409 425 425 428 436 442 442 433 435 433 435 429 439 437 439 438 435 433
437 437 444 441 440 441 439 439 438 437 441 442 441 437 427 423 424 428 428 431 425 423 420 426
418 416 419 418 416 419 425 421 422 422 417 420 417 418 419 419 417 419 422 423 422 421 421 419
418 421 420 413 413 408 409 415 415 420 420 424 426 423 423 425 431 436 436 440 436 443 445 439
443 445 450 461 471 467 462 456 464 463 465 464 456 460 458 453 453 449 447 453 450 459 457 453
455 453 450 456 461 463 463 461 465 473 473 475 499 485 491 496 504 504 509 511 524 525 541 531
529 530 531 527 525 519 514 509 505 513 525 519 519 522 522
To see more time series data, visit:
http://www.maths.usyd.edu.au/u/shelton/tsdata.html
3
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Document Summary
Stat3011/3911 - stochastic processes and time series - 2018, semester 1. Section i - time series analysis: weeks 1-6. Lecturer: associate professor shelton peiris, carslaw 819 - ext 15764. General information for time series analysis - section i: in 2018, lectures on time series analysis section (section i of stat3013/3913) will begin in. Therefore, the rst lecture will be given on monday, 5 march: the weekly tutorials and practicals will begin on friday, 16 march in week2 and end on friday. Practical examination will be held on friday 27 april in week7: classes are in common for both stat3011 and stat3911. Objectives: establish some methods of modelling and analysing of time series data (ie. data containing serially dependence structure). We consider a number of standard procedures on iden- ti cation, estimation, dignostic model checking decision making and prediction. The r statistical package will be used to analyse time series data. Time series data, components of a time series.
