I need short explain when you choose your answer books name : Introduction to Ec

Question

I need short explain when you choose your answer
books name :
Introduction to Econometrics 3rd Edition by James H. Stock and Mark W. Watson
Applied Econometric Time Series 4 rd Edition by Walter Enders

13- Consider a non-stationary time series that follows a random walk drift The first difference of the time series will result in a stationary time series, The deterministic time deterministic time detrending methods will result in a stationary time series. a- b- c Both the first difference and deterministic time detrending methods will result in a stationary time series. d- None of the above will result in a stationary time series. 14- Two or more time-series that have a common stochastic trend are said to be..... a- Integrated b- Endogenous c cointegrated d- None of the above 15- A problem where stochastic trends can lead two time series to appear related when they are n... is called a- Robust regression b- Spurious regression c Unit root d- Autocorrelation

Explanation / Answer

13) A random walk with a drift can be transformed to a stationary process by differencing (subtracting Yt-1 from Yt, taking the difference Yt - Yt-1) correspondingly to Yt - Yt-1 = t or Yt - Yt-1 = + t and then the process becomes difference-stationary. The process loses one observation each time the difference is taken- disadvantage of differencing.

A non-stationary process with a deterministic trend becomes stationary after removing the trend, or detrending. For example, Yt = + t + t is transformed into a stationary process by subtracting the trend t: Yt - t = + t. No observation is lost when detrending is used to transform a non-stationary process to a stationary one.

In the case of a random walk with a drift and deterministic trend, detrending can remove the deterministic trend and the drift, but the variance will continue to go to infinity. As a result, differencing must also be applied to remove the stochastic trend. Therefore correct option is C.

14) cointegrated. we need cointegration because the standard regression analysis fails when dealing with non-stationary variables, leading to spurious regressions that suggest relationships even when there are none.

For example, suppose we regress two independent random walks against each other, and test for a linear relationship. A large percentage of the time, we'll find high R-squared values and low p-values when using standard OLS statistics, even though there's absolutely no relationship between the two random walks. we can apply one common unit root to two individual values and can test by cointegration methods.

15) autocorrelation- also known as serial correlation or cross-autocorrelation,is the cross-correlation of a signal with itself at different points in time (that is what the cross stands for). It is the similarity between observations as a function of the time lag between them. a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonicfrequencies. It is often used in signal processing for analyzing functions or series of values, such as time domainsignals.

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