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Time Series Analysis of Standard and Poors Price to Earnings Ratio from 1900 to 2008: Monthly Data

Time Series Analysis of Standard and Poors Price to Earnings Ratio from 1900 to 2008: Monthly Data. Presenter: Jane Doe. Price to Earnings Ratio (P/E). Benchmark statistic for single company Low P/E means either stock is undervalued or company on decline

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Time Series Analysis of Standard and Poors Price to Earnings Ratio from 1900 to 2008: Monthly Data

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  1. Time Series Analysis of Standard and Poors Price to Earnings Ratio from 1900 to 2008: Monthly Data Presenter: Jane Doe

  2. Price to Earnings Ratio (P/E) • Benchmark statistic for single company • Low P/E means either stock is undervalued or company on decline • High P/E means either stock is overvalued or company on the rise • Overall market confidence indicator • Low indicates confidence is low • High indicates confidence is High

  3. Plots of Data

  4. Model Fitting

  5. ARIMA(20,1,1)

  6. Diagnostics

  7. SARIMA(20,1,1)X(1,0,1)4

  8. Diagnostics

  9. ARIMA vs. SARIMA selection • Nature of Data set • Expected market statistic to have seasonal component at lag 4 • Residual Diagnostics show virtually no change between two models. • Coefficients of SARIMA model insignificant • Nature of the P/E ratio may be counteracting the seasonality • Final selection criteria: ability to forecast will be examined in a moment

  10. Forecasting • Final selection criteria for ARIMA vs. SARIMA standard error comparisons • ARIMA has lower standard error at every point greater than lag=5

  11. GARCH Model fitted to Residuals • GARCH(1,1)

  12. Selected Model • ARIMA(20,1,1) with a GARCH(1,1) fitted to the residuals

  13. Forecasting Forecast for Logged Data Forecast for Original Data

  14. Forecast comparisons of t+1 to actual data points

  15. Using first 1293 data points to predict last 12

  16. Price to Earnings/Long-Term Interest Rates Irrational Exuberance [Princeton University Press 2000, Broadway Books 2001]

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