1. (a) Explain the concept of covariance stationarity. Write down an MA(1) and AR(1) process. Do...

 

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1. (a) Explain the concept of covariance stationarity. Write down an MA(1) and AR(1) process. Do these processes satisfy the requirements for covariance stationarity? Explain your answer. b) You have some time series data on the world oil price and GDP for the United States for the period 1968-2018. You suspect that neither of these variables are covariance stationary. Explain how you would conduct a Dickey-Fuller test to check for the time series properties of these variables. Write down the estimation equation and clearly state the null hypothesis. Based on the table of test statistics below what can you conclude about the time series properties of these variables? Variable tested DF t-stat OilPrice -4.39 OilPrice,- OilPrice+-1 -5.63 GDP -5.01 GDP-GDP -8.32 Dickey-Fuller 5% critical value = -3.52 c) Following on from the results in part (b) you decide to estimate the regression model below using OLS: GDP =Bo+B.OilPrice, + et Do you think this provides consistent estimates of the OLS parameters and t- statistics? Suppose that the error term contained auto-correlation so that Cov(e, e-1) 0 Explain the impact of this on the OLS estimates here. d) Suppose you establish that two variables are I(1). Explain how you can check for cointegration between them. 1. (a) Explain the concept of covariance stationarity. Write down an MA(1) and AR(1) process. Do these processes satisfy the requirements for covariance stationarity? Explain your answer. b) You have some time series data on the world oil price and GDP for the United States for the period 1968-2018. You suspect that neither of these variables are covariance stationary. Explain how you would conduct a Dickey-Fuller test to check for the time series properties of these variables. Write down the estimation equation and clearly state the null hypothesis. Based on the table of test statistics below what can you conclude about the time series properties of these variables? Variable tested DF t-stat OilPrice -4.39 OilPrice,- OilPrice+-1 -5.63 GDP -5.01 GDP-GDP -8.32 Dickey-Fuller 5% critical value = -3.52 c) Following on from the results in part (b) you decide to estimate the regression model below using OLS: GDP =Bo+B.OilPrice, + et Do you think this provides consistent estimates of the OLS parameters and t- statistics? Suppose that the error term contained auto-correlation so that Cov(e, e-1) 0 Explain the impact of this on the OLS estimates here. d) Suppose you establish that two variables are I(1). Explain how you can check for cointegration between them.

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a Covariance stationarity refers to a time series process in which the mean and variance of the seri... View the full answer