How to measure autocorrelation and heteroscedasticity?

Answer 1

To measure autocorrelation and heteroscedasticity, you can use various statistical tests and graphical techniques. Here are the steps to measure each:

Measuring Autocorrelation:
1. Plotting Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF): Visualize the ACF and PACF plots to identify any significant autocorrelation patterns. These plots indicate the correlation between a time series and its lagged values.
2. Durbin-Watson Test: This test evaluates autocorrelation in the residuals of a regression model. It provides a statistic value between 0 and 4, where values around 2 indicate no autocorrelation.
3. Ljung-Box Test: This test assesses the presence of autocorrelation in a time series by analyzing a group of lagged autocorrelations. It generates a p-value, and a significant p-value suggests the presence of autocorrelation.

Measuring Heteroscedasticity:
1. Plotting Residuals vs. Fitted Values: Plot the residuals against the predicted values from a regression model. Observe if there is any systematic pattern or change in variability in the residuals across different fitted values.
2. White Test: The White test detects heteroscedasticity in regression models. It examines the residuals' squared values against the predicted values from the model. A significant p-value indicates the presence of heteroscedasticity.
3. Breusch-Pagan Test or Park Test: These tests also detect heteroscedasticity by assessing the relationship between residuals and one or more independent variables. They generate p-values, with significant values suggesting heteroscedasticity.

Remember that these techniques can be applied depending on the type of data and the specific statistical model you are using. Additionally, it's advisable to consult with a statistical expert for further guidance and interpretation.