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Would I be "mining the data" in a time series analysis if I add more lags than theory suggests? For instance, for annual data analysis, it is recommended that two lags would be sufficient to capture the dynamic interactions among the variables and account for potential serial correlations. Similarly, in models that use quarterly data, using four lags is a norm. However, in many instances, there is a conflict between what theory says and what one could observe in actual data.

Just wondering if it amounts to "data mining" when I augment the model with more than 2 lags of annual data. Assume the lag order is selected using an information criterion.

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The critical points here are the phrases "it is recommended that...", and "using four lags is a norm". "Recommended" and "norm" based on what? On a specific prevailing theoretical model, or on past experience with the specific kind of data? If it is the latter, you do not conflict with any economic theory, if you try something different.

This is also a good example of the need to arrive at a synthesis where the model is both theoretically supported and also statistically adequate (consult the works, especially the books, of prof. Aris Spanos on this important methodological matter).

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If you adopt a general-to-specific (Gets) modelling strategy, your specification search begins with a general unrestricted model (GUM), which should contain as many lags that you think could be relevant. In choosing the initial lag length(s), you can be generous enough since you want to be able to learn from the data (i.e. the dynamics contained in it). Of course, economic theory also guides the specification of the GUM, but if you want to allow for discovery (as opposed to merely imposing theory), theory should not determine the GUM. Having specified the GUM, it ought to be reduced into a parsimonious and interpretable form with any superfluous lags being removed. Once the dynamics have been settled, you can transform the model into its long-run form (which most economists will be interested in). From this perspective, putting additional lags into a model is not unwise - it's actually desirable! Basically, it all depends on how the lags enter your model in the first place. The efficient and systematic approach offered by the Gets approach is therefore advised.

On the other hand, you could adopt a specific-to-general modelling strategy. By employing this strategy, models grow in size as the econometric modelling process advances, which is contrary to the reduction (models become smaller) that takes place when using Gets. An expanding search is probably more susceptible to data mining than a contracting one.

In choosing lag lengths, it's also important to consider the purpose of the model and the general characteristics of the data (the number of observations and frequency).

Lastly, it's difficult to answer this question given that the phrases "mining the data" and "data mining" are undefined. For example, are these supposed to be interpreted as derogatory terms?

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