JoeyDVivre

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

Salest = b0 + b1 Sales t-1+ εt

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

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

B) (Salest - Salest-1)= b0 + b1 (Sales t-1 - 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.

JoeyDVivre

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

JoeyDVivre

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

A) first difference the data because b1 = 1.

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

C) not first difference the data because b1 − b0 = 1.0 − 0.5 = 0.5 < 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.

JoeyDVivre

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.

JoeyDVivre

A time series x that is a random walk with a drift is best described as:

A) xt = b0 + b1xt − 1 + εt.

B) xt = b0 + b1 xt − 1.

C) xt = xt − 1 + εt.

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The best estimate of random walk for period t is the value of the series at (t − 1). If the random walk has a drift component, this drift is added to the previous period’s value of the time series to produce the forecast.

JoeyDVivre

Which of the following statements regarding time series analysis is least accurate?

A) We cannot use an AR(1) model on a time series that consists of a random walk.

B) If a time series is a random walk, first differencing will result in covariance stationarity.

C) An autoregressive model with two lags is equivalent to a moving-average model with two lags.

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An autoregression model regresses a dependent variable against one or more lagged values of itself whereas a moving average is an average of successive observations in a time series. A moving average model can have lagged terms but these are lagged values of the residual.

JoeyDVivre

David Brice, CFA, has tried to use an AR(1) model to predict a given exchange rate. Brice has concluded the exchange rate follows a random walk without a drift. The current value of the exchange rate is 2.2. Under these conditions, which of the following would be least likely?

A) The residuals of the forecasting model are autocorrelated.

B) The forecast for next period is 2.2.

C) The process is not covariance stationary.

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The one-period forecast of a random walk model without drift is E(xt+1) = E(xt + et ) = xt + 0, so the forecast is simply xt = 2.2. For a random walk process, the variance changes with the value of the observation. However, the error term et = xt - xt-1 is not autocorrelated.

JoeyDVivre

Given an AR(1) process represented by xt+1 = b0 + b1×xt + et, the process would not be a random walk if:

A) b1 = 1.

B) E(et)=0.

C) the long run mean is b0 + b1.

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For a random walk, the long-run mean is undefined. The slope coefficient is one, b1=1, and that is what makes the long-run mean undefined: mean = b0/(1-b1).

JoeyDVivre

The main reason why financial and time series intrinsically exhibit some form of nonstationarity is that:

A) most financial and economic relationships are dynamic and the estimated regression coefficients can vary greatly between periods.

B) serial correlation, a contributing factor to nonstationarity, is always present to a certain degree in most financial and time series.

C) most financial and time series have a natural tendency to revert toward their means.





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Because all financial and time series relationships are dynamic, regression coefficients can vary widely from period to period. Therefore, financial and time series will always exhibit some amount of instability or nonstationarity.

MarginofSafety

Which of the following statements regarding the instability of time-series models is most accurate? Models estimated with:

A) a greater number of independent variables are usually more stable than those with a smaller number.

B) shorter time series are usually more stable than those with longer time series.

C) longer time series are usually more stable than those with shorter time series.

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Those models with a shorter time series are usually more stable because there is less opportunity for variance in the estimated regression coefficients between the different time periods.