Why Am I Getting Different p-Values for the Same ADF Test in R and Stata?
When conducting time series analysis, particularly to check for the stationarity of a series, the Augmented Dickey-Fuller (ADF) test is often used. However, it is not uncommon to encounter discrepancies in the results obtained from different software packages, such as R and Stata. This article will explain why you might receive different p-values for the same ADF test in these two popular statistical tools, and how to ensure consistency and accurate results.
The ADF Test in R and Stata
The Augmented Dickey-Fuller (ADF) test is a statistical test used to determine if a time series is stationary or not. Stationarity is a crucial assumption in many time series models, and the ADF test helps to assess whether a series can be considered stationary.
In R, there are different packages that implement the ADF test, with the most common being the tseries package and the fUnitRoots package. The adf.test function in the tseries package and the adfTest function in the fUnitRoots package both perform the ADF test, but they may have slight differences in their default settings and arguments.
On the other hand, Stata includes the dfuller command as part of its base installation, which also implements the ADF test.
When you say “the same” ADF test, it is important to identify which specific function you are using and understand the differences in their default behaviors. For instance, the default settings for the adf.test in R might differ from the default settings for the dfuller command in Stata.
Common Differences in ADF Test Implementations
The differences in results between R and Stata can arise from several factors, including the default settings of the functions, the inclusion of constants and trends, and the choice of lags. Here’s a detailed look at these factors:
1. Default Settings and Arguments
The adf.test function in R from the tseries package defaults to include a constant in the model, while the dfuller command in Stata defaults to exclude a constant. This difference in default behavior can significantly affect the results.
Additionally, the adf.test function in R does not allow you to control whether a trend term is included in the model, which is set to `true` by default. In Stata, the dfuller command excludes the trend by default but allows you to include it by specifying the `trend` option.
2. Choice of Lags
The number of lags used in the ADF test can also differ between R and Stata. While the adf.test in R allows you to specify the number of lags, the dfuller in Stata often uses a fixed default number of lags, which might not be optimal for your specific dataset.
Ensuring Consistency and Accurate Results
To obtain consistent and accurate results when performing the ADF test in both R and Stata, follow these steps:
1. Explicitly Set Default Settings
To ensure that both R and Stata are performing the ADF test in the same way, explicitly set the default settings to match. This includes setting the constant and trend terms, and choosing an appropriate lag number.
For instance, in R, you can specify the options for the ADF test using the `lag` parameter and the `alternative` parameter to control for the trend term. Similarly, in Stata, you can specify the `trend` and `lags` options to align with the R settings.
2. Use the Correct Function Parameters
Use the parameters provided by the functions in both R and Stata to control the test specifications. For example, in R, you can use the `alternative` parameter to specify whether to include a trend term or not:
adf.test(x, alternative c("", "less", "greater"), k 0, drift FALSE)
For Stata, you can include a trend term using the `trend` option:
dfuller x, trend
3. Optimize the Lag Selection
The choice of lags can significantly affect the results of the test. Use information criteria such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) to determine the optimal number of lags. Both R and Stata have functions and options to help with this selection process.
In Stata, you can use the `dfuller` command with the `lags` option to choose the number of lags. In R, you can use the `adf.test` function with the `k` parameter to specify the number of lags:
adf.test(x, k 2) # Example of specifying a lag in R
By carefully selecting the parameters, you can ensure that the ADF test results in both R and Stata align more closely.
Conclusion
The discrepancies in the p-values obtained from the ADF test in R and Stata can be due to differences in default settings, the inclusion of constants and trends, and the choice of lag numbers. By understanding these differences and adjusting the settings to match, you can ensure consistency and accuracy in your time series analysis.
Next time you face similar issues, consider the specified factors and adjust the parameters accordingly. This will help you obtain reliable results and make informed decisions based on your time series data.