3 mo treasury yield borrowing costs Dow industrials NY Times 18 Sept 2008 front page.

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Presentation transcript:

3 mo treasury yield borrowing costs Dow industrials NY Times 18 Sept 2008 front page

Stat Sept 2008 D. R. Brillinger Chapter 3 mean function variance function autocovariance

Strictly stationary Normal/gaussian - all joint distributions jointly normal Wide sense stationary vs. second-order

Properties of autocovariance

Useful models Purely random Building block

Random walk not stationary

*

Moving average, MA(q) From * stationary

Backward shift operator Linear process. Need convergence condition

autoregressive process, AR(p) first-order, AR(1) Markov Linear process For convergence/stationarity *

a.c.f. From * p.a.c.f.

In general case, Very useful for prediction

ARMA(p,q)

ARIMA(p,d,q).

Yule-Walker equations for AR(p). Correlate, with X t-k, each side of For AR(1)