Reading 13- LOS e : Q1- 4 monthly, class, presented, border

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1.e regression results from fitting an AR(1) to a monthly time series are presented below. What is the mean-reverting level for the model?

Model: ΔExpt = b0 + b1ΔExpt–1 + εt
	Coefficients	Standard Error	t-Statistic	p-value
Intercept	1.3304	0.0089	112.2849	< 0.0001
Lag-1	0.1817	0.0061	30.0125	< 0.0001

A)   1.6258.

B)   0.6151.

C)   7.3220.

D)   −0.5499.

2.ppose that the time series designated as Y is mean reverting. If Y_t+1 = 0.2 + 0.6 Y_t, the best prediction of Y_t+1 is:

A)   0.3.

B)   0.6.

C)   0.8.

D)   0.5.

3．ich of the following statements regarding a mean reverting time series is FALSE?

A)   If the time-series variable is x, then x_t = b₀ + b₁ x_t.

B)   The series tends to fall when values are above its mean and to rise when values are below its mean.

C)   If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease.

D)   If the current value of the time series is above the mean reverting level, the prediction is that the time series will increase.

4．vid Brice, CFA, has used an AR(1) model to forecast the next period’s interest rate to be 0.08. The AR(1) has a positive slope coefficient. If the interest rate is a mean reverting process with an unconditional mean, a.k.a., mean reverting level, equal to 0.09, then which of the following could be his forecast for two periods ahead?

A)   0.125.

B)   0.113.

C)   0.072.

D)   0.081.

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1.e regression results from fitting an AR(1) to a monthly time series are presented below. What is the mean-reverting level for the model?

Model: ΔExpt = b0 + b1ΔExpt–1 + εt
	Coefficients	Standard Error	t-Statistic	p-value
Intercept	1.3304	0.0089	112.2849	< 0.0001
Lag-1	0.1817	0.0061	30.0125	< 0.0001

A)   1.6258.

B)   0.6151.

C)   7.3220.

D)   −0.5499.

The correct answer was A)

The mean-reverting level is b₀/(1 – b₁) = 1.3304 /( 1 – 0.1817) = 1.6258.

2.ppose that the time series designated as Y is mean reverting. If Y_t+1 = 0.2 + 0.6 Y_t, the best prediction of Y_t+1 is:

A)   0.3.

B)   0.6.

C)   0.8.

D)   0.5.

The correct answer was D)

The prediction is Y_t+1 = b₀ / (1-b₁) = 0.2 / (1-0.6) = 0.5

3．ich of the following statements regarding a mean reverting time series is FALSE?

A)   If the time-series variable is x, then x_t = b₀ + b₁ x_t.

B)   The series tends to fall when values are above its mean and to rise when values are below its mean.

C)   If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease.

D)   If the current value of the time series is above the mean reverting level, the prediction is that the time series will increase.

The correct answer was D)

If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease; if the current value of the time series is below the mean reverting level, the prediction is that the time series will increase.

4．vid Brice, CFA, has used an AR(1) model to forecast the next period’s interest rate to be 0.08. The AR(1) has a positive slope coefficient. If the interest rate is a mean reverting process with an unconditional mean, a.k.a., mean reverting level, equal to 0.09, then which of the following could be his forecast for two periods ahead?

A)   0.125.

B)   0.113.

C)   0.072.

D)   0.081.

The correct answer was D)

As Brice makes more distant forecasts, each forecast will be closer to the unconditional mean. So, the two period forecast would be between 0.08 and 0.09, and 0.081 is the only possible answer.