Question 2 (a) The following table gives the sample autocorrelation coefficients and partial autocorrelation coefficients for...
Question 2 (a) The following table gives the sample autocorrelation coefficients and partial autocorrelation coefficients for a time series with 100 observations. 4 ,-0.55 -0.17 0.09 0.0.00.010.040.07 -0.55 | -0.4 0.29 | -0.22 -0.11- -0.13 -0.14 0,05 Suppose the sample mean of the time series is zero. Based on the above information, suggest an ARMA model for the data. Briefly explain your answer. (5 marks) (b) Let X, be a time series satisfying the following AR(2)model: X, = 0.3X,-1 +0.04X,-2...
2. FoRECASTING wITH MA PROCESSES. (i) How to check the invertibility of an MA(1) model? (ii) Suppose we use an MA model to model the process represented in Figure 2. Write down the model and find the estimates of the coefficients. (15 marks) 200 225 250 275 300 325 350 375 400 Sample: 1 2000 Included observations: 1999 Autocorrelation Partial Correlation AC PAC 10.498 0.498 2-0.042-0.386 -0.081 0.220 40.042 -0.183 5 0.003 0.157 6 0.013-0.127 7 0.019 0.131 8 0.013-0.112...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Y0 = ceo and Y1-CgY0-ei. Then let Y,-φ1Yt-it wt-1-et for t > ï as in an AR(2) process. Show that the process mean, E(Y.), is zero. (b) Suppose that (a is generated according to }.-10 e,-tet-+扣-1 with e,-N(0.) 0 Find the mean and covariance functions for (Y). Is (Y) stationary? Justify your...
2. (a) Consider the following process: where {Z) is a white noise process with unit variance. [1 mark] ii. Find the infinite moving average representation of X,i.e., find the scquence [6 marks] i. Explain why the process is stationary. (6) such that Xt = Σ b,2-j. iii. Calculate the mean and the autocovariance "Yo, γι and 72 of the process. 7 marks iv. Given 40 = 0.1 and Xo = 1.8, find the 2-step ahead forecast of the time series...
Question 4 [20 marks] By utilising Annexure A, answer the following questions: (a) 15 samples of n 8 have been taken from a cleaning operation. The average sample range for the 20 samples was 0.016 minute, and the average mean was 3 minutes. Determine the three-sigma control limits for this process. (4 marks) (b) 15 samples of n 10 observations have been taken from a milling process. The average sample range is 0.01 centimetres. Determine upper and lower control limits...
Use Table 8.1, a computer, or a calculator to answer the following. Suppose a candidate for public office is favored by only 47% of the voters. If a sample survey randomly selects 2,500 voters, the percentage in the sample who favor the candidate can be thought of as a measurement from a normal curve with a mean of 47% and a standard deviation of 1%. Based on this information, how often (as a %) would such a survey show that...
Exercise 6,7,8, and 9 use data from exercise 5 for exercise 6. use data from the graph for 7,8,9 d. LY, for some integer k> 0 5. The following table contains quarterly nominal GDP in U.S. (billions of dol- lars). Let Y, denote the GDP at time t and let y, = ln (Y). (Show your calculations in a spreadsheet, e.g., in Microsoft Excel.) a. Plot the time series (Y). Can the underlying stochastic process be weakly b. Calculate the...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares Squares F Regression 2 60 Error 18 120 Total 20 180 Determine the Regression Mean Square (MSR): Determine the Mean Square Error (MSE): Compute the overall Fstat test statistic. Is the Fstat significant at the 0.05 level? A linear regression was run on auto sales relative to consumer income. The Regression Sum of Squares (SSR) was 360 and...