Please answer all parts with detailed solutions. 4. Figure 1 shows the sample au

Question

Please answer all parts with detailed solutions.

4. Figure 1 shows the sample autocorrelation SACF and sample partial autocorrelation functions SPACF of (a) amount of deviations from a specified target value that an industrial machining process produced, (b) price of oil, (c) number of guests at a hotel. Use the SACF and SPACF of these series given in Figure 1 to answer the following questions (a) Are the series stationary? Why? (b) If any of the series is nonstationary, is it a seasonal time series? Can you identify the period of the series? If yes, state the period. Does the series contain a trend component? Why? Justify your answers (c) For the stationary series, identify and write down possible stationary models for the series. Justify your answers.

Explanation / Answer

a ) Series 1 is stationary, Because of the PACF being zero after finite lag (l=2)

  Series 2 is stationary, Because of the PACF being zero after finite lag (l=2)

  Series 3 is Not stationary, Because of the ACF has sinusoidal-like shape

b) Mathematically is was proven that period of Sample ACF and period of time series is same.So for the series 3 time period of the series is 8 lags.

c ) If The ACF is Zero after finite lag, then Time series follows MA Model.

If The PACF is Zero after finite lag, then Time series follows AR Model.

PACF of Series 1 zero, after lag 1 and ACF of Series 1 zero, after lag 4 . So possible models for Series 1 are MA(4) or AR(1)

PACF of Series 1 zero, after lag 1  So possible model for Series 1 is AR(1).

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