Financial Time Series I/Methods of Statistical Prediction

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Presentation transcript:

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. 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.

Time Series Plot

Seasonality

Differencing

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?

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