Box, Jenkins & Reinsel: Time Series Analysis
(This is the book that introduced ARMA models)
Shumway & Stoffer: Time Series Analysis and Its Applications
(ARMA models and Fourier analysis.)
Taylor & Karlin: An Introduction to Stochastic Modeling
(Contains much about finite state Markov models, mostly discreet
time but a little about continuous time processes also.)
West & Harrison: Bayesian Forecasting and Dynamic Models
(Built around the Kalman filter. Hidden Markov Models having
linear normal updates and with (mostly) known parameters.)
Examples covered in the presentation
Regression on two independently simulated time series:
"Water temperature" simulation and estimation with known
variance: R code. The expectation and
auto correlation is here estimated simply by mean and
observational auto correlation. The data I simulated is found
in this file: watertemp_sim.txt.
"Water temperature" simulation and estimation with unknown
variance. ML estimation using "optim": R
Wright-Fisher (single locus with neutral allele) model
Single locus with genotypes with differential fitness - one
stage reproduction and survival simulation: R
Single locus with genotypes with differential fitness - two
stage simulation with reproduction and survival as the separate
stages (hidden component model): R code.
The Kalman filter program used in the presentation was
developed by me and is found here.
The name of the program is layer_analyzer.
The data used can also be found there.
The program uses a program library called
which also has been developed by me.