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

• A) 4
• B) 2
• C) 1
• D) 3

Which of the the following is a condition of diagnostic checking of fitted model:

• A) $m > p - q$
• B) $m > p + q\,\,$
• C) $m < pq$
• D) $m < \frac{p}{q}$

$In{\text{ }}the{\text{ }}equation,\;{r_1}\,\,{\hat \theta _1}^2 - {\hat \theta _1} + r = 0\,,\,for{\text{ }}a\;MA\left( 1 \right){\text{ }}process,{\text{ }}we{\text{ }}assume\,\,{\theta _1}:$

• A) invertible
• B) stationary
• C)
• D)

In an AR(p) process, ${y_t} = {\phi _1}{y_t}_{ - 1} + {\phi _2}{y_{t - 2}} + ... + {\phi _p}{y_{t - p}} + {z_t}$, the likelihood function is defined as:

• A) $L = f\left( {{y_1},{y_2},...,{y_p}} \right).\prod\limits_{t = p + 1}^n {\left( {{y_{p + 1}}|{y_1},{y_2},...,y} \right)}$
• B) $L = f\left( {{y_1},{y_2},...,{y_p}} \right).\sum\limits_{t = p + 1}^n {\left( {{y_{p + 1}}|{y_1},{y_2},...,y} \right)}$
• C)
• D)

Approximate LSEs of AR (2) process are equivalent to the estimates of:

• A) AR (1)
• B) MA (2)
• C) ARIMA
• D) Yule- Walker

In the equation ${\hat \phi _1} = {R^{ - 1}}r$ , R and r represent:

• A) sample information
• B) population information
• C)
• D)

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

• A) p
• B) p+1
• C) p+2
• D) p-1

In case of IID sample, the joint distribution is the _______ of marginal distributions.

• A) sum
• B) division
• C) product
• D) difference

To obtain the least squares estimates, we need to formulate an:

• A) subjective function
• B) objective function
• C)
• D)

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)