Requirements of Assign2

HaiyueSeptember 22, 2023About 3 min

math#john@assign2

Requirements

Instructions

Quesion 1 (15 marks)

The tasks for this question are listed below.

Take the 2011 output (the training set) and find the best ARMA(p,q) model for the data.
Take the noise $Z_t$ from that model and check its SACF.
Calculate $Z_t^2$ and show that it has the ARCH effect.
Find the best ARCH or GARCH model for it.
Take the developed models for the output and also for the noise and apply them to the 2012 output data.
Evaluate the performance of the models for one step ahead forecasting with error bounds by calculating the coverage and mean prediction interval width, for both 90% and 95% values.
Compare the results with constructing the prediction intervals by using the appropriate quantiles.

Question 2 (15 marks)

The tasks for this question are listed below.

Test the months December, January, February, July, August for normality.
For the months that do not follow a normal distribution, test for a Gamma fit.
Test December, January, February for correlation, and July, August separately.
Generate 1000 years of synthetic December, January, February, add the months to get seasonal totals, and generate empirical CDFs for the totals versus the CDFs for the real data.
Do the same for July, August.

Question 3 (10 marks)

The tasks for this question are listed below.

Take the monthly rainfall data from MtGambierRainfall.xlsx and model the seasonality. Then subtract this from the data.
Use exponential smoothing to see the overall trend in the series - try various values of α below 0.2.
Find the trend for the whole series for the smoothed data, and then find the trends for any sections that you think display differing characteristics.
Take the data for the month of December and the Annual mean temperature from MtGambierByMonthsTemperature.xlsx and find the trend over time.
How much has the mean temperature changed over time in each case?