Econometrics-Autoregressive Linear Regression (ISS (Statistical Services) Statistics Paper III): Questions 1 - 6 of 6

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Question number: 1

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Write down the auto correlation function of order k. For an AR (1) model X t =0.7X t-1t, where {ϵ t} is a white noise process. Show that this model can be expressed as a moving average process of infinite order. Check the model of stationary.

Explanation

Autocorrelations are measures of dependence between variables in a time series. Suppose that Y 1, Y 2, …, Y n are square integrable random variables with the property that the covariance

Equation

of observations with lag k does not depend on t. Then

Equation

is called the auto… (141 more words) …

Question number: 2

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Discuss second order autoregressive series. For this series, obtain complementary function (CF) only.

Explanation

Second order autoregressive series:

Sometimes, the values of a time series data are highly correlated with the values that precede and succeed them. i. e. , The value of a time series at any time “t” may depend upon its own value at times t-1, t-2, …, t-k, the relationship… (149 more words) …

Question number: 3

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Equation , - ∞ < t < ∞, where Equation are i, i. d. with Equation and Equation . Show that the process is stationary with correlation.

Explanation

It is given that Equation

Equation ……………. (i)

Equation

Equation

Equation using (i)

Similarly, we will get

Equation

Equation

But Equation From (i)

Hence, Equation

Equation

EquationEquation

Equation From (i)

Auto -correlation of order k is

Equation, which is independent of k.

Hence, the process is stationary… (2 more words) …

Question number: 4

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

For the auto-regressive scheme Equation , show that if e is a random variable and the series is long, then

Equation

and hence show that, variance of the generated series may be much greater than that of e itself.

Explanation

Given auto-regressive scheme Equation is a second order Auto-regressive series.

Equation ……………. . (i)

Since the series is long and Equation, we have

Equation and VarEquation

Squaring both sides of (i) and taking the expectations, we get

Equation

Equation

Equation…………. . (i)

Multiplying both sides… (66 more words) …

Question number: 5

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2012

Short Answer Question▾

Write in Short

Obtain the general solution of first-order auto-regression model.

Question number: 6

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Obtain the complementary function and particular integral of first order regressive model. Show that Equation is a moving average of random elements with weights, Equation

Explanation

Let us consider the first order auto regressive model

Equation ……. . (i)

this is a linear difference equation of order 1. its complementary function (C. F. ) is the so; ution of

Equation

which is a homogeneous linear difference equation of order 1.

if Equation is the trial solution,… (117 more words) …

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