QUESTION 6Cointegration means that:a. Two time series integrated of order 1 willmove closely together in the short runb. Two time series integrated of order 1 willbe equal in the long runC. A linear combination of the time serieswill be integrated of order zerod. There will be a nonsense relationshipbetween the two time series

Given: Cointegration means that: a. Two time series integrated of order 1 will move closely together…

Answered: QUESTION 6 Cointegration means that: a.…

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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For each of the time series models below undertake the following steps: Write each time series in characteristic polynomial form using backshift operator (MA or AR or ARMA polynomials as required) Factorise the relevant polynomials and find the roots of the polynomials. • You are given the following additional information regarding the relationship between stationarity and the characteristic polynomial roots. ● ● An AR(p) process is a stationary process if and only if the modulus of all the roots of the AR characteristic polynomial are greater than one. An MA(q) process is always stationary if the MA coefficients are finite. An ARMA (p,q) model admits a unique stationary solution when the AR characteristic poly- nomial and the MA characteristic polynomial have no common roots and the AR polynomial satisfies that it has no unit roots. ● Use this information to determine which of the below models is stationary. (Make sure to justify your answer.) (e) Let {Y} be a stationary process with…
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)
QUESTION 9 Manufacturer claims that the average length of time the new smartphone battery holds until the empty battery is 9 hours. You believe that actually the battery holds less time. What is the correct hypothesis statement? Ho: μ = 9 Ha:μ #9 Ho:μ>9 Ha:μ9
3. Jobs arrive in a computer queue in the manner of a Poisson process with intensity λ. The central processor handles them one by one in the order of their arrival, and each has an exponentially distributed runtime with parameter , the runtimes of different jobs being independent of each other and of the arrival process. Let X (t) be the number of jobs in the system (either running or waiting) at time t, where X (0) = 0. Explain why X is a Markov chain, and write down its generator. Show that a stationary distribution exists if and only if λ < μ, and find it in this case.
Problem 3. (Exercise 8, Section 9.5.7) Resistors of a certain type have resistances that are exponentially distributed with parameter 1 = 0.04. An operator connects 50 independent resistors in series, which causes total resistance in the circuit to be the sum of individual resistances.
In a certain village accidents occur Infrequently. It is known that the probability of an accident on any given day is 0.02 and accidents are independent of each other. What is the probability that in any given period of 250 days there will be an accident on one day? Use Poisson approximation. O a.0.073 O b.0.034 O c.0.966 Od. 0.271
QUESTION 1 In a certain village accidents occur infrequently. It is known that the probability of an accident on any given day is 0.02 and accidents are independent of each other. What is the probability that in arry give of 400 days there will be an accident on one day? Use Poisson approximation. a. 0.0027 b. 0.9973 c. 0.0150 O d. 0.2710 QUESTION 2 The probability that a patient recovers from a rare blood disease is 0.3. If 12 people are known to have contracted this disease, what is the probability that at least 5 survive? O a. 0.0017 O b.0.2763 O c. 0.0095 O d. 0.0386 QUESTION 3 Click Save and Submit to save and submit. Click Save All Answers to save all answers. DOLL
(2) At the Taza Chocolate facility, chocolate is piped from the room where it is mixed to another room where it is packaged. Because only one such pipe exists, they have a delicious detection problem each time they swap from making one flavor to another. One worker tastes the output and, when they estimate the onset of flavor B, instead of flavor A, they push a button so that it is packaged as flavor B. FOr each of the statements below: ● Explain the meaning such that it is easily understood by somebody who has no formal statistics experience. • Describe the contents and labelling of a disc of chocolate produced under this error (e.g. chocolate A is labelled as chocolate B) Hint: it may help to note that the worker is attempting to detect the start of flavor B so our null hypothesis, Ho, refers to the event that it is still flavor A while H₁, our detection event, refers to when flavor B is now coming out of the pipe. (a) The worker has a Type I error rate of less than 3%. (b) The…
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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.
Consider two assets with returns: rị = 3 (:) r2 = in two states. If the 1 has a return (:) portfolio z = find the value of a.

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