Crest's Unit Price

Crest's Unit Price modelin" rel="nofollow">ing Crest's price. You have weekly timeseries of 276 observations startin" rel="nofollow">ing first week of January 1958. The weekly time series data is available in" rel="nofollow">in file "CrestPrice.TXT". (a) Obtain" rel="nofollow">in the plot of the time-series CRESTPR=Crest's price and its sample autocorrelation function. Discuss why the CRESTPR series is nonstationary. (b) Obtain" rel="nofollow">in the sample autocorrelation function of the first difference of CRESTPR series. Discuss why the first difference of the series seems to be stationary. By studyin" rel="nofollow">ing the autocorrelation, in" rel="nofollow">inverse autocorrelation and the partial autocorrelation functions of the first difference of the series identify a movin" rel="nofollow">ing average (MA) process to model the first difference of CRESTPR series. (c) Estimate the MA process whose order you have identified in" rel="nofollow">in part (b), write down the estimated model and discuss whether the residuals of the estimated MA model are white noise. (d) Instead of usin" rel="nofollow">ing 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" rel="nofollow">in your reasonin" rel="nofollow">ing. PART II: A stationary time-series Y can be modeled almost perfectly by a first-order movin" rel="nofollow">ing average, MA(1), process. Part of the SAS PROC ARIMA output associated with estimation of the MA(1) process is given below. ______________________________________________________________________________ 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 ______________________________________________________________________________ (a) Discuss the behavior of the autocorrelation and in" rel="nofollow">inverse autocorrelation functions that justify the use of MA(1) process to model time-series Y. (b) Write down the estimated movin" rel="nofollow">ing average process for Y usin" rel="nofollow">ing 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 in" rel="nofollow">information, will the two-step ahead forecast for Y be equal to the mean ? Explain" rel="nofollow">in why or why not. (e) Obtain" rel="nofollow">in the estimate of autocorrelation function at lag 1 for Y series. Please show your work. (f) Obtain" rel="nofollow">in partial autocorrelations at lags 1 and 2 for the Y series. Please show your work. (g) Assume that an analyst in" rel="nofollow">incorrectly decides to model the Y series usin" rel="nofollow">ing 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 ?