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TEMPLT ; TEMPLATE = V3 ; TREPLAY 1: GPLOT 2: GPLOT1 3: GPLOT2 ; RUN ; DELETE _ALL_ ; QUIT ; ✝ ✡ In the first data step, the raw data are read from a file. Because the electric production is stored in different variables for each month of a year, the sum must be evaluated to get the annual output. Using the DIF function, the resulting variables delta1 and delta2 contain the first and second order differences of the original annual sums. To display the three plots of sum, delta1 and delta2 against the variable year within one graphic, they are first plotted using the procedure GPLOT.

The description can be found on page 176. It shows high and decreasing correlations at regular intervals. 1. Correlogram of the first order differences of the Sunspot Data. ✞ *** Program 1 _3_1 ***; TITLE1 ’ Correlogram of first order differences ’; TITLE2 ’ Sunspot Data ’; DATA data1 ; INFILE ’c :\ data \ sunspot . 5 W =1; PROC GPLOT DATA = corr ; PLOT CORR * LAG / VAXIS = AXIS1 HAXIS = AXIS2 VREF =0; 31 32 Chapter 1. Elements of Exploratory Time Series Analysis RUN ; QUIT ; ✝ ✡ ✆ In the data step, the raw data are read into the variable spot.

The assertion is an immediate consequence of the binomial expansion p (t − 1)p = k=0 p k t (−1)p−k = tp − ptp−1 + · · · + (−1)p . k The preceding lemma shows that differencing reduces the degree of a polynomial. 2 Linear Filtering of Time Series 25 is a polynomial of degree at most p−q. The function ∆p f (t) is therefore a constant. The linear filter ∆Yt = Yt − Yt−1 with weights a0 = 1, a1 = −1 is the first order difference filter. The recursively defined filter ∆p Yt = ∆(∆p−1 Yt ), t = p, . .

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A First Course on Time Series Analysis Examples with SAS by Falk M.

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