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A Look at the U.S. Total Retail Sales

A Look at the U.S. Total Retail Sales. The data on the next slide consist of the total U.S. retail sales (excluding motor vehicle and parts dealers) in billions of dollars for four years We’ll use the time series decomposition macro on these data and discuss the results. Total U.S. Retail Trade.

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A Look at the U.S. Total Retail Sales

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  1. A Look at the U.S. Total Retail Sales • The data on the next slide consist of the total U.S. retail sales (excluding motor vehicle and parts dealers) in billions of dollars for four years • We’ll use the time series decomposition macro on these data and discuss the results

  2. Total U.S. Retail Trade 2004200520062007 Jan 220.458 231.134 253.084 264.342 Feb 217.362 227.910 247.107 256.234 Mar 240.615 258.297 280.039 293.112 Apr 242.168 257.794 276.634 284.152 May 251.154 266.893 293.456 309.461 Jun 245.942 265.450 287.487 299.831 Jul 249.349 263.898 282.706 296.300 Aug 250.073 274.253 294.334 306.475 Sep 240.047 263.754 274.788 283.135 Oct 251.036 272.449 280.158 297.128 Nov 258.980 278.908 290.971 313.157 Dec 314.591 334.955 348.342 360.089 Table 4.7

  3. Using the KPK Macros – Excel 2007

  4. The Input Window

  5. Moving Centered Ratio to Total Moving Moving Year Month t (1) Yt(2) (3) Average (4) Average (5) 2004 Jan 1 220.458 Feb 2 217.362 Mar 3 240.615 Apr 4 242.168 May 5 251.154 Jun 6 245.942 Jul 7 249.349248.9261.002 Aug 8 250.073249.8101.001 Sep 9 240.047250.9870.956 Oct 10 251.036252.3750.995 Nov 11 258.980253.6811.021 Dec 12 314.591255.1501.233 2981.775 2992.451 3002.999 3020.681 3036.307 3052.046 3071.554 Moving Averages and Ratios - 2004

  6. Moving Centered Ratio to Total Moving Moving Year Month t (1) Yt (2) (3) Average (4) Average (5) 2007 Jan 37 264.342290.4360.910 Feb 38 256.234291.5080.879 Mar 39 293.112292.3621.003 Apr 40 284.152293.4170.968 May 41 309.461295.0481.049 Jun 42 299.831296.4621.011 Jul 43 296.300 Aug 44 306.475 Sep 45 283.135 Oct 46 297.128 Nov 47 313.157 Dec 48 360.089 3492.025 3504.166 3512.513 3529.483 3551.669 3563.416 Moving Averages and Ratios - 2007

  7. Summary of Ratios Month Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 20041.0021.0010.9560.9951.0211.233 20050.9010.8830.9930.9841.0121.0000.9881.0200.9751.0001.0171.213 20060.9110.8840.9970.9821.0391.0140.9931.0310.9600.9761.0101.204 20070.9100.8791.0030.9681.0491.011 Average 0.907 0.8820.9970.9781.0331.0080.9941.0170.9640.9901.0161.216 Seasonal 0.907 0.882 0.997 0.978 1.033 1.008 0.994 1.017 0.963 0.990 1.016 1.216 Index Table 4.9

  8. Deseasonalized Retail Trade - 2004 Year Month t Yt Stdt 2004 Jan 1 220.4580.907243.093 Feb 2 217.3620.882246.559 Mar 3 240.6150.997241.306 Apr 4 242.1680.978247.667 May 5 251.1541.033243.169 Jun 6 245.9421.008243.967 Jul 7 249.3490.994250.874 Aug 8 250.0731.017245.886 Sep 9 240.0470.963249.211 Oct 10 251.0360.990253.601 Nov 11 258.9801.016255.013 Dec 12 314.5911.216258.700 Table 4.10

  9. Deseasonalized Retail Trade - 2007 Year Month t Yt Stdt 2007 Jan 37 264.3420.907291.483 Feb 38 256.2340.882290.652 Mar 39 293.1120.997293.954 Apr 40 284.1520.978290.605 May 41 309.4611.033299.622 Jun 42 299.8311.008297.424 Jul 43 296.3000.994298.112 Aug 44 306.4751.017301.343 Sep 45 283.1350.963293.944 Oct 46 297.1280.990300.164 Nov 47 313.1571.016308.360 Dec 48 360.0891.216296.115 Table 4.10 (cont.)

