STAT GR5221 & GU4221 TIME SERIES ANALYSIS
1. Assume that Xt = t Zt ARCH(1), where Zt N (0, 1). Derive an expression for the
fourth moment E(Xt4 ) of Xt in terms of the model coefficients.
2. Consider the first time series in the data set DJAO2
Introduction to Time Series and Forecasting
1.1 Examples of time series
Ex 1.1.1 (Australian red wine sales; WINE.TSM)
xt = monthly sales of red wine (in kilolitres)
t = (Jan, 1980), (Feb, 1980), . . . , (Oct, 1991)
t=1, 2, . . . , 142.
STAT W4437: Time Series Analysis
February 2, 2016
Day/Time: TR 1:10pm - 2:25pm
Location: 207 Mathematics Building
Name: Abolfazl Safikhani
Office: School of Social Work (SSW), 1255 Amsterdam Avenue, office 1033
Financial time series and modeling volatility
Stylized Facts of Financial Returns
Define Xt = 100*(ln (Pt) - ln (Pt-1) (log returns)
P(|X1| > x) ~ C x-,
0 < < 4.
X (h) near 0 for all lags h > 0 (MGD
ARMA Modeling and Forecasting (Chap 5)
5.1 Preliminary Estimation
order identification (requires the fitting of a number of
initial parameter estimates for likelihood optimization.
ARMA(p,q) Model: Based on observations x1,