计量经济学 - 时间序列

EconometricsSchool ofMathematics

Econometrics School of Mathematics

Econometrics26. Time Series Data

Econometrics 26. Time Series Data

Modeling an Economic Time SeriesObserved Yo, Yi, ... , Yt.....口What is the “sample”咖Random sampling?The “observation window7

Modeling an Economic Time Series  Observed y0 , y1 , ., yt ,.  What is the “sample”  Random sampling?  The “observation window

Estimators Functions of sums of observations Law of large numbers?Nonindependent observationsWhat does “increasing sample size"' mean?Asymptotic properties? (There are no finitesample properties.)

Estimators  Functions of sums of observations  Law of large numbers? ◼ Nonindependent observations ◼ What does “increasing sample size” mean?  Asymptotic properties? (There are no finite sample properties.)

Interpreting a Time SeriesTime domain: A“process"口y(t) = ax(t) + by(t-1) + ..Regression like approach/interpretatiorFrequency domain: A sum of terms■y(t)=Z,β,Cos(α,t) + ε(t)Contribution of different frequencies to the observed series(High frequency data and financial econometrics口frequency"’ is used slightly differently here.)

Interpreting a Time Series  Time domain: A “process” ◼ y(t) = ax(t) + by(t-1) + . ◼ Regression like approach/interpretation  Frequency domain: A sum of terms ◼ y(t) = ◼ Contribution of different frequencies to the observed series.  (“High frequency data and financial econometrics – “frequency” is used slightly differently here.) ( ) ( ) j j j    +  Cos t t