<p>Time Series Analysis</p><p>1. Classical Decomposition – additive or multiplicative effects  Trend – long run  Seasonal – periodic business patterns (months, weeks, days)  Cyclical – business conditions (recessions, inflations)  Error – randomness</p><p>Use in Bureau of Labor Statistics: http://www.bls.gov/lau/laumthd.htm Wikipedia: http://en.wikipedia.org/wiki/Decomposing_of_time_series</p><p>Data set 1977 births in New York state http://wweb.uta.edu/faculty/eakin/busa3321/1977NewYorkStatebirths.xls</p><p>2. Models</p><p>2.1 Descriptive </p><p> Exponential Smoothing – giving recent values different weights than old values</p><p>Used in Forecasting costs: http://www.dtic.mil/dtic/tr/fulltext/u2/a483271.pdf search for exponential smoothing</p><p> Moving Averages (average values before and after a date)</p><p>Used in the minutes of the Federal Open Market Committee: http://www.federalreserve.gov/monetarypolicy/fomcminutes20090318.htm</p><p> Index numbers – ratio of current value to a value in a specific previous time period</p><p>Used in costs trends: http://www.usbr.gov/tsc/techreferences/mands/cct.html</p><p>2.2 Inferential</p><p>2.2.1 Least Squares Models</p><p>2.2.1.1 Trend Models </p><p>2.2.1.1.1 Simple linear models </p><p> Measuring the effect of one variable on another over time or  The effect of time on the variable 2.2.1.1.1 Exponential Trend Models</p><p>Log10(Yt) = 0 + 1Xt or Loge(Yt) = 0 + 1Xt </p><p>Coefficient interpretation: For each one-unit increase in X, the estimated average value of Y increases by 101</p><p>Example if predicted log sales = 10 + 0.0015(advertising), then </p><p>(10)0.0015= 1.0035</p><p>For each dollar of advertising, the estimated average sales increase by 0.35%.</p><p>Mentioned in Business Week: http://www.businessweek.com/the_thread/economicsunbound/archives/20 09/01/after_the_crisi.html</p><p>2.2.1.2 Seasonal Effects</p><p> Use dummy variables to represent the season.</p><p> For example, for quarterly data use 3 dummy variables</p><p>2.2.1.3 Cyclical Effects</p><p>Determine leading indicators of business conditions</p><p>2.2.1.4 Problems with Least Squares in Time Series Data</p><p>2.2.1.4.1 Positively correlated errors due to sampling over time.</p><p>2.2.1.4.1.1 Estimated standard errors too small – All inferences are invalid.</p><p>2.2.1.4.1.2 Detection: Durbin-Watson test</p><p>If calculated DW value is small than a table value, significant positive correlated errors. </p><p>2.2.1.4.1.3 Remedy: </p><p> o Estimate and remove positive correlation</p><p> o First, Second, and Percentage differences Discussed in an addendum of the Federal Trade Association http://www.fta.dot.gov/printer_friendly/planning_environment_2427 .html</p><p>2.2.1.4.2 Unequal variance</p><p>Remedy – Transform dependent variable</p><p>2.2.1.4.3 Predicting Outside Range of data</p><p>No way to travel into the future.</p><p>2.2.2 Autoregressive Moving Average Models</p><p> Use to estimate correlation of errors over time </p><p> Beyond scope of notes</p><p> Mentioned in a Bureau of Labor Statistics report: http://www.bls.gov/cpi/cpisahoma.htm</p>