This problem is concerned with the dynamic relationship between the spot and futures prices of the S&P 500 index. The data file sp5may. dat has three columns: \(\log\) (futures price), \(\log\) (spot price), and cost-of-carry \((\times 100)\). The data were obtained from the Chicago Mercantile Exchange for the S&P 500 stock index in May 1993 and its June futures contract. The time interval is 1 minute (intraday). Several authors used the data to study index futures arbitrage. Here we focus on the first two columns. Let \(f_{t}\) and \(s_{t}\) be the \(\log\) prices of futures and spot, respectively. Consider \(y_{t}=f_{t}-f_{t-1}\) and \(x_{t}=s_{t}-s_{t-1}\). Build a regression model with time series errors between \(\left\{y_{t}\right\}\) and \(\left\{x_{t}\right\}\), with \(y_{t}\) being the dependent variable.