Question 8 (1 point) Assuming that ‘gdp.ts’ is defined as a monthly time series

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Question 8 (1 point)

Assuming that ‘gdp.ts’ is defined as a monthly time series containing GDP values, the object ‘trend’ is a time index and the object ‘season’ is a categorical variable representing month of the year, the command tslm(gdp.ts ~ trend + I(trend^2) + season) would

Estimate a lag-2 difference model for seasonality in the time series ‘gdp’.

Estimate a quadratic trend and multiplicative seasonality in the time series ‘gdp’.

Estimate a linear trend and additive seasonality in the time series ‘gdp’.

Estimate a quadratic trend and additive seasonality in the time series ‘gdp’.

Question 9 (1 point)

After fitting a trend and/or seasonal model to a time series using regression analysis, and re-estimating the model using the entire data set (training + validation periods), you create k-step ahead forecasts by

None of these, because regression models cannot be used for forecasting, only for testing for the statistical existence of trend or seasonal components.

Creating a k-period trailing moving average from the estimated values of the time series.

Substituting future values for trend and season variables into the estimated equation.

Summing the residuals of the estimated regression model for the last k periods.

Question 10 (1 point)

I use 40 quarterly observations on a time series beginning with the first quarter of 2007 to estimate the following model:

Y = 5 + 0.25 Trend + 1 Q2 – 2 Q3 + 0.5 Q4

Where Trend is a time index equal to 1 for the first observation and increases by 1 each quarter; Q2 is a dummy variable equal to 1 for all observations on the second quarter of a year and equal to 0 for all other observations; Q3 and Q4 are similarly defined.

What are the forecasted values of Y for the four quarters of 2017? (time periods 41, 42, 43 and 44)?

24.25; 28.5; 25.75; 30.0

15.25; 16.5; 13.75; 16.5

5.25; 6.5; 3.75; 6.5

46.25; 48.25; 46.25; 49.75

Estimate a lag-2 difference model for seasonality in the time series ‘gdp’.

Estimate a quadratic trend and multiplicative seasonality in the time series ‘gdp’.

Estimate a linear trend and additive seasonality in the time series ‘gdp’.

Estimate a quadratic trend and additive seasonality in the time series ‘gdp’.

Explanation / Answer

First question is answered below

Correct option: (d) Estimate a quadratic trend and additive seasonality in the time series ‘gdp’.

Reason: Since trend is used in square term as well as single term, the equation is quadratic in time and also a term to capture seasonality is added

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