Financial Time Series I/Methods of Statistical Prediction

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

• Templt- 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 lt- 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 (d2), 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.