Reading 13: Time-Series Analysis-LOS j 习题精选 center, likely, 2011

土豆妮

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

LOS j: Discuss the implications of unit roots for time-series analysis, explain when unit roots are likely to occur and how to test for them, and demonstrate how a time series with a unit root can be transformed so it can be analyzed with an AR model.

 

 

Barry Phillips, CFA, has the following time series observations from earliest to latest: (5, 6, 5, 7, 6, 6, 8, 8, 9, 11). Phillips transforms the series so that he will estimate an autoregressive process on the following data (1, -1, 2, -1, 0, 2, 0, 1, 2). The transformation Phillips employed is called:

A) beta drift.

B) first differencing.

C) moving average.

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Phillips obviously first differenced the data because the 1=6-5, -1=5-6, .... 1 = 9 - 9, 2 = 11 - 9.

土豆妮

Barry Phillips, CFA, has estimated an AR(1) relationship (x_t = b₀ + b₁ × x_t-1 + e_t) and got the following result: x_t+1 = 0.5 + 1.0x_t + e_t. Phillips should:

A) not first difference the data because b0 = 0.5 < 1.

B) not first difference the data because b1 ? b0 = 1.0 ? 0.5 = 0.5 < 1.

C) first difference the data because b1 = 1.

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The condition b₁ = 1 means that the series has a unit root and is not stationary. The correct way to transform the data in such an instance is to first difference the data.

土豆妮

A time series that has a unit root can be transformed into a time series without a unit root through:

A) calculating moving average of the residuals.

B) first differencing.

C) mean reversion.

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First differencing a series that has a unit root creates a time series that does not have a unit root.

土豆妮

Suppose that the following time-series model is found to have a unit root: 

Sales_t = b₀ + b₁ Sales _t-1+ ε_t

What is the specification of the model if first differences are used?

A) (Salest - Salest-1)= b0 + b1 (Sales t-1 - Sales t-2) + εt.

B) Salest = b0 + b1 Sales t-1 + b2 Sales t-2 + εt.

C) Salest = b1 Sales t-1+ εt.

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Estimation with first differences requires calculating the change in the variable from period to period.