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Reading 13: Time-Series Analysis-LOS d 习题精选

Session 3: Quantitative Methods for Valuation
Reading 13: Time-Series Analysis

LOS d: Discuss the structure of an autoregressive (AR) model of order p, and calculate one- and two-period-ahead forecasts given the estimated coefficients.

 

 

An analyst wants to model quarterly sales data using an autoregressive model. She has found that an AR(1) model with a seasonal lag has significant slope coefficients. She also finds that when a second and third seasonal lag are added to the model, all slope coefficients are significant too. Based on this, the best model to use would most likely be an:

A)
AR(1) model with no seasonal lags.
B)
AR(1) model with 3 seasonal lags.
C)
ARCH(1).


 

She has found that all the slope coefficients are significant in the model xt = b0 + b1xt–1 + b2xt–4 + et. She then finds that all the slope coefficients are significant in the model xt = b0 + b1xt–1 + b2xt–2 + b3xt–3 + b4xt–4 + et. Thus, the final model should be used rather than any other model that uses a subset of the regressors.

The model xt = b0 + b1 xt-1 + b2 xt-2 + b3 xt-3 + b4 xt-4 + εt is:

A)
an autoregressive model, AR(4).
B)
an autoregressive conditional heteroskedastic model, ARCH.
C)
a moving average model, MA(4).


This is an autoregressive model (i.e., lagged dependent variable as independent variables) of order p=4 (that is, 4 lags).

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The model xt = b0 + b1 xt ? 1 + b2 xt ? 2  + εt is:

A)
an autoregressive model, AR(2).
B)
an autoregressive conditional heteroskedastic model, ARCH.
C)
a moving average model, MA(2).


This is an autoregressive model (i.e., lagged dependent variable as independent variables) of order p = 2 (that is, 2 lags).

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Consider the estimated model xt = -6.0 + 1.1 xt-1 + 0.3 xt-2 + εt that is estimated over 50 periods. The value of the time series for the 49th observation is 20 and the value of the time series for the 50th observation is 22. What is the forecast for the 51st observation?

A)
24.2.
B)
30.2.
C)
23.


Forecasted x51 = -6.0 + 1.1 (22) + 0.3 (20) = 24.2.

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Consider the estimated model xt = ?6.0 + 1.1 xt ? 1 + 0.3 xt ? 2 + εt that is estimated over 50 periods. The value of the time series for the 49th observation is 20 and the value of the time series for the 50th observation is 22. What is the forecast for the 52nd observation?

A)
24.2.
B)
42.
C)
27.22.


Using the chain-rule of forecasting,
Forecasted x51 = ?6.0 + 1.1(22) + 0.3(20) = 24.2.
Forecasted x52 = ?6.0 + 1.1(24.2) + 0.3(22) = 27.22.

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