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Time Series Analysis Course by W.H. Laverty at University of Saskatchewan

Learn fundamental Time Series Analysis concepts, models, and forecasting techniques. Explore State-Space modeling and Spectral Analysis.

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Time Series Analysis Course by W.H. Laverty at University of Saskatchewan

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  1. Statistics 349.3(02) Analysis of Time Series

  2. Course Information • Instructor: • W. H. Laverty • 235 McLean Hall • Tel: 966-6096 Email: laverty@math.usask.ca • Class Times • MWF 12:30-1:20pm AGRI 1E69 • Mark break-up • Final Exam – 60% • Term Tests and Assignments – 40%

  3. Course Outline 1. Introduction and Review of Probability Theory • Probability distributions, Expectation, Variance, correlation • Sampling distributions • Estimation Theory • Hypothesis Testing

  4. Course Outline -continued 2. Fundamental concepts in Time Series Analysis • Stationarity • Autocovariance function, autocorrelation and partial autocorrelation function 3. Models for Stationary Time series • Autoregressive (AR), Moving average (MA), mixed Autoregressive-Moving average (ARMA) models 4. Models for Non-stationary Time series • ARIMA (Integrated Autoregressive-Moving average models)

  5. Course Outline -continued 5. Forecasting ARIMA Processes 6. Model Identification and Estimation 7. Models for seasonal Time series 8. Spectral Analysis of Time series

  6. Course Outline -continued 9. State-Space modeling of time series, Hidden Markov Model (HMM) • Kalman filtering 10. Multivariate (Multi-channel) time series analysis 11. Linear filtering

  7. Comments • The Text Book • Time Series Analysis: Univariate And Multivariate Methods Wei (Paperback - 2006 Ed. 02) Recommended • I will present the material in power point slides that will be available on my web site. • Hopefully this makes purchasing the text book optional. It is useful for students to purchase text books and build up a library.

  8. Some examples of Time series data

  9. IBM Stock Price (closing)

  10. Time Sequence plot

  11. Concentration of residue after production of a chemical

  12. Time Sequence plot

  13. Yearly sunspot activity (1770 -1869)

  14. Time Sequence plot

  15. Time Sequence Plots

  16. Example Measuring brain activity in an insect as an object is approaching. Time t = 0 is at the point of impact.

  17. Simulation To aid in the understanding of time series it is useful to simulate data

  18. Generating observations from a distribution

  19. Generating a random number from a distribution Let • f(x) denote the density function • F(x) denote the cumulative distribution function = P[X ≤ x] • F-1(x) denote the inverse cumulative distribution function

  20. f(x) F(x) denote the cumulative distribution function F(x) x

  21. f(x) u F(x) denote the cumulative distribution function F-1(u) If u is chosen at random from 0 to 1 then x = F-1(u) is chosen at random from the density f(x). In EXCEL the following function generates a random observation from a normal distribution. = NORMINV(RAND(), mean, standard deviation)

  22. Example Random walk A random walk is a sequence of random variables {xt} satisfying: xt = xt – 1 + ut where {ut} is a sequence of independent random variables having mean 0, standard deviation s. (usually normally distributed) The excel functions • NORMINV(prob, mean, standard deviation) computes F-1(prob) for the normal distribution. • RAND() computes and random number from the Uniform distribution from 0 to 1. • NORMINV(RAND(), mean, standard deviation) computes and random number from the Normal distribution with a given mean and standard deviation.

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