Question 1 [24 Marks]For ALL of the following statements, say whether each one is TRUE or FALSE. Then, justify your answer with a careful explanation. Please note that explanations may also involve mathematical and or/ graphical illustrations. Please also note that marks will depend on the accuracy of each answer provided. Each correct and fully … Continue reading “variance of a stochastic process is finite | My Assignment Tutor”
Question 1 [24 Marks]For ALL of the following statements, say whether each one is TRUE or FALSE. Then, justify your answer with a careful explanation. Please note that explanations may also involve mathematical and or/ graphical illustrations. Please also note that marks will depend on the accuracy of each answer provided. Each correct and fully explained answer is worth 8 marks.a. If the variance of a stochastic process is finite, I can conclude that the process is weakly stationary.b. If I fail to reject the null hypothesis of a Dickey Fuller test, I conclude that the process has no unit roots. c. You can have more confidence in long term than short term forecasts.Question 2 [23 Marks]a. What might Ramsey’s RESET test be used for?b. Consider the following graph:[5 Marks] Does this series look like it is stationary? Explain your answer.[10 Marks] c. Why is it important to test for non-stationarity in time series data before attempting to build an empirical model? [5 Marks] d. What kind of variables are likely to be non-stationary? Give an example. [3 Marks] Question 3 [30 Marks]a. The Table 1 below reports the autocorrelation function (ACF) and partial autocorrelation function (PACF) for the nominal returns of S&P500 (the first difference of the log S&P500 index) using monthly data for the period 1970-2018. In the Table 1 below k represents the number of lags and SE stands for the standard error. Identify the model that you should utilize in your analysis by examining Table 1 below. Explain in detail your answer. b. Table 2 below reports the estimated Akaike (AIC) and Schwarz Bayesian (SBC) criteria for various lags of order q (for the moving average part) and p (for the autoregressive part). The data utilized to estimate the criteria below are the nominal returns of S&P500 (the first difference of the log S&P500 index) using monthly data for the period 1970-2018. What is the suggested model(s) under both the AIC and SBC criteria? Explain in detail your answer.[10 Marks] c. Suppose that the best specification you found based on the criteria outlined in part (a) is provided by the AR(1) model: ?? = ???−1 + ??. What conditions need to be imposed on the parameter ? for the model to be non-stationary?[5 Marks]d. Discuss how to test for the presence of unit roots after you estimate the AR(1) model in part (c).[5 Marks] Question 4 [23 Marks]a. Test whether the following AR(2) model (eq. 2) for the time series {? }?? ?=1 is stationary: ?? = 0.7??−1 + 0.10??−2 + ??,Show in detail your calculations.[15 Marks]b. Consider a simple model of the S&P500 stock price index (named “sp500price”). The data are daily over the period 2015 through 2020. We also generate the natural logarithm of the variable sp500price which is named ln_sp500price. Suppose that you run the following command in Stata:regress D.ln_sp500priceestat archlm, lags(1)Table 3 below presents the results from the Engle’s LM test of the autoregressive conditional heteroskedasticity test: The post Why is it important to test for non-stationarity in time series data before attempting to build an empirical model?Explain appeared first on Essay Hotline.
