For a MA process, if $\left| B \right| = 0.4$ then process will called:

• A) Invertible
• B) Not Invertible
• C)
• D)

PACF of ARMA (p, q) is a mixture of exponential and damped sine waves after:

• A) p+q Lag
• B) q Lag
• C) p Lag
• D) p-q Lag

In an ARMA model $\phi \left( B \right){y_t} = \theta \left( B \right){z_t}$, the term $\phi \left( B \right)$ represents:

• A) MA polynomial
• B) AR polynomial
• C)
• D)

In an ARMA model $\phi \left( B \right){y_t} = \theta \left( B \right){z_t}$, the term $\theta \left( B \right)$ represents:

• A) AR polynomial
• B) MA polynomial
• C)
• D)

Behavior of ACF of ARMA (p, q) is similar to:

• A) ACF OF MA (p)
• B) PACF of MA (p)
• C) PACF of AR (p)
• D) ACF of AR (p)

In computational efficiency of an algorithm, ---------------- played an important role.

• A) initial values
• B) parametric values
• C) all of these
• D) statistics values

Which of the following is for diagnostic checking?

• A) underfitting
• B) over fitting
• 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 term ${z_t}$ follows:

• A) normal distribution
• B) standardized normal distribution
• C)
• D)

For large sample size, the approximate LSE of ${\hat \phi _1}$ is given as:

• A) ${{\hat \phi }_1} = {r_1} + {r_2}$
• B) ${{\hat \phi }_1} = {r_1} - {r_2}$
• C) ${{\hat \phi }_1} = {r_1}\,$
• D) ${{\hat \phi }_1} = {r_1}^2$

Mostly, in AR process-MLE, white noise term Zt follow the distribution as:

• A) ${Z_t} \sim N(\mu ,{\sigma ^2})$
• B) ${Z_t} \sim N(0,{\sigma ^2})$
• C)
• D)

In Yule-Walker estimation, Replacing process auto-correlation with the sample aut-ocorrelation, we obtain an equation ------------- for solving Yule-Walker estimates:

• A) ${{\hat \phi }_1} = {r_1}{r_2}$
• B) ${\hat \phi _1} = {r_1}\,$
• 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) 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)