  10. Deseasonalized Data Figure 4.21

  11. The Trend Line

  12. dt dt 3-Month Moving Average (Ct) ^ tdt dt — (= Ct • It) ^ 1 243.093240.585 + 1.354(1) = 241.9391.0048 — 2 246.559 240.585 +1.354 (2) = 243.2931.01341.002 3 241.306 240.585 + 1.354 (3) = 244.6470.9863 1.002 4 247.667 240.585 +1.354 (4) = 246.002 1.0068 0.992 5 243.169 240.585 +1.354 (5) = 247.3560.98310.990 6 243.967 240.585 +1.354 (6) = 248.7100.98090.989 . . . . . . . . . . . . . . . Cyclical Components Table 4.12

  13. Three-Month dt/dt Moving Year Month tdtdt(= Ct∙It) Average (Ct) 2004 Jan 1 243.093241.9391.0048 — Feb 2 246.559243.2931.01341.002 Mar 3 241.306244.6470.98631.002 Apr 4 247.667246.0021.00680.992 May 5 243.169247.3560.98310.990 Jun 6 243.967248.7100.98090.989 Jul 7 250.874250.0641.00320.987 Aug 8 245.886251.4180.97800.989 Sep 9 249.211252.7720.98590.987 Oct 10 253.601254.1260.99790.994 Nov 11 255.013255.4800.99821.001 Dec 12 258.700256.8341.00730.998 ^ ^ Cyclical Components - 2004 Table 4.13

  14. Three-Month dt/dt Moving Year Month tdtdt(= Ct∙It) Average (Ct) 2007 Jan 37 291.483290.6861.00270.996 Feb 38 290.652292.0400.99521.000 Mar 39 293.954293.3941.0019 0.994 Apr 40 290.605294.7480.98591.000 May 41 299.622296.1021.01190.999 Jun 42 297.424297.4560.99991.003 Jul 43 298.112298.8100.99771.000 Aug 44 301.343300.1641.00390.992 Sep 45 293.944301.5180.97490.990 Oct 46 300.164302.8720.99110.993 Nov 47 308.360304.2261.01360.991 Dec 48 296.115305.5800.9690 — ^ ^ Cyclical Components - 2007 Table 4.13 (cont.)

  15. Plot of Cyclical Activity Figure 4.22

  16. Time Series Components - 2004 Year Month ytTRt St CtIt 2004 Jan 220.458241.9390.907 Feb 217.362243.2930.8821.0021.012 Mar 240.615244.6470.9971.0020.984 Apr 242.168246.0020.9780.9921.015 May 251.154247.3561.0330.9900.993 Jun 245.942248.7101.0080.9890.992 Jul 249.349250.0640.9940.9871.016 Aug 250.073251.4181.0170.989 0.989 Sep 240.047252.7720.9630.9870.999 Oct 251.036254.1260.9900.9941.004 Nov 258.980255.4801.0161.0010.997 Dec 314.591256.8341.2160.9981.010 Table 4.14

  17. Time Series Components - 2007 Year Month ytTRt St CtIt 2007 Jan 264.342290.6860.9070.9961.007 Feb 256.234292.0400.8821.0000.995 Mar 293.112293.3940.997 0.994 1.008 Apr 284.152294.7480.9781.0000.986 May 309.461296.1021.0330.9991.013 Jun 299.831297.4561.0081.0030.997 Jul 296.300298.8100.9941.0000.997 Aug 306.475300.1641.0170.9921.012 Sep 283.135301.5180.9630.9900.985 Oct 297.128302.8720.9900.9930.998 Nov 313.157304.2261.0160.9911.023 Dec 360.089305.5801.216 Table 4.14 (cont.)

  18. Computer Plots Figure 4.23

  19. Section 4.10 - Index Numbers • An index number measures the change in an item (such as price) across two or more time periods • A price index compares prices from one year to a past year, referred to as the baseyear • An aggregate price index compares prices for more than one item for one year to the base year

  20. LongLife Prices of Four Items The reference year The base year Item 2000 (P0)2007 (P1) A$40$60 B$10$15 C$2$3 D$1$2 $53 $80 Table 4.17

  21. Simple Aggregate Price Index • A simple aggregate price index divides the two totals on the previous slide and is equal to x 100 = x 100 = 150.9 • Problem: This index doesn’t consider the quantity of each item that is typically purchased each year

  22. Including the Quantities Item Qty. (Q)2000 (P0) 2007 (P1) A 1$40$60 B 8$10$15 C 10$2$3 D 40$1$2

  23. Weighted Aggregate Price Index • A weighted aggregate price index considers the quantities (Q) and is equal to x 100 • The calculations for this index are shown on the next slide

  24. 20002007 Item P0Q P0QP1QP1Q A $40 1 $40 $60 1 $60 B $10 8 $80 $15 8 $120 C $2 10 $20 $3 10 $30 D $1 40 $40 $2 40 $80 ∑P0Q = 180 ∑P1Q= 290 Weighted Aggregate Price Index Table 4.18

  25. Weighted Aggregate Price Index Consumers spent 61.1% more for these four items in 2007 as compared to 2000.

  26. How to Pick the Quantities • There are two ways to go here ∙ Use the quantities for the base year - This is called a LaspeyresIndex ∙ Use the quantities for the reference year - This is called a Paasche Index

  27. The Consumer Price Index • The Consumer Price Index (CPI) is the most famous Laspeyres Index. • Government shoppers collect prices for about 90,000 items and services to prepare the index • The CPI is the federal government’s most watched gauge of inflation at the retail level • The main complaint: It’s too large

  28. The Consumer Price Index (CPI) The first three represent 75% of the items

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