Time Series Methods

Course Outline

Day 1
Models prior to testing for serial correlation
⁃ ⁃Regression, Trends, Seasonality review
⁃ ⁃How to build a good regression model
⁃ ⁃Residuals analysis
⁃ ⁃Trend analysis with sin and cos terms

Time Series Fundamentals
Types of Data, Objectives, Graphics
What is serial correlation? How to test for it?
Effects of autocorrelation on hypothesis tests
Effective sample size

Time series analysis
1 Nonparametric Tests of temporal correlation
2 Parametric Tests of temporal correlation
3 Autocorrelation function
4 Partial autocorrelation functions
5 Diagnostic plots: ACFs and PACFs
6 ACF when some data are missing

Day 2
Time series models
01 Generalized Least Squares method
02 Determining the 'best' correlation structure
03 ARMA models
04 Model estimation
05 Correction of p-values for the correlation structure

Multivariate Time Series
01 Basic concepts
02 Cross Correlation Function
03 Computation & Significance of the CCF

Estimating a WQ variable from another, frequently measured variable
01 Problems with using regression for forecasts and record fill-in
02 Line of Organic Correlation vs classical linear regression
03 Individual estimates vs. forecasting a collection of data (percentiles)
04 Comparisons to standards and 1:1 lines

Bootstrap methods for time series

01 ARMA models for forecasting

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