1. A data series required one seasonal difference and two non seasonal differenc

Question

1. A data series required one seasonal difference and two non seasonal differences to make it stationary. You have found two early spikes in the partial autocorrelation function after the non seasonal differences with converging autocorrelations. In addition you found one spike in the autocorrelation function for the seasonal differenced data along with converging partial autocorrelations. Which is the appropriate ARIMA menu for the model?

a)

b)

c)

d)

(1,2,0)(2,1,0)

2. The major disadvantages of differencing to smooth data include

a)

b)

c)

d)

a)

(1,0, 1)(2,2,0)

b)

(2,2,0)(0,1,1)

c)

(2,2,1)(2,1,0)

d)

(1,2,0)(2,1,0)

2. The major disadvantages of differencing to smooth data include

a)

observations (degrees of freedom) will be lost and it requires a large amount of data.

b)

lost observations (n) have influence on the significance of the ARIMA model.

c)

too many differences are taken the differenced data series becomes more autoregressively unstable.

d)

all of the above.

Explanation / Answer

1) Solution: (2,2,1)(2,1,0)

Explanation: Since two early spikes in the partial autocorrelation function after the non seasonal differentials with converging autocorrelations; and we found one spike in the autocorrelation function along with converging partial autocorrelations for the seasonal differenced data the AMIS will be (2,2,1)(2,1,0)

2) Solution: Observations (degrees of freedom) will be lost to make the data series stationary relative to seasonality and trend/cycle.

Explanation: The major drawback of differencing to smooth data is the lost of degree of freedom while making the data series stationary relative to trend and additive seasonal pattern

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