Econometrics-Autoregressive Linear Regression (ISS 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

Cov(Yt+k,Yt)=E[(Y… (601 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… (308 more words) …

Question number: 3

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Ut=aξ+et , - ∞ < t < ∞, where ets are i, i. d. with E(et)=0 and V(et)=1 . Show that the process is stationary with correlation.

Explanation

It is given that E(et)=0

} ……………. (i)

V(Ut)=V(aξ+et)

=a2V(ξ)+V(et)+2aCov(ξ… (238 more words) …

Question number: 4

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

For the auto-regressive scheme Ut+2+aUt+1+bUt=et+2 , show that if e is a random variable and the series is long, then

Var(U)Var(e)=(1+b)(1b)[(1+b)2a2]

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

Explanation

Given auto-regressive scheme Ut+2+aUt+1+bUt=et+2 is a second order Auto-regressive series.

Ut+2+aUt+1+bUt=et+2 ……………. . (i)… (695 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 Ut is a moving average of random elements with weights, 1,a,a2,at1

Explanation

Let us consider the first order auto regressive model

Ut+1=aUt+εt+1 ……. . (i)

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

Ut+1=… (345 more words) …

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