Answered: Find the mean xt , E(Xt) and the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Economics

Now suppose that the time series process {X_t}, is expressed as X_t = z + e_twhere e_t is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and e_t are uncorrelated:

i. Find the mean x_t , E_(Xt)and the variance X_t, var(X_t). Do they depend on t?

ii. Determine the covariance of x_t and x_t+h for h > 0, Cov(X_t, x_t+h)

iii. Is x_t stationary? Explain.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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