what do these results tell you about the ols residuals are they stationary

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Homework Assignment #3

 The data file DATA02.xlsx contains monthly data for the period Jan-1991 through Mar-2021 (Mar-2021 CPIU is estimated).

There are three data series, RIGS, WTI, and CPIU.

RIGS is the total rig count in the lower 48 states for oil and gas wells.

WTI is the underlying commodity of the New York Mercantile Exchange's oil futures contracts. It is the marker price for oil in the U.S.

CPIU is the consumer price index for all urban consumers.

Rigs are the large apparatus you will find in oil and gas fields that explore for oil and natural gas.  They are very expensive and are usually leased on a daily or weekly basis.

1. Estimate , , and  by OLS (these are free points -- you should have already done this in Homework 01).

 2. Examine the OLS residuals

a. Calculate , the correlation between  and . Construct a correlogram of the OLS residuals, using 24 lags. With evidence from  and the correlogram, what is your impression of the validity of the standard errors? How does this impact the t-statistics?

b. Square the OLS residuals and graph them with Date on the x-axis. Does there appear to be heteroskedasticity?

c. If there is heteroskedasticity, what is the implication for t-statistics and p-values. Can the p=values be trusted?

 3. With high t-statistics and severe autocorrelation, one should reflexively suspect non-stationary data.  You should also suspect that RIGS and WTI are cointegrated. Run a cointegration test between RIGS and WTI. Use the weighted version of these variables (RIGS and WTI multiplied by ).

a. What is your conclusion? (Use the p-value generated by the R function adf.test).

b. How many lags are needed?

 

c. What do these results tell you about the OLS residuals (are they stationary?). 

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