Jon C. W. Pevehouse

Concluding Thoughts for the Time Series Analyst

We began this book by suggesting that scholars in the social sciences are often interested in how processes – whether political, economic, or social – changeover time. Throughout, we have emphasized that although many of our theories discuss that change, often our empirical models do not give the concept of change the same pride of place. Time series elements in data are often treated as a nuisance – something to cleanse from otherwise meaningful information – rather than part and parcel of the data-generating process that we attempt to describe with our theories. We hope this book is an antidote to this thinking. Social dynamics are crucial to all of the social sciences. We have tried to provide some tools to model and therefore understand some of these social dynamics. Rather than treat temporal dynamics as a nuisance or a problem to be ameliorated, we have emphasized that the diagnosis, modeling, and analysis of those dynamics are key to the substance of the social sciences. Knowing a unit root exists in a series tell us something about the data-generating process: shocks to the series permanently shift the series, integrating into it. Graphing the autocorrelation functions of a series can tell us whether there are significant dynamics at one lag (i.e., AR(1))or for more lags (e.g., an AR(3)). Again, this tells us something about the underlying nature of the data: how long does an event hold influence? The substance of these temporal dynamics is even more important when thinking about the relationships between variables.

Time Series Models as Difference Equations

INTRODUCTION The material in this appendix is aimed at readers interested in the mathematical underpinnings of time series models. As with any statistical method, one can estimate time series models without such foundational knowledge. But the material here is critical for any reader who is interested in going beyond applying existing “off the shelf” models and conducting research in time series methodology. Many social theories are formulated in terms of changes in time. We conceptualize social processes as mixes of time functions. In so doing, we use terms such as trend and cycle. A trend usually is a function of the form α × t where α is a constant and t is a time counter, a series of natural numbers that represents successive time points. When α is positive (negative), the trend is steadily increasing (decreasing). The time function sin α t could be used to represent asocial cycle, as could a positive constant times a negative integer raised to the time counter: α(−1) t . In addition, we argue that social processes experience sequences of random shocks and make assumptions about the distributions from which these shocks are drawn. For instance, we often assume that processes repeatedly experience a shock, ∈ t , drawn independently across time from a normal distribution with mean zero and unit variance. Social processes presumably are a combination of these trends, cycles, and shocks.