Analyzing Time Series Data: Regression, Autocorrelation, and Testing

This assignment focuses on time series modeling using regression analysis, specifically addressing the challenges posed by autocorrelation in time series data. It uses quarterly data for milk production and cow numbers to illustrate the concepts. The solution demonstrates the application of PROC REG in SAS, including the Durbin-Watson test to detect autocorrelation. The assignment highlights the limitations of ordinary least squares (OLS) estimation when autocorrelation is present and introduces the Cochrane-Orcutt estimation as a method to correct for it. The solution includes SAS code, outputs, and interpretations, showing how to transform the data and re-estimate the model to obtain more reliable parameter estimates and address the issue of misleading test results caused by autocorrelation. The Durbin-Watson test, its statistic, and its interpretation are also explained in detail. The assignment also covers issues like the impact of autocorrelation on parameter estimates and p-values, and how the Cochrane-Orcutt method can help improve the accuracy of the analysis. The solution includes the steps to perform Cochrane-Orcutt estimation using a DATA step and PROC REG, along with an explanation of how this transformation corrects for autocorrelation. The analysis highlights the importance of addressing autocorrelation in time series data to ensure accurate statistical inference.