Quantitative Methods - QBanks

Which of the following is a seasonally adjusted model? A) (Salest - Sales t-1)= b0 + b1 (Sales t-1 - Sales t-2) + b2 (Sales t-4 - Sales t-5) + εt. B) Salest = b1 Sales t-1+ εt. C) Salest = b0 + b1 Sales t-1 + b2 Sales t-2 + εt.

A) (Salest - Sales t-1)= b0 + b1 (Sales t-1 - Sales t-2) + b2 (Sales t-4 - Sales t-5) + εt. Explanation This model is a seasonal AR with first differencing. (Module 2.4, LOS 2.l)

Troy Dillard, CFA, has estimated the following equation using quarterly data: xt = 93 - 0.5×xt- 1 + 0.1×xt- 4 + et. Given the data in the table below, what is Dillard's best estimate of the first quarter of 2007? A) 67.20. B) 66.40. C) 66.60.

A) 67.20. Explanation To get the answer, Dillard will use the data for 2006: IV and 2006: I, xt- 1 = 66 and xt- 4 = 72 respectively: E[x2007:I] = 93- 0.5×xt- 1 + 0.1×xt- 4 E[x2007:I] = 93- 0.5×66 + 0.1×72 E[x2007:I] = 67.20 (Module 2.2, LOS 2.d)

Which of the following statements regarding heteroskedasticity is least accurate? A) Heteroskedasticity only occurs in cross-sectional regressions. B) Conditional heteroskedasticity can be detected using the Breusch-Pagan chi-square statistic. C) When not related to independent variables, heteroskedasticity does not pose any major problems with the regression.

A) Heteroskedasticity only occurs in cross-sectional regressions. Explanation If there are shifting regimes in a time-series (e.g., change in regulation, economic environment), it is possible to have heteroskedasticity in a time-series. Unconditional heteroskedasticity occurs when the heteroskedasticity is not related to the level of the independent variables. Unconditional heteroskedasticity causes no major problems with the regression. Breusch-Pagan statistic has a chi-square distribution and can be used to detect conditional heteroskedasticity. (Module 1.3, LOS 1.h)

The regression results from fitting an AR(1) model to the first-differences in enrollment growth rates at a large university includes a Durbin-Watson statistic of 1.58. The number of quarterly observations in the time series is 60. At 5% significance, the critical values for the Durbin-Watson statistic are dl = 1.55 and du = 1.62. Which of the following is the most accurate interpretation of the DW statistic for the model? A) The Durbin-Watson statistic cannot be used with AR(1) models. B) Since dl < DW < du, the results of the DW test are inconclusive. C) Since DW > dl, the null hypothesis of no serial correlation is rejected.

A) The Durbin-Watson statistic cannot be used with AR(1) models. Explanation The Durbin-Watson statistic is not useful when testing for serial correlation in an autoregressive model where one of the independent variables is a lagged value of the dependent variable. The existence of serial correlation in an AR model is determined by examining the autocorrelations of the residuals. (Module 2.2, LOS 2.e)

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 process is not covariance stationary. C) The forecast for next period is 2.2.

A) The residuals of the forecasting model are autocorrelated. Explanation 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. (Module 2.3, LOS 2.i)

Alexis Popov, CFA, wants to estimate how sales have grown from one quarter to the next on average. The most direct way for Popov to estimate this would be: A) a linear trend model. B) an AR(1) model with a seasonal lag. C) an AR(1) model.

A) a linear trend model. Explanation If the goal is to simply estimate the dollar change from one period to the next, the most direct way is to estimate xt = b0 + b1 × (Trend) + et, where Trend is simply 1, 2, 3, ....T. The model predicts a change by the value b1 from one period to the next. (Module 2.5, LOS 2.o)

One of the main assumptions of a multiple regression model is that the variance of the residuals is constant across all observations in the sample. A violation of the assumption is most likely to be described as: A) heteroskedasticity. B) unstable remnant deviation. C) positive serial correlation.

A) heteroskedasticity. Explanation Heteroskedasticity is present when the variance of the residuals is not the same across all observations in the sample, and there are sub-samples that are more spread out than the rest of the sample. (Module 1.3, LOS 1.h)

Which of the following is least likely a consequence of a model containing ARCH(1) errors? The: A) model's specification can be corrected by adding an additional lag variable. B) variance of the errors can be predicted. C) regression parameters will be incorrect.

A) model's specification can be corrected by adding an additional lag variable. Explanation The presence of autoregressive conditional heteroskedasticity (ARCH) indicates that the variance of the error terms is not constant. This is a violation of the regression assumptions upon which time series models are based. The addition of another lag variable to a model is not a means for correcting for ARCH (1) errors. (Module 2.5, LOS 2.m)

When two or more of the independent variables in a multiple regression are correlated with each other, the condition is called: A) multicollinearity. B) conditional heteroskedasticity. C) serial correlation.

A) multicollinearity. Explanation Multicollinearity refers to the condition when two or more of the independent variables, or linear combinations of the independent variables, in a multiple regression are highly correlated with each other. This condition distorts the standard error of estimate and the coefficient standard errors, leading to problems when conducting t-tests for statistical significance of parameters. (Module 1.3, LOS 1.j)

Suppose you estimate the following model of residuals from an autoregressive model: εt2 = 0.25 + 0.6ε2t-1 + µt, where ε = ε^ If the residual at time t is 0.9, the forecasted variance for time t+1 is: A) 0.790. B) 0.736. C) 0.850.

