EC6063: Clearly explain the differences between an Autoregressive time-series process and a Moving Average time series: Applied Time Series Analysis Assignment, UCC, Ireland

Question 1:

• Clearly explain the differences between an Autoregressive time-series process and a Moving Average time series process, including examples of specifications of AR and MA processes.
• What is the Autocorrelation Function? What is the Partial Autocorrelation Function? Show with the aid of diagrams, and clearly explain, the theoretical patterns of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) for AR(1) and MA(1) processes and more generally for AR(p) and MA(q) processes.
• Table 1 below presents results for a number of alternative ARIMA models. Which specification appears to be the most appropriate ARIMA model? Clearly explain your reasoning.

Question 2:

• Outline the main differences, including advantages and disadvantages, between VAR models and single equation time series models, with appropriate examples to illustrate.
• Clearly explain the methodology underlying the Granger causality test.
• The data file usdata.xlsx contains annual data for US real GDP growth and US inflation from 1960 to 2019. Assume both variables are integrated of order 0 i.e. I(0).
• Copy the data into STATA and create a time variable called ‘date’ in STATA and use this new variable to declare the data set to be time-series data.
• Estimate two VAR models with (i) 1 extra lag of growth and inflation and (ii) 2 extra lags of growth and inflation. Which model is preferred? Explain your answer.
• Carry out the Granger causality test on your preferred model to see if growth ‘granger causes’ inflation and vice versa. Based on the results of the granger causality tests, do you think a VAR model was appropriate in this instance? Explain your answer. Generate an impulse response function graph for your preferred model and comment on the results

Question 3:

• Clearly explain the terms auto-regressive conditional heteroscedasticity, with reference to the specification of an ARCH(1) model.
• Clearly explain the differences between the ARCH and GARCH models. In an ARCH(1) model how would you interpret the coefficients? In a GARCH(1, 1) model how would you interpret the coefficients?