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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 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 • 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
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
Forecasting • Final selection criteria for ARIMA vs. SARIMA standard error comparisons • ARIMA has lower standard error at every point greater than lag=5
GARCH Model fitted to Residuals • GARCH(1,1)
Selected Model • ARIMA(20,1,1) with a GARCH(1,1) fitted to the residuals
Forecasting Forecast for Logged Data Forecast for Original Data
Price to Earnings/Long-Term Interest Rates Irrational Exuberance [Princeton University Press 2000, Broadway Books 2001]