# 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

### Describe in Detail

Write down the auto correlation function of order k. For an AR (1) model X _{t} =0.7X _{t-1} +ϵ _{t}, 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

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

is called the auto

## Question number: 2

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### 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

## Question number: 3

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### Describe in Detail

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

### Explanation

It is given that

→ ……………. (i)

using (i)

Similarly, we will get

But From (i)

Hence,

From (i)

Auto -correlation of order k is

, which is independent of k.

Hence, the process is stationary

## Question number: 4

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### Describe in Detail

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

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

### Explanation

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

……………. . (i)

Since the series is long and , we have

and Var

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

→

→…………. . (i)

Multiplying both sides

## Question number: 5

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2012

### Write in Short

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

## Question number: 6

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2013

### Describe in Detail

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

### Explanation

Let us consider the first order auto regressive model

……. . (i)

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

which is a homogeneous linear difference equation of order 1.

if is the trial solution,