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Time Series 2 Time Series 1

Time Series 2 Time Series 1. TS2=5*cos(2*t) TS1=cos(2*t). R 2 = 1 Perfectly correlated. Time Series 2 Time Series 1. *. R 2 = 0 No LINEAR correlation. TS2=5*cos(2*t) TS1=cos(t). Time Series 1 Time Series 2. TS1=sin(t) TS2=cos(t). R 2 = 0 No correlation. Time Series 2

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Time Series 2 Time Series 1

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  1. Time Series 2 Time Series 1 TS2=5*cos(2*t) TS1=cos(2*t) R2 = 1 Perfectly correlated

  2. Time Series 2 Time Series 1 * R2 = 0 No LINEAR correlation TS2=5*cos(2*t) TS1=cos(t)

  3. Time Series 1 Time Series 2 TS1=sin(t) TS2=cos(t) R2 = 0 No correlation

  4. Time Series 2 Time Series 1 TS2=cos(t-pi/4) TS1=cos(t)

  5. Which linear fit minimizes the error in a least squares sense? Hint, what is the fraction of the variance explained implied by each fit? B A C R2= a12 x’2 y’2

  6. Answer C RMS error = .707 implies R2=.5 RMS error = .767

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