c. Consider the following change in the time series model:Yt = P1Yt-1+ UzWhere ut follows a white noise process. What is the condition we need to impose on p1 inorder for the series yt to be weakly stationary? Why?d. Consider the following change in the time series model:Yt = Bo + B1xt-1 + B2Xt-2 + U;Where Ytis some outcome variable of interest, and Xt-1 and Xt-2 are strictly exogenousexplanatory variables. How would you test for the presence of serial correlation in theresidual ?e. Briefly explain how you would carry out econometric analysis of the model in (d) if U:isfound to be stationary, but positively serially correlated.

This is the answer of question C.

Answered: c. Consider the following change in the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that {u: t = ...,-2,-1,0,1,2,...} is an independent time series with mean zero, variance σ²= 9.0. Suppose that the time series {x+: t = ...,-2,-1,0,1,2,...} satisfies the equation: 2 X= 1.5 X-1 - .5 X-2 +3.0+u- U-1- 3 a) Identify the time series. b) c) d) i) Determine the autocovariance function and autocorrelation function of the time series X+ - Xt-1- Find the random shock form of the time series. Suppose that the first five observations of the time series are x₁ = 2.5, x2 = 4.0, X3 = 3.7, x4 =1.0 and x5 1.5. = Use these observations to compute prediction intervals for the next 5 observations. (Compute both 95% and 66.7% prediction limits) ii) If the sixth observation turns out to be x6 = 4.3 use this information to re-compute prediction intervals for the next 4 observations. (Compute both 95% and 66.7% prediction limits)
The data in the following table give quarterly sales of the popular game Oligopoly at the J-Mart variety store for the last two years. O A. B. Year Quarter Oligopoly Sales 1 O C. QUESTION 1 The four-point moving averages for the data are 31; 32; 33; 34; 37 2 Assume an additive decomposition time series model. Perform a complete estimation of the time series components to answer the following questions. 31; 33; 34; 36; 37 32; 33; 34; 35, 36 1 2 3 4 1 2 3 20 25 35 44 28 29 43 48
2: 7-20 A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under con- sideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk in- dex on a scale of 1–10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The following table provides a summary of the return and risk: STOCK ESTIMATED RETURN RISK INDEX Petrochemical $ 00 12% 9. Utility 6% The investor would like to maximize the return on the investment, but the average risk index of the in- vestment should not be higher than 6. How much should be invested in each stock? What is the aver- age risk for this investment? What is the estimated return for this investment?) $240
Solve (b), (c) and (d) please. Please fully solve the questions. (DO NOT just explain what to do in words) if you are going to use a software, R only (NO other programs) Thank you.
1.1 Consider a time series process given by (1-B)x, =(1-6,B)z,, where the sequence {z, ) is a white noise with mean zero and variance o. Determine the first four weights of process x, if an ARMA (1,1) model fitted to the data gave =0.8 and 9 = 0.34 (4) Consider an AR(2) model: x=(x)+(x2-x)+2,, where z, - wn(0,0²). 1.2 QUESTION 1 Show that = A(-A) and = 1-A using LSE method.
Let us consider the following time series: Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Sales 119 126 133 142 153 168 189 202 185 149 (a) Write down the use of moving average method. Apply a 3 year moving average (MA) method to find the trend for the following above time series. (b) Suppose the least squares estimate for the above times series is : Yˆ(t) = 123 + 3.8X(t), where Y (t)= sale and X(t)=time. Obtain the forecasted average sale for year 2009 and 2012. Explain for which year the forecasting error/uncertainity would be lower? and why? (c) What is the motivation of weighting in the exponential moving average methods?
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Consider the following time series date Week: 1 2 3 4 5 6 Value: 16 15 17 13 16 13 Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7 if required, round your answers to two decimal places Week Value Forecast 1 16 2 15 3 17 4 13 # 5 16 # 6 13 # MSE: The forecast for week 7: Use alpha=0.2 to compute the exponential smoothing values fro time series. Compute MSE and a forecast for week 7 if required, round your answers to two decimal places Week value forecast 1 16 2 15 16 3 17 15.8 4 13 16.04 5 16 15.43 6 13 15.55 MSE: 3.69 The forecast for week 7:
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In this question you will consider ergodicity and time series averages. Consider the following MA (2) time series model: Ytt 01€t-1 - 0₂€t-2 - Var (Y) = 7+²7 ²2 (1-1) T (2-1) +2 + (-0₁ +010₂) (1 + 0² +02) (1 + 0² +02) (1) (d) You are told that o² = 1, 0₁ = 0.2 and 0₂ = -0.1 is the variance for the time series mean estimator less efficient or more efficient than the T = 20 sample size ensemble average i.i.d. case? Justify your answer with a relevant calculation and explanation using the formula in Equation (1) provided above in part (c) of this question.

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