Quant Convariance Stationary question(Schweser Qbank Question ID#: 86427)

can someone tell me how to do question B? there’s no confidence interval given in this problem. I was going to test if b1=1 by using (1.0926-1)/0.0673, and then test if the T-calc is significant different from 0. but without level of significance given, how am i supposed to look up the T table?

Albert Morris, CFA, is evaluating the results of an estimation of the number of wireless phone minutes used on a quarterly basis within the territory of Car-tel International, Inc. Some of the information is presented below (in billions of minutes):

Wireless Phone Minutes (WPM)t = bo + b1 WPMt-1 + ε t

ANOVA

Degrees of Freedom

Sum of Squares

Mean Square

Regression

1

7,212.641

7,212.641

Error

26

3,102.410

119.324

Total

27

10,315.051

Coefficients

Coefficient

Standard Error of the Coefficient

Intercept

-8.0237

2.9023

WPM t-1

1.0926

0.0673

The variance of the residuals from one time period within the time series is not dependent on the variance of the residuals in another.

The value for WPM this period is 544 billion. Using the results of the model, the forecast for three periods in the future is:

A) 691.30. B) 586.35. C) 683.18.

Your answer: C was correct!

The one-period forecast is −8.023 + (1.0926 × 544) = 586.35.

The two-period forecast is then −8.023 + (1.0926 × 586.35) = 632.62.

Finally, the three-period forecast is then −8.023 + (1.0926 × 632.62) = 683.18.

Is the time series of WPM covariance stationary?

A) Yes, because the computed t-statistic for a slope of 1 is significant. B) No, because the Coefficient of WPMt-1 is not less than 1. C) Yes, because the computed t-statistic for a slope of 1 is not significant.

Your answer: B was correct!

For an AR(1) model − the type specified in this problem, when b1 is not less than 1, the time series is said to be covariance nonstationary.

The above model was specified as a(n):

A) Autoregressive (AR) Model. B)Moving Average (MA) Model. C) Autoregressive (AR) Model with a seasonal lag.

Your answer: C was incorrect. The correct answer was A) Autoregressive (AR) Model.

The model is specified as an AR Model, but there is no seasonal lag. No moving averages are employed in the estimation of the model.

Based upon the information provided, Morris would get more meaningful statistical results by:

A) first differencing the data. B) adding more lags to the model. C) doing nothing. No information provided suggests that any of these will improve the specification.

Your answer: A was correct!

Since the slope coefficient is greater than one, the process is not covariance stationary. A common technique to correct for this is to first difference the variable to perform the following regression: Δ(WPM)t = bo + b1 Δ(WPM)t-1 + ε t.

There are two ways to check for nonstationarity - 1) look at a plot of the time series and observe of the mean, variance, etc. looks OK; 2) verify if the coefficients are less than one.

In the example above, the time series has a coefficient greater than one. Which means it has a unit root. A unit rooted time series is nonstationary.

No need for the t-test.

but isn’t unit root is b1=1? if the b1 is greater than 1, b0/(1-b1) wouldn’t be undefined? which means there is no unit root?

nevermind, i figured it out…misread the book…so if the absolute value of b1 is less than 1, then it’s covariance stationary