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.) (c) Yt+1+ Yt - (1 − B)(1 + B)Yt+1 = Vet

Q: what is the generating function of an  an+1=4an-an-1 (n>2)  a0=1, a1=1, a2=4

A: We have been given a recurrence relation . an+1=4an-an-1 , a0=1 , a1=1,a2=4  For , homogenous…

Q: (b) Compute the values of each of the following expressions: i. () ii. (1), (1) iii. (2), ), iv. 6).…

A: The expressions are given in the form .It represents the combination of  out of .The formula for…

Q: Find the Fourier series representation of the even extension of the function represented by the…

A:

Q: 1-x We want to compute dr.

A:

Q: (a) Given that 2 2-1x 4*+y = 128 and 9シーェ 27ソー4 = 1, find the value of each of the integers x and y…

A:

Q: Assume that orders arrive at a mean rate of λ orders per minute, and that interarrival times are…

A: The arrival rate of orders per minuteThe interarrival times have an exponential distribution.The…

Q: D. f(s) = 3/2 = 0 = 3/2 = 3 = 3/2 s=0 $1 0<s<5 si s=5 si 5 < s <10 si s = 10 $1

A:

Q: How long does it take until 5% of the isotope technetium-99m d) nains? Round to the nearest tenth of…

A: Topic:- exponential decaying function

Q: A discrete time function is defined as x[n] = {0, 0, 0, 6, 0} and  x[n] = x[n + 5]. This Find the…

A: Given a periodic function xk with period N, the Fourier series is expressed as xk=∑n=0N-1cne2πiknN…

Q: Sind Laflace inverse; 1

A:

Q: Compute Pearson's r wth the computational formula and use 4 decimal places for all computations.…

A: We have given that data  I want to find Pearson's (r) r= SSXY/sqrt(SSXY × SSYY)

Q: Apply the Newton–Raphson algorithm to the function f(x) = x'/3 whose graph is drawn in Fig. 10(a).…

A: Acc. to Newton- Raphson Method  x1 = x0 -f'(x0)f(x0) f(x) = x13 f'(x) = 13x23 Now x0= 1 Hence  x1=…

Q: Question 2 (a) i. Find the z-transform of the following sequences: {9k +7}=0 ii. {5k + k}=0

A:

Q: QUESTION 1 Suppose x is N(30, 4). Find P(x < 29.5). Calculate answer to at least 4 decimal places of…

A: As per our guidelines we are suppose to do only one question1)Givenx~N(30,4)Mean(μ)=30standard…

Q: For each of the time series models below undertake the following steps: • Write each time series in…

A: Given the time series model as ϕBYt=12∇2εt+121+2Bεt where one of the roots of the polynomial ϕB lie…

Q: Find at least three nonzero terms (including a, and at least two cosine terms and two sine terms if…

A:

Q: 1 -1 3 Express the periodic function as a Fourier Series Expansion. Simplify to lowest terms. 3.

A:

Q: 6. Interval, - TT <x < TT; function, f(x) = 0, = x2 - TT<x<T 0 <x< TT

A:

Q: Find the taylor series for f(x) = -4ex about x=5

A: The Taylor series of a function f(x) is given by  f(x)=∑n=0∞fn(a)n!(x-a)n Here, the given function…

Q: Determine discrete numeric function corresponding to the following generating function: A(Z)=1/1-Z³

A: Given generating function is A(z)=11-z3 We can write it as A(z)=1-z3-1⇒A(z)=1+z3+z6+z9+....

Q: There is one male baby seal for every nine female baby seals. Let X be the number of male baby seals…

A: Let p=P(male baby seal) = 1/9 Here n=5 Note that X follows a Binomial distribution with n=5 and…

Q: an= ant + an-z (n23, 90=0, a,=l, ag=2) %3D

A: Given that a0=0, a1=1 , a2=2 and an=an-1+an-2. Take n=3 in the equation an=an-1+an-2, a3=2+1=3 Take…

Q: If you have a sequence x[n] with the following Fourier Transform: X(elu) = 4cos(3w) then the Fourier…

A: Given that, xejw=4cos3w From the properties of discrete sine fourier transform,…

Q: Find the Fourier series for g(x) = 1 + x,-π < x < π. Use the same orthogonal set used in class (the…

A:

Q: 4. A sawtooth wave is a kind of waveform that ramps upward and then drops off sharply. They are…

A: According to graph we see that  simpson's 1/3 rule is best method for accurate result .

Q: Find the Fourier Series Expansion of the following periodic functions.

A: Given function is f(x)=x3, 0&lt;x&lt;c Let the Fourier series be…

Q: A coin is tossed repeatedly, and heads turns up with probability p on each toss. Let hn be the…

A:

Q: 1- Find Z-transform if x (n) = bln|

A: The given function is xn=bn To find its Z-transform.

Q: Question 2 Write the letter of the chosen answer in the Box below: Question 2, Part: 1 2 3 4 5…

A:

Q: Explain the time series regression model assumptions?

A:

Q: Determine the sequence of the generating function A(8) = – log. (1 – s)\s |

A:

Q: 3. Using the definition of big-O, show that n = O(2"). Give a particular c and no. 4. Identify a…

A: See answer

Q: 19) You run cross validation using the Caret package and get the following output. model log$results…

A: 19) Given cross validation output, From the given output, the accuracy indicates the average…

Q: A survey asked 500 random people how often they use the bathroom on a daily basis. Nineteen percent…

A: Let X=the no.of times a person goes to the bathroom on a daily basis.

Q: 3.2-2. Telephone calls arrive at a doctor's office according to a Poisson process on the average of…

A: There are 2 calls every 3 minutes.Let X be the waiting time until the first call and it follows an…