XLSTAT: Cochrane-Orcutt Estimation in Excel

 

Background

The Cochrane-Orcutt estimation method to transform the original regression model to eliminate serial correlation, making ordinary least squares estimates more efficient.

 

Dataset For Example

The attached dataset involves household consumption as the dependent variable and money stock as the explanatory variable.

Assuming the error term in the linear regression model is serially correlated, the Cochrane-Orcutt procedure is used to correct for first-order autocorrelation by iteratively estimating the autocorrelation coefficient and refitting the model on transformed variables, leading to more reliable parameter estimates.

 

Setting Up

• Open XLSTAT.

• Click on the Time series analysis menu and select the Cochrane-Orcutt model feature:

 

• Once you've clicked on the button, the dialog box appears.

In the General tab:

• Select the data on the Excel sheet (20 observations, 2 variables).

• Select Expend as the dependent variable.

• Select Stock as the explanatory variable.

• Since the column headers were included in the selection, make sure the Variable labels option is checked.

In the Options tab:

• Leave the Tolerance value at its default setting.

• Leave the Confidence interval level at the default value (usually 95%).

Note: This ensures standard assumptions are used unless you have specific analysis requirements.

• The computations begin once you have clicked OK.

• The results will then be displayed in a new sheet.

 

Interpreting the Results

The first results displayed are the statistics for the various variables. Next, a table displays the goodness of fit coefficients of the model. The R² (coefficient of determination) indicates the % of variability of the dependent variable which is explained by the explanatory variables. The closer to 1 the R² is, the better the fit.

It is important to examine the results of the analysis of variance table (see below). The results enable us to determine whether or not the explanatory variable bring significant information (null hypothesis H0) to the model. In other words, it's a way of asking yourself whether it is correct to use the mean to describe the whole population, or whether the information brought by the explanatory variable is of value or not.

The following tables give details on the model parameters. These tables are helpful when predictions are needed, or when you need to compare the coefficients of the model for a given population with the ones obtained for another population.