How do you choose the appropriate lag length and frequency for nonstationary data?

2 How to choose lag length

There is no definitive rule or formula for choosing the optimal lag length for nonstationary data. However, there are some general guidelines and criteria that you can follow. First, you should have a theoretical or empirical justification for the lag length that you use, based on the nature and dynamics of your data and variables. Second, you should use statistical tests and information criteria to compare different lag lengths and select the one that minimizes the error or maximizes the fit of your model. Some common tests and criteria are the Akaike information criterion (AIC), the Bayesian information criterion (BIC), the likelihood ratio test (LR), and the final prediction error (FPE).

3 How to choose frequency

Similarly, there is no universal rule or formula for choosing the best frequency for nonstationary data. However, there are some factors and trade-offs that you should consider. First, you should match the frequency of your data with the frequency of your research question or hypothesis. For example, if you want to study the impact of a policy change that occurred in a specific month, you should use monthly data rather than annual data. Second, you should balance the benefits and costs of higher or lower frequency data. Higher frequency data may provide more information and variation, but they may also introduce more noise and measurement error. Lower frequency data may reduce noise and error, but they may also lose information and variation.

4 How to deal with nonstationarity

One of the main challenges of analyzing nonstationary data is that they may violate the assumptions of standard statistical methods, such as regression or correlation analysis. For example, nonstationary data may produce spurious correlation, which means that two variables appear to be related but they are not. To avoid this problem, you should test for nonstationarity and apply appropriate transformations or methods to make your data stationary or cointegrated. Some common tests for nonstationarity are the augmented Dickey-Fuller (ADF) test, the Phillips-Perron (PP) test, and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. Some common transformations or methods for stationarity or cointegration are differencing, detrending, logging, or using error correction models (ECMs) or vector autoregression models (VARs).

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?