Time series analysis can be more useful than ordinary least squares (OLS) regression analysis when dealing with time series data. OLS regression analysis cannot appropriately model a time series, specifically its systematic fluctuations, such as seasonality and systematically patterned residuals. As a result, the standard errors of regression coefficients are likely to be biased, and independent variables may appear to be statistically more significant or less significant than they actually are.
Time series analysis can be employed in several ways in the social sciences. The most basic application is the visual inspection of a long-term behavior (trend) of a time series. For example, Stanley (1988) visually inspected the percentages of Republicans, Democrats, and independents from 1952 to 1984 to survey the extent of partisan change in the southern region of the United States.
When estimating trends, time series analysis is bivariate OLS regression analysis where the independent variable is Time with a regular interval. This time series analysis is called univariate time series analysis. The trend in time series analysis is the slope of Time in bivariate OLS regression analysis. For example, Cox and McCubbins (1991) regressed the percentage of times individual legislators voted with their party leaders from the 73rd to the 96th Congress on Time, showing that party voting significantly declined only for the Republicans.
In many cases, a time series contains systematic short-term fluctuations other than a long-term trend. These systematic patterns in time series variables should be removed to examine accurately the relationship between them. When systematic patterns are present in two time series variables, the correlation between the two can simply be a product of the systematic patterns.
For example, Norpoth and Yantek’s (1983) study of the lagged effect of economic conditions on presidential popularity raised a question about Mueller (1970, 1973), Kramer (1971), and Kernell (1978). Their estimates of economic effects, according to Norpoth and Yantek, are vulnerable to serial correlation within the independent variables, the monthly observations of unemployment or inflation. Norpoth and Yantek identified stochastic processes (ARIMA) for the inflation series and for the unemployment series, removing the estimated stochastic processes from the observed series.
Since the inflation series and the unemployment series were no longer serially correlated, the relationship between inflation (or unemployment) and presidential popularity could not be an artifact of autocorrelation of the inflation series or of the unemployment series. Norpoth and Yantek found that past values of the inflation and unemployment series did not significantly influence current approval ratings of presidents with any particular lag structure.
Autocorrelation among residuals is a serious violation of a vital assumption concerning the error term in regression analysis. With the serially correlated residuals, the least-squares estimates are still unbiased but may not be the best, with the minimum variance. Also, the significance tests and the confidence intervals for regression coefficients may be invalid. With time series analysis, we can directly check and estimate a systematic pattern that remains after we fitted a trend line to a time series.
If we are concerned only about the trend estimation, we can remove the systematic pattern from residuals before we fitted a trend line to a time series by smoothing the time series. In multiple time series analysis, we can deal with autocorrelated residuals in several different ways. For example, we can estimate and then eliminate systematic patterns from each time series before we conduct multiple time series analysis. Alternatively, we can estimate a multiple regression model with autoregressive processes by adjusting regression coefficients according to estimated autocorrelation coefficients.
Once we estimate an autoregressive process of a time series, we can utilize the autoregressive process to determine how long the time series’s time-dependent behavior or its impact on the dependent variable will persist. For example, comparing the autoregressive parameters of two independent variables, Mackuen, Erikson, and Stimson (1989) show that the impact of consumer sentiment on aggregate-level party identification lasts longer than that of presidential approval, although the immediate effect of consumer sentiment is stronger than that of presidential approval.
