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Unformatted text preview: 1 Lecture Notes 9 1. Time Series Analysis 1. Examine data collected over time. Models are simple No independent variables, i.e. no x’s Models are mechanical Time series is both (i) Data (ii) A process Observations are related to each other over time, i.e. covariance Each observation has *Mean or expected value, i.e. called a first moment Also includes expected products – related to covariance *A variance, i.e. called a second moment Thus, time series analysis only examines data for patterns and then we use those patterns to forecast. 2. Sample Autocorrelation Function (ACF) Usually we plot the ACF A plot to analyze the data You have a time series, n X X , 1 Time series has n observations (i) You calculate the sample mean n t t X n X 1 1 (ii) Then calculate the autocovariance function h n t t h t X X X X n h 1 1 ˆ h is the number of lags 2 If h =1 , then 1 1 1 1 1 ˆ n t t t X X X X n Thus, this is almost a covariance i.e. COV(X t , X t-1 ) of X t with past values If h = 0 , then n t t X X n 1 2 1 ˆ Thus, this is almost a variance (iii) Then calculate an ACF ACF is very similar to the standard Pearson correlation...
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This note was uploaded on 04/05/2012 for the course ECON 421 taught by Professor Blair during the Fall '11 term at Rutgers.
- Fall '11