time series 1 indexing ppt

time series 1 indexing ppt - Time Series Analysis Chapter...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Time Series Analysis Chapter 16 and elsewhere Time Series 1: Indexing 1 Chapter Outline 1. 2. 3. 4. 5. 6. 7. 8. Business forecasting Components of a series Smoothing an annual series Least squares trend fitting Autoregressive models Choosing a model Seasonal data Index numbers (Online) Time Series 1: Indexing 2 Business Forecasting Many statisticians specialize in this area. Lots of unique techniques and practices. Many of the things we will look at are based on regression analysis. Time Series 1: Indexing 3 A great site for time series data Over 200,000 series A subscription site but UF has one Just need to come in from a UF internet address http://www.economagic.com/ Time Series 1: Indexing 4 Preliminary adjustments Federal government (Census, BLS, Federal Reserve) agencies publish large collections of time series. Most have websites. Often find a published series has been adjusted for some type of behavior. The most common adjustments are for inflation and seasonality. Section 16.8 (Online) Index numbers Time Series 1: Indexing 5 Adjusting for inflation Yt = our time series variable; data collected up to time T (t = 1,2,...,T) It = some index of prices (CPI or other), usually set at 100 in the "base period" At = series in constant dollars = 100*Yt/It Time Series 1: Indexing 6 A Series From Economagic Hourly Earnings of Production Workers 20.00 17.00 A $10/hr increase over 22 years 14.00 11.00 But, are they better off now? Jan-91 Jan-94 Jan-97 Jan-00 Jan-03 Jan-06 Jan-09 7 8.00 Jan-88 Time Series 1: Indexing Adjust for Inflation It = Consumer price index, all items Unweighted, not seasonally adjusted Set at 100 for July 1983, passed 200 in April 2006 Date J an-88 Feb-88 Mar-88 : : Dec-94 J an-95 Feb-95 : : Apr-06 May-06 J un-06 : : J ul-10 Aug-10 Sep-10 Oct-10 HourlyEarn 9.33 9.31 9.32 : : 11.49 11.56 11.56 : : 16.72 16.62 16.63 : : 18.94 19.03 19.10 19.19 CPI-U 116.0 116.2 116.5 : : 150.1 150.5 150.9 : : 200.7 201.3 201.7 : : 217.6 218.2 218.4 218.9 AdjEarn 8.043 8.012 8.000 : : 7.655 7.681 7.661 : : 8.331 8.256 8.245 : : 8.704 8.721 8.745 8.767 Time Series 1: Indexing 8 Earnings in 1983 Dollars Earnings in 1983 Dollars 9.000 8.500 8.000 7.500 7.000 Jan-88 Jan-91 Jan-94 Jan-97 Jan-00 Jan-03 Jan-06 Jan-09 Time Series 1: Indexing 9 Things Now Revealed Workers have gained about 70 cents per hour. There is a swing of 10 cents within each year. In the original data, we completely missed the productivity rebound of the late 1990s due to technology changes. Time Series 1: Indexing 10 How is an index constructed? This will be what is called an aggregate price index We start off by specifying a typical "bundle" of goods that we think consumers buy. We record the price of this bundle in our selected base time period. We record the price of the bundle in every other time period. The index is just the ratio of prices. Time Series 1: Indexing 11 unweighted The deli index Item Bread (loaf) Cheese (lb.) Ham (lb.) Mustard (jar) Lettuce (head) Total Price 1990 1.56 2.69 5.99 1.09 .89 12.22 Time Series 1: Indexing Price Now 3.39 4.19 8.99 1.85 1.69 20.11 12 Other types of indices Weighted: The prices are weighted by the quantities used. For example, a transportation cost index would factor in how much gas a consumer would use. Laspeyres: The quantities consumed in the base period are used for all time periods (they don't change over time). The all-items CPI is a Laspeyres type. Time Series 1: Indexing 13 Redoing our previous example Item Bread (loaf) Cheese (lb.) Ham (lb.) Mustard (jar) Lettuce (head) Total Used 10% 15% 20% 1% 5% Price 1990 Wtd1990 Price Now WtdNow 1.56 0.1560 3.39 0.3390 2.69 0.4035 4.19 0.6285 5.99 1.1980 8.99 1.7980 1.09 0.0109 1.85 0.0185 0.89 0.0445 1.69 0.0845 12.22 1.8129 20.11 2.8685 Time Series 1: Indexing 14 The CPI There are over 2000 different versions of the CPI on Economagic. Here are a few: CPI: U.S. city average; Food and beverages; 1982-84= CPI: U.S. city average; Food; 1982-84=100; SA CPI: U.S. city average; Meats, poultry, fish, and eggs; 1 Time Series 1: Indexing 15 The base period For the CPIs we used earlier, the index period is 1982 to 1984. They use the average prices over those years as the basis. Usually the index is at 100 for July 1983. It might be a month or so off for different CPIs. Time Series 1: Indexing 16 The meaning of the index For the one we used earlier, it was 100 in July 1983. In October 2010 it was 218.9 That means it took $218.90 to buy the same bundle of goods in 2010 that you could buy for $100 in July 1983. Time Series 1: Indexing 17 "Constant Dollars" In our wage example, hourly earnings were $19.19 in October 2010, and the CPI was 218.9. The adjusted earnings were: 100*19.19/218.9 = 8.767 So in October 2010 workers were earning 8.76 "1983 dollars" per hour Time Series 1: Indexing 18 Re-indexing If you want to change base periods, it is a fairly simple task. If we thought Oct 2002 was a good base period, we would want to construct a new index that is 100 in that month. Formula is 100*(old Index value)/181.3 Time Series 1: Indexing 19 Our new index in 5 different months Month Jan-76 Jul-83 Jan-95 Oct-02 Jun-05 CPI - 84 55.8 100.0 150.5 181.3 194.1 Time Series 1: Indexing CPI - 02 30.78 55.16 83.01 100.00 107.06 20 Most recent month???? ...
View Full Document

Ask a homework question - tutors are online