Stat 436: Time Series Analysis

This course is an introduction to time series analysis. Where we try to Identify their components, and to modelling them mathematically using appropriate methods. In this course we use computer programs extensively to analyze data and write reports on the findings.

Course Cataloge:

Week                                                                               Subjects
    1
 
Introduction-examples of time series data- goals of time series analysis- measuring forecasting errors-choosing the appropriate method for forecasting- types of change in time series
    2
 
Covariance function-autocorrelation function (importance – estimation)- form of the ACF for some cases (non-stationary series , oscillating series, seasonal series)- partial autocorrelation function- estimating the PACF
    3 Time series operators (backshift operator, difference operator), using the difference operator for non-stationary series in the mean- variance stabilizing transformations-Box-Cox transformations
    4 Stochastic time series models- meaning of linearity in regression models and in time series models-white noise process- stationarity of W.N. process- general linear process- invertibility formula- white noise formula- autoregressive processes (AR)- autoregressive process of order one (stationarity condition, ACF, PACF)
    5
 
AR(2) (stationarity conditions, ACF, PACF)-  general AR(p)- moving average processes (MA)- MA(1) (invertibility condition, ACF, PACF)
    6 MA(2) (invertibility condition, ACF, PACF)- general MA(q)- ARMA(p,q) models- ARMA(1,1) model (stationarity condition, invertibility condition ACF, PACF)- integrated ARIMA(p,d,q) models
    7 Parameter estimation- moments method - estimating WN variance- least squares method
    7 First Midterm exam – exact date and time will be announced later
    8 Forecasting – minimum mean square error forecast- forecasting for AR(1), MA(1) , some results for the general ARMA(p,q), forecast error variance- constructing confidence limits for the forecasts-updating the forecasts
    9
 
Box-Jenkins methodology- design and construction of forecasting model- model identification- choosing difference order- choosing model order- checking model validity- diagnostics- residual analysis- criteria for choosing the best model (AIC, BIC)- first differences of the residuals- analysis of higher (lower) order models
   10 Seasonal models- seasonal autoregressive models- moving average models- mixed seasonal models- multiplicative seasonal models
 
  11 Seasonal models- seasonal autoregressive models- moving average models- mixed seasonal models- multiplicative seasonal models
  12 Applications of time series analysis in the lab
  12 Second Midterm exam– exact date and time will be announced later
   13 Applications of time series analysis in the lab
   14 Applications of time series analysis in the lab.
  (Provide students with a data set to analyze and write a report on their findings)
   15 Applications of time series analysis in the lab
   16 Review – (Deadline to hand in the data analysis report)
Course Materials