Crest’s Unit Price
In this assignment we will be interested in modeling Crest’s price. You have weekly timeseries
of 276 observations starting first week of January 1958. The weekly time series data is available
in file “CrestPrice.TXT”.
(a) Obtain the plot of the time-series CRESTPR=Crest’s price and its sample autocorrelation
function. Discuss why the CRESTPR series is nonstationary.
(b) Obtain the sample autocorrelation function of the first difference of CRESTPR series.
Discuss why the first difference of the series seems to be stationary. By studying the autocorrelation,
inverse autocorrelation and the partial autocorrelation functions of the first difference of the series
identify a moving average (MA) process to model the first difference of CRESTPR series.
(c) Estimate the MA process whose order you have identified in part (b), write down the
estimated model and discuss whether the residuals of the estimated MA model are white noise.
(d) Instead of using an MA process, estimate a first order AR process for the first
difference of CRESTPR series. Based on the analysis would you say that AR(1) is an
appropriate model for the first difference of CRESTPR series ? Please explain your reasoning.
PART II: A stationary time-series Y can be modeled almost perfectly by a first-order
moving average, MA(1), process. Part of the SAS PROC ARIMA output associated with estimation of
the MA(1) process is given below.
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Unconditional Least Squares Estimation
Standard Approx
Parameter Estimate Error t Value Pr > |t| Lag
MU 24.97770 0.06070 411.52 <.0001 0
MA1,1 0.80214 0.02827 28.38 <.0001 1
Autocorrelation Check of Residuals
To Chi- Pr >
Lag Square DF ChiSq ——————–Autocorrelations——————–
6 5.41 5 0.3683 0.066 -0.030 0.003 -0.057 -0.017 -0.055
12 7.46 11 0.7607 0.001 0.043 -0.001 0.039 0.009 0.031
18 16.08 17 0.5183 0.048 -0.006 -0.023 -0.018 -0.094 -0.080
24 24.67 23 0.3675 -0.058 0.003 -0.062 -0.023 0.094 0.039
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(a) Discuss the behavior of the autocorrelation and inverse autocorrelation functions that
justify the use of MA(1) process to model time-series Y.
(b) Write down the estimated moving average process for Y using back-shift operator
notation.
(c) What can you conclude about the the residuals from the estimated MA(1) process for
series Y ? Please justify your answer.
(d) Based on the given information, will the two-step ahead forecast for Y be equal to the
mean ? Explain why or why not.
(e) Obtain the estimate of autocorrelation function at lag 1 for Y series. Please show your
work.
(f) Obtain partial autocorrelations at lags 1 and 2 for the Y series. Please show your work.
(g) Assume that an analyst incorrectly decides to model the Y series using a second order
autoregressive process, that is, by an AR(2) process. What will be the analyst’s Yule-Walker estimates
of the coefficients and ?    
PLEASE SUBMIT YOUR TYPED