TimeSeries

# TimeSeries - Student Lecture Notes TS-1 Time-Series...

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Student Lecture Notes TS-1 TimeSeries 1 TimeSeries 1 Time-Series ± Numerical data that measures status of a process or activity over time with observations at regular time intervals ± The time intervals can be annually, quarterly, daily, hourly, minute, etc. ± Examples: PPI, CPI, GDP, T-bill rate, sales Year: 1994 1995 1996 1997 1998 Sales: 75.3 74.2 78.5 79.7 80.2 TimeSeries 2 Time Series Models ± AR: Autoregressive time series model ± Value at time period t is a function of value(s) at past time periods (t-1, t-2, etc) ± Concept is that past values are best predictor ± Past values are the predictor ‘x’ variables ± MA: Moving Average time series model ± ARIMA: Autoregressive Integrated Moving Average combines AR and MA in one model ± Moving Average as a smoothing process

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Student Lecture Notes TS-2 TimeSeries 2 TimeSeries 3 Principal of Parsimony Assume Multiple Good Models ± Select the simplest model ± Simplest model types: ± Least-squares linear ± Least-square quadratic ± 1st order autoregressive ± More complex types: ± 2nd and 3rd order autoregressive ± Least-squares exponential TimeSeries 4 Objectives of Time Series Analysis ± Model the behavior of time dependent observations ± Smoothing of time series data ± Moving averages (long term trend) ± Exponential smoothing ± Annual or other period ± Example: Stock market 50-day and 200-day moving average ± Forecasting once a model has been developed ± Inflation, unemployment, GDP, deficit, sales, college enrollment, interest rates, etc.: objective is planning ± Forecasting assumes the process that governs the time series behavior in the past will hold in the future
Student Lecture Notes TS-3 TimeSeries 3 TimeSeries 5 Time Series Components ± Time Series data can be decomposed into ± Trend: longer term ± Cyclical: repeating cyclic variations ± Seasonal: seasonal factors ± Random: nondeterministic factors ± Time series models can incorporate these components ± Additive ± Multiplicative TimeSeries 6 U p w a r d tr e n Trend Component ± Overall upward or downward movement ± Data taken over a period of years Sales Time

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Student Lecture Notes TS-4 TimeSeries 4 TimeSeries 7 Cyclical Component ± Upward or downward swings ± May vary in length Sales 1 C y cle TimeSeries 8 Seasonal Component ± Upward or downward swings ± Regular patterns ± Observed within 1 year Sales Time (Monthly or Quarterly) Winter Spring Summer Fall Winter
Student Lecture Notes TS-5 TimeSeries 5 TimeSeries 9 Random or Irregular Component ± Erratic, nonsystematic, random, “residual” fluctuations ± Due to random variations inherent in process ± Nature ± Accidents ± Psychology of behavior ± Short duration and non-repeating ± Assumed to have a constant mean and variance TimeSeries 10 Example Quarterly Sales with Seasonal Components Quarterly with Seasonal Components 0 5 10 15 20 25 0 5 10 15 20 25 30 35 Time Sales

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Student Lecture Notes TS-6 TimeSeries 6 TimeSeries 11 Quarterly Sales with Seasonal Components Removed Quarterly without Seasonal Components 0 5 10 15 20 25 0 5 10 15 20 25 30 35
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## This note was uploaded on 09/25/2009 for the course IDS 371 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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TimeSeries - Student Lecture Notes TS-1 Time-Series...

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