Isye 6402 Practice Exam Questions With Correct Detailed Answers | Already Graded A+Recent Version

ISYE 6402 PRACTICE EXAM QUESTIONS WITH CORRECT DETAILED ANSWERS | ALREADY GRADED A+RECENT VERSION 1. Statistical Estimation refers to:? - ANSWER Obtaining an approximation of the parameter of a distribution given the data. 2. Statistical Inference refers to: - ANSWER Making statistical statements about an unknown parameter of a distribution, for example, if it is larger than a given value. 3. Time Series can be characterized by: A)Constant or non-constant variability over time. B)Constant, linear or non-linear trend over time. C)Cyclical patterns which may happen at regular or irregular time periods. D)All of the above. - ANSWER d) All of the above 4. Trend in a time series can be estimated using the following approach: A)Using non-parametric regression with time being the predictor if we assume no given shape to the trend. B)Using multiple linear regression if we assume a linear or polynomial trend. C)Using nonlinear regression if we assume a known nonlinear trend up to a set of unknown parameters. D) All of the above. - ANSWER d) All of the above. 5. Seasonality can be estimated using the following approach: A)Using parametric regression with time being the predicting variable. B)Fitting a linear regression model with time entering the model as a linear predictor. C)Fitting a linear regression model with seasonality represented by a categorical variable. D)None of the above. - ANSWER c)Fitting a linear regression model with seasonality represented by a categorical variable. 6. Which of the statements is true? A)There are multiple approaches that can be used to estimate the seasonality. B)Seasonality can be ignored since it can be captured as part of the trend estimation. C)After removing seasonality and trend from a time series, the resulting process is guaranteed to have no additional time dependencies. D) None of the above. - ANSWER a)There are multiple approaches that can be used to estimate the seasonality. 7. Stationarity property of a time series means that: A)The probability distribution of the time series process does not change when shifted in time. B)The mean of the time series process is constant over time. C)The variability in the time series process is finite. D)All of the above. - ANSWER d)All of the above. 8. Which of the statements is true? A)The White noise process is not a stationary process. B)The random walk is a stationary process since it is unpredictable. C)The autocovariance function can be defined for a stationary process. D)None of the above. - ANSWER c)The autocovariance function can be defined for a stationary process. 9. A linear process is A)A moving average (MA) process with the sum of the absolute value of the MA coefficients being finite. B)A time series with a linear trend. C)A time series without seasonality and trend. D)A non-stationary process. - ANSWER A moving average (MA) process with the sum of the absolute value of the MA coefficients being finite. 10. T/F: Time series processes generally can be decomposed into a component modeling systematic variation (trend and seasonality) and a component modeling stochastic stationary variation. - ANSWER True 11. T/F: 2. Consecutive observations in time series data are independent and identically distributed. - ANSWER False 12. T/F: We have the following formula Var(a+by)=bvar(Y) - ANSWER False 13. If the time series ytyt can be represented as trend plus Gaussian white noise with Yt=βt+ϵtyt=βt+ϵt , then its expectation is E( Yt ) = β. - ANSWER False. It would be E(Yt) = E(βt) + E(εt) = βt + 0. 14. If {Xt} is a stationary process, then its autocorrelation function has an expected value of 0 for lag values greater than 0. - ANSWER True 15. A time series generally can be decomposed into three components mt, st and Xt. Where mt is the trend, st is the seasonality, and Xt is a residual time process after accounting for trend and seasonality. - ANSWER True 16. Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. - ANSWER FALSE (The statement would only be true if you knew the two variables were independent.) 17. If the mean of a time series doesn't depend on time t, then the time series is stationary. - ANSWER False. (While constant mean is a necessary condition for stationarity, non-constant variance or significant auto-correlation may be present.) 18. For a random walk process St=∑tj=1Xjwhere Xt∼IID(0,σ2), we have that Var(St) Var(St-1) - ANSWER True 19. The mean of a random walk process depends on time. - ANSWER False 20. All auto-regressive processes are stationary. - ANSWER False 21. Consecutive observations in a white noise process are independent. - ANSWER False 22. The random walk process is not variance stationary. - ANSWER True 23. Whether or not X and Y are independent, we have Cov(a+bx,c+dy)=bdcov(X,Y)Cov(a+bx,c+dy)=bdcov(X,Y). - ANSWER True 24. If the correlation between variables XX and YY is 0, then the two variables must be independent. - ANSWER False 25. If the correlation between X and Y is 1, then one variable must cause the other. - ANSWER False 26. One model for the trend component of a time series is the simple linear regression model in which time is used as an explanatory variable. - ANSWER True 27. The condition that the covariance between Yi and Yi−j depends only on j is sufficient for the process to be stationary. - ANSWER False. (This condition is necessary, but not sufficient. Presence of a trend or non-constant variance would result in a violation of stationarity assumptions.) 28. If {Xt} is white noise, then {−Xt} is stationary. - ANSWER True 29. The main benefit of parametric models is that they have higher degrees of freedom. - ANSWER False 30. If ρ=Corr(X,Y)=0, then X and Y are independent. - ANSWER False 31. Consecutive observations in time series data are serially correlated. - ANSWER True 32. Splines regression is an example of non-parametric trend estimation. - ANSWER True