B) 0.736. Explanation The variance at t = t + 1 is 0.25 + [0.60 (0.9)2] = 0.25 + 0.486 = 0.736. See also, ARCH models. (Module 2.5, LOS 2.m)

Which of the following is least likely a method used to detect heteroskedasticity? A) Breusch-Pagan test. B) Breusch-Godfrey test. C) Scatter plot.

B) Breusch-Godfrey test. Explanation The Breusch-Godfrey test is used to detect serial correlation. The Breusch-Pagan test is a formal test used to detect heteroskedasticity while a scatter plot can give visual clues about presence of heteroscedasticity. (Module 1.3, LOS 1.h)

When interpreting the results of a multiple regression analysis, which of the following terms represents the value of the dependent variable when the independent variables are all equal to zero? A) p-value. B) Intercept term. C) Slope coefficient.

B) Intercept term. Explanation The intercept term is the value of the dependent variable when the independent variables are set to zero. (Module 1.1, LOS 1.b)

Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated: AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt - 2.0 INSt with a PI calculated t-statistic of 0.45, a TEEN calculated t-statistic of 2.2, and an INS calculated t-statistic of 0.63. The equation was estimated over 40 companies. Using a 5% level of significance, which of the independent variables significantly different from zero? A) PI only. B) TEEN only. C) PI and INS only.

B) TEEN only. Explanation The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant. (Module 1.1, LOS 1.b)

One possible problem that could jeopardize the validity of the employment growth rate model is multicollinearity. Which of the following would most likely suggest the existence of multicollinearity? A) The variance of the observations has increased over time. B) The F-statistic suggests that the overall regression is significant, however the regression coefficients are not individually significant. C) The Durbin-Watson statistic is significant.

B) The F-statistic suggests that the overall regression is significant, however the regression coefficients are not individually significant. Explanation One symptom of multicollinearity is that the regression coefficients may not be individually statistically significant even when according to the F-statistic the overall regression is significant. The problem of multicollinearity involves the existence of high correlation between two or more independent variables. Clearly, as service employment rises, construction employment must rise to facilitate the growth in these sectors. Alternatively, as manufacturing employment rises, the service sector must grow to serve the broader manufacturing sector. The variance of observations suggests the possible existence of heteroskedasticity. If the Durbin-Watson statistic may be used to test for serial correlation at a single lag. (Module 1.2, LOS 1.f)

Assume that in a particular multiple regression model, it is determined that the error terms are uncorrelated with each other. Which of the following statements is most accurate? A) Serial correlation may be present in this multiple regression model, and can be confirmed only through a Durbin-Watson test. B) This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated. C) Unconditional heteroskedasticity present in this model should not pose a problem, but can be corrected by using robust standard errors.

B) This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated. Explanation One of the basic assumptions of multiple regression analysis is that the error terms are not correlated with each other. In other words, the error terms are not serially correlated. Multicollinearity and heteroskedasticity are problems in multiple regression that are not related to the correlation of the error terms. (Module 1.3, LOS 1.i)

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) 30.2. B) 23. C) 24.2

C) 24.2. Explanation Forecasted x51 = -6.0 + 1.1 (22) + 0.3 (20) = 24.2. (Module 2.2, LOS 2.d)

Which of the following uses of data is most accurately described as curation? A) A data technician accesses an offsite archive to retrieve data that has been stored there. B) An investor creates a word cloud from financial analysts' recent research reports about a company. C) An analyst adjusts daily stock index data from two countries for their different market holidays.

C) An analyst adjusts daily stock index data from two countries for their different market holidays. Explanation Curation is ensuring the quality of data, for example by adjusting for bad or missing data. Word clouds are a visualization technique. Moving data from a storage medium to where they are needed is referred to as transfer. (Module 4.1, LOS 4.a)

A fund has changed managers twice during the past 10 years. An analyst wishes to measure whether either of the changes in managers has had an impact on performance. R is the return on the fund, and M is the return on a market index. Which of the following regression equations can appropriately measure the desired impacts? A) The desired impact cannot be measured. B) R = a + bM + c1D1 + c2D2 + c3D3 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the second manager, and D3 = 1 is the return is from the third manager. C) R = a + bM + c1D1 + c2D2 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager.

C) R = a + bM + c1D1 + c2D2 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager. Explanation The effect needs to be measured by two distinct dummy variables. The use of three variables will cause collinearity, and the use of one dummy variable will not appropriately specify the manager impact. (Module 1.4, LOS 1.l)

Wilson estimated a regression that produced the following analysis of variance (ANOVA) table: The values of R2 and the F-statistic to test the null hypothesis that slope coefficients on all variables are equal to zero are: A) R2 = 0.25 and F = 0.930. B) R2 = 0.20 and F = 13.333. C) R2 = 0.25 and F = 13.333.

C) R2 = 0.25 and F = 13.333. Explanation R2 = RSS / SST = 100 / 400 = 0.25 The F-statistic is equal to the ratio of the mean squared regression to the mean squared error. F = 100 / 7.5 = 13.333 (Module 1.2, LOS 1.e)

The table below shows the autocorrelations of the lagged residuals for quarterly theater ticket sales that were estimated using the AR(1) model: ln(salest) = b0 + b1(ln salest − 1) + et. Assuming the critical t-statistic at 5% significance is 2.0, which of the following is the most likely conclusion about the appropriateness of the model? The time series: A) would be more appropriately described with an MA(4) model. B) contains ARCH (1) errors. C) contains seasonality.

C) contains seasonality. Explanation The time series contains seasonality as indicated by the strong and significant autocorrelation of the lag-4 residual. (Module 2.4, LOS 2.l)