# Running White Noise Tests for ARIMA (1,1,1) in Stata: A Step-by-Step Guide

Jan 23, 2024

Statistical tests are crucial in understanding the validity of our models, and a white noise test for ARIMA (1,1,1) in Stata is no exception. In this article, we provide a step-by-step guide on running a white noise test on your ARIMA (1,1,1) model using Stata, helping you ensure your time series analysis has a solid foundation.

**What is the White Noise Test?**

White noise tests are used in time series analysis to check whether the errors or residuals of a model are purely random or not. In other words, it tests for the presence of autocorrelation, a relationship between the error terms in different time periods. If the residuals exhibit autocorrelation, the model's estimates may be inefficient or biased, negatively impacting the accuracy of forecasts.

**How to Run the White Noise Test for ARIMA (1,1,1) in Stata?**

Here is a step-by-step guide on running a white noise test on an ARIMA (1,1,1) model in Stata:

**Ensure Stata is installed**: Make sure you have a working copy of Stata installed on your system.**Load your data**: Load your time series data into Stata using the appropriate commands (e.g.,`import delimited`

,`insheet`

) based on your data file format.**Set time-variable**: Declare the time variable in your dataset using the`tsset`

command in Stata. For example, if your time variable is named year, then use`tsset year`

.**Run the ARIMA (1,1,1) model**: Estimate the parameters of the ARIMA (1,1,1) model with the desired dependent variable, using the`arima`

command. For example, if your dependent variable is gdp, use the following command:`arima gdp, ar(1) ma(1)`

**Save the residuals**: After estimating the ARIMA model, save the residuals using the`predict`

command. For example, you can save the residuals in a new variable named residuals by running the following command:`predict residuals, res`

**Run the white noise test**: Run the white noise test on the saved residuals using the`wntestq`

command in Stata. For example, you can run the test using the following command:`wntestq residuals`

This command returns test statistics, including the Ljung-Box Q-statistic, and p-values. If the p-value is greater than a chosen significance level (e.g., 0.05), you can conclude that the residuals are not significantly autocorrelated, indicating that your ARIMA (1,1,1) model is appropriate.

**Conclusion**

Following these steps will help you run a white noise test for your ARIMA (1,1,1) model in Stata. Ensuring your model's errors are white noise is essential, as it indicates that the model is adequately capturing the time series' dynamics, and you can make reliable predictions and inferences.