STAT 910 UPenn

1 Statistics 910: Time Series Analysis Spring 2009 Syllabus Robert Stine Department of Statistics 444 Huntsman Hall / 6302 Oce hours are in the afternoons on the days that we have class, running from about 3:30 to 5 p.m. on Tuesdays and Thursdays. F

Statistics 910, #2 1 Examples of Stationary Time Series Overview 1. Stationarity 2. Linear processes 3. Cyclic models 4. Nonlinear models Stationarity Strict stationarity (Defn 1.6) Probability distribution of the stochastic process {Xt }is invari

Statistics 910, #5 1 Regression Methods Overview 1. Examples of estimation (in R) 2. Main idea: nd stationary component 3. Properties of estimators 4. Comparisons and relative eciencies Idea Decomposition Well-known way to approach time series ana

Statistics 910, #10 1 Covariances of ARMA Processes Overview 1. Review ARMA models: causality and invertibility 2. AR covariance functions 3. MA and ARMA covariance functions 4. Partial autocorrelation function 5. Discussion Review of ARMA process

Statistics 910, #4 1 Properties of Descriptive Estimators Overview 1. Properties of X 2. Simulation of estimator compared to ^ 3. Properties of (h) ^ 4. Simulation of pointwise and \"sequence-wide\" properties See S&S, Appendix A, for further detai

Statistics 910, #6 1 Harmonic Regression Overview 1. Example: variable star data 2. Discrete Fourier transform (periodogram) 3. Examples of the DFT Example: Periodic Data Magnitude of variable star This integer time series is reported to be the ma

Statistics 910 1 Homework #3 Chapter 3, Shumway and Stoffer 3.2 AR(1) process with starting values, initialization (a) Write the process as xt = wt + wt-1 + 2 wt-2 + + t w1 The mean is the sum of the means, E xt = 0 and the variance is t Varxt

Statistics 910, #11 1 Predicting ARMA Processes Overview 1. ARMA models, notation 2. Best linear predictor 3. Prediction equations, Levinsons algorithm 4. Prediction errors 5. Discussion ARMA processes ARMA process A stationary solution {Xt } (or

Statistics 910, #7 1 Regression in Practice Overview 1. Model selection, variable selection 2. Orthogonal case 3. General regression 4. Cross-validation 5. Origins of selection criteria 6. (White estimator, computing) Model Selection in Regression