Reference no: EM133117830

Instruction

The data used in this assignment are contained in the file "emp.csv", which therefore need to be loaded and converted in time series format in order to solve this exercise. The csv file "emp" reports data on the US Employment Level from January 1948 to December 2007. Data have monthly frequency. You are supposed to know what are the relevant packages to be used for this assignment.

You can work in groups of up to 4 people, and contribute to only one group.

Part 1

1. Plot the data and the autocorrelation function. Decompose your time series into trend, cycle, and seasonal component with a methodology of your choice (classical decomposition, SEATS, etc). Discuss the properties of the series and the limitation of the methodology you choose.

2. Transform your data by taking natural logarithm or with Box and Cox methodology. Repeat the analysis of point 1.1: how does it change? Decide whether to use original or transformed data in the rest of the assignment. Motivate your choice.

3. Based on the results in point 1.1 and the choice in point 1.2, discuss what is the most accurate functional form for the KPSS and ADF tests. Then, perform both tests to check stationarity and discuss the results.

4. If the series is not stationary, follow the approach presented in class to make it stationary. When the series is stationary, look at the autocorrelation and partial autocorrelation function, choose an ARIMA model for the series and write down the equation of the model in the form ARIMA(p,d,q)(P,D,Q)[m]. (Hint: if there is a deterministic trend, you need to detrend the time series)

Part 2

In this part use the data based on the decision in point 1.2 (i.e. either the original data or the log/box-cox transformed data).

1. Split your sample into a train set and a test set. Estimate one ARIMA model by using AIC: is the estimated model coherent with the information acquired in point 1.3? Discuss the properties of the residuals. Can the model be improved? If it is the case, modify it discuss the new model performance.

2. Perform a forecast with the model selected in point 2.1 and in point 1.4 (note: if you had detrended or differentiated you need to change something in the formula). Plot the forecasts of each model with the original data in two separate graphs and discuss the measures of accuracy: what is the best model?

Attachment:- Natural logarithm.rar