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Financial Time Series I/Methods of Statistical Prediction

Financial Time Series I/Methods of Statistical Prediction. Suggested Answers to Project 3  Project : Time Series Modeling 1/20/2003. Time Series Plot and Seasonality. Temp<- scan(“d:/temperature.txt”) See figure in next page. The trend component (mean and variance) is not clear.

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Financial Time Series I/Methods of Statistical Prediction

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  1. Financial Time Series I/Methods of Statistical Prediction Suggested Answers to Project 3 Project : Time Series Modeling 1/20/2003

  2. Time Series Plot and Seasonality • Temp<- scan(“d:/temperature.txt”) • See figure in next page. • The trend component (mean and variance) is not clear. • Is there a seasonal effect? • It is not clear what is the reasonable period. • Use boxplot on a few chosen (exploratory) periods for this time series. • Use the differencing technique to remove trend. • temp.diff <- diff(temp, lag = 1, differences =1) • Before removing seasonal component, • The autocorrelation plot shows a mixture of exponentially decaying and damped sinusoidal components. • This suggests that we may need to consider seasonal effect. • We just use a differencing technique to remove seasonal effect. • An autoregressive model with order greater than one is needed. • Based on the 95% SACF and SPACF plots, it suggests that we want to start with an ARMA(3,4) model to build the model. • Use AIC and ARIMA(3,1,4) as a candidate model to start with.

  3. Time Series Plot

  4. Seasonality

  5. Differencing

  6. Outliers • Do differencing twice (d=2), the time series plot will show a strange pattern between day 60 and day 80. • The variance during that period of time is not constant. • We may need to investigate those data carefully. • Is there a storm or unusual weather situation?

  7. Mortality and Smoke • The analysis is similar to it on temperature. • There is no outlier. • Use AIC to choose a proper ARIMA.

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