Stationary Processes (Chapter 2)
2.1 Basic Properties Basic Properties
{Xt} stationary time series Mean: = Xt for all t. ACVF: (h) = cov(Xt+h, Xt), h=0, +1, . . .
( h) ACF: (h) = ( 0)
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DEFINITION. {Xt} is a Gaussian time series if all of its jo
ARMA Models (Chapter 3)
Motivation: For `most' time series {Xt} , Wold Decomposition {Xt} is a linear TS
Xt =
j= 0
j Zt-j , {Zt} ~ WN(0,2),
= () Zt , where () = 1 + 1B + 1B2+ . . . We approximate () using a ratio of polynomials which leads us
ARMA Modeling and Forecasting (Chap 5)
5.1 Preliminary Estimation
Useful for
order identification (requires the fitting of a number of
competing models).
initial parameter estimates for likelihood optimization.
ARMA(p,q) Model: Based on observati
Non-Stationary and Seasonal Time Series (Chap 6) 6.1 ARIMA Models
DEFINITION: {Xt} is an ARIMA(p,d,q) process if Yt := (1 - )d Xt is a causal ARMA(p,q) process. Remarks : 1. {Xt} satisfies the difference equation *() Xt = (1 - )d () Xt = () Zt
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whe
Introduction to Time Series (Chapter 1) 1.1 Examples of time series
Ex 1.1.1 (Australia red wine sales; WINE.DAT)
xt = monthly sales of red wine (1000 litres) t = (Jan, 1980), (Feb, 1980), . . . , (Oct, 1991) or t=1, 2, . . . , 142.
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Figure 1.1: A