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.