1 / 17

Comprehensive Guide to Time Series Analysis: Stationary Models, Prediction Techniques, and Applications

Understand the importance of stationary time series, learn methods to convert nonstationary series, dive into Wold decomposition, explore different prediction techniques, and discover various models like AR, ARMA, ARIMA, and more for effective time series analysis. References included.

adenise
Download Presentation

Comprehensive Guide to Time Series Analysis: Stationary Models, Prediction Techniques, and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Time Series Analysis InKwan Yu

  2. Time Series? • A set of observations indexed by time t • Discrete and continuous time series

  3. Stationary Time Series • (Weakly) stationary • The covariance is independent of t for each h • The mean is independent of t

  4. Why Stationary Time Series? • Stationary time series have the best linear predictor. • Nonstationary time series models are usually slower to implement for prediction.

  5. Converting Nonstationary Time Series to Stationary Time Series • Remove deterministic factors • Trends • Polynomial regression fitting • Exponential smoothing • Moving average smoothing • Differencing (B is a back shift operator)

  6. Converting Nonstationary Time Series to Stationary Time Series • Remove deterministic factors • Seasonality (usually combined with trends removal) • Differencing

  7. Converting Nonstationary Time Series to Stationary Time Series • Example

  8. Converting Nonstationary Time Series to Stationary Time Series

  9. Converting Nonstationary Time Series to Stationary Time Series • After conversion, remaining data points are called residuals • If residuals are IID, then no more analysis is necessary since its mean value will be the best predictor

  10. Wold Decomposition • Stationary time series can be represented as the following

  11. Pn is a prediction function of Xn+h with forward lag h from Xn. The prediction error is measured in the minimum mean square Stationary Time Series Prediction

  12. Stationary Time Series Prediction • Since S is a quadratic function, the minimum value will be obtained when all the partial derivatives are 0.

  13. Stationary Time Series Prediction • In another form

  14. Stationary Models • AR (AutoRegressive) • AR’s predictor

  15. Stationary Models • ARMA • Reduces large autocovariance functions • A transformed linear predictor is used

  16. Other Models • Mutivariate Cointegration • ARIMA • SARIMA • FARIMA • GARCH

  17. References • Introduction to Time Series and Forecasting 2nd ed., P. Brockwell and R. Davis, Springer Verlag • Adaptive Filter Theory 4th ed., Simon Haykin, Prentice Hall • Time Series Analysis, James Douglas Hamilton, Princeton University Press

More Related