Yule-Walker estimates are used for:

• A) variance
• B) mean
• C) identification
• D) stationarity

Which of the following term is less dependent on discrepancy direction?

• A) residual analysis
• B) reliability analysis
• C) all of these
• D) data analysis

The auto-correlations have……variance, and they are correlated at low lags:

• A) zero
• B) small
• C) large
• D) all of these

Over fitting requires knowledge of discrepancy:

• A) direction
• B) estimates
• C)
• D)

How many Yule-Walker equations are required for an AR(2) process?

• A) 2
• B) 4
• C) 1
• D) 3

Which of the following is a major advantage of an effective LSE iteration start?

• A) minimize computational cost
• B) reduce time duration
• C)
• D)

We can approximate the ----------- estimates by using the estimated auto-correlation coefficients in the linear Yule-Walker equations.

• A) Both of these
• B) LSEs
• C) None of these
• D) MLEs

The sum of squared errors for an AR(2) process are defined as:

• A) $​​​​S = \sum\limits_{t = p + 1}^n {z_t^2}$
• B) $​​​​S = \sum\limits_{t = p +2}^n {z_t^2}$
• C) $S = \sum\limits_{t = p}^n {z_t^2}$
• D) $​​​​S = \sum\limits_{t = p - 1}^n {z_t^2}$

Which of the following process is considered a little difficult as compared to other?

• A) AR
• B) MA
• C)
• D)

The Portmanteau-test is used to determine the significance of first m:

• A) partial correlation
• B) co-variance
• C) auto-correlation
• D) correlation

The sum of squared errors for an AR (1) model is defined as:

• A) $S = \sum\limits_{t = 2}^n {{z^2}_{t + 1}}$
• B) $S = \sum\limits_{t = 2}^n {{z_t}^2}$
• C)
• D)

In iterative LS estimation, the value of $\theta$ corresponding to minimum S is selected as:

• A) LSE
• B) MLE
• C)
• D)

In iterative LS estimation, requirement/s of algorithm is/are:

• A) all of these
• B) stopping rule
• C) initial values of parameters
• D) specification of step size

In AR (1) process each observation depends on its:

• A) previous value
• B) current value
• C)
• D)

Which of the following is the best initiative to begin iteration of the LSE of MA (1) process?

• A) lag series
• B) sample summaries
• C)
• D)

$An{\text{ }}estimate{\text{ }}of\mu \,for\,AR\,(P)\,is\,equal\,to:$

• A) $\frac{1}{{1 - {\phi _1} - ... - {\phi _p}}}\left[ {\bar y\left( {1 - {\phi _1} - ... - {\phi _p}} \right)} \right]$
• B) $\frac{1}{{1 + {\phi _1} + ... + {\phi _p}}}\left[ {\bar y\left( {1 - {\phi _1} - ... - {\phi _p}} \right)} \right]$
• C)
• D)

In LSE MA(1) process, the equation \({r_1}{\hat \theta _1}^2 - {\hat \theta _1} + r = 0\) has number of roots:

• A) 3
• B) 4
• C) 1
• D) 2

In iterative LS estimation, the value of \theta corresponding to minimum S is selected as:

• A) MLE
• B) LSE
• C)
• D)

We can obtain the LSEs of {\phi _1}and {\phi _2} upto {\phi _p} by solving ---------equation simultaneously:

• A) p-1
• B) p+2
• C) p
• D) p+1

An{\text{ }}estimate{\text{ }}of\mu \,for\,AR\,(P)\,is\,equal\,to:

• A) \frac{1}{{1 - {\phi _1} - ... - {\phi _p}}}\left[ {\bar y\left( {1 - {\phi _1} - ... - {\phi _p}} \right)} \right]
• B) \frac{1}{{1 + {\phi _1} + ... + {\phi _p}}}\left[ {\bar y\left( {1 - {\phi _1} - ... - {\phi _p}} \right)} \right]
• C)
• D)