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Time Series Analysis Course

Learn about probability theory, stationarity, models for time series, forecasting, spectral analysis, and more in this comprehensive time series analysis course.

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Time Series Analysis Course

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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 Biol 125 • 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. Some examples of Time series data

  8. IBM Stock Price (closing)

  9. Time Sequence plot

  10. Concentration of residue after production of a chemical

  11. Time Sequence plot

  12. Yearly sunspot activity (1770 -1869)

  13. Time Sequence plot

  14. Time Sequence Plots

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

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

  17. Generating observations from a distribution

  18. 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

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

  20. 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)

  21. 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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