Stat 336 – Time Series Analysis

Week	Subjects
1	Meeting students, Course goals, expected knowledge after completing the course, explain methods of evaluating the student’s performance
2	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
3	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
4	Time series operators (backshift operator, difference operator), using the difference operator for non-stationary series in the mean- variance stabilizing transformations-Box-Cox transformations
5	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)
6	AR(2) (stationarity conditions, ACF, PACF)-  general AR(p)- moving average processes (MA)- MA(1) (invertibility condition, ACF, PACF)
7	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
8	Parameter estimation- moments method - estimating white noise variance- least squares method
9	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
10	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)-  analysis of higher (lower) order models
11	Midterm exam 04/09/1443…..9:30-11:30 PM
12	Seasonal models- seasonal autoregressive models- moving average models- mixed seasonal models- multiplicative seasonal models
13	Applications of time series analysis in the lab. Handing over the data analysis project
14	Data analysis exam in the lab
15	Applications of time series analysis in the lab. Last date to hand over the